![xi
Contents
9.2.1 Cucurbit[n]uril................................................................................. 159
9.2.2 Fullerene Cages Cn [n = 60, 70, 80, 90, etc.] ...................................160
9.3 Catalysis Using Cucurbituril Cavities ........................................................... 161
9.4 Catalysis Using Fullerene Cages ................................................................... 162
9.5 Bonding inside Fullerene Cages.................................................................... 163
9.6 Conclusion .....................................................................................................164
9.6.1 Acknowledgment............................................................................. 165
9.6.2 Confict of Interest........................................................................... 165
References ................................................................................................................165
Chapter 10 Computational Studies on the NLO Properties of Molecules and Clusters
Containing Excess Electrons.................................................................................... 168
Wei‑Ming Sun
10.1 Introduction ................................................................................................... 168
10.2 Background of the Excess Electron............................................................... 168
10.3 Computational Methodology......................................................................... 169
10.3.1 Theoretical Background .................................................................. 169
10.3.2 Computational Methods .................................................................. 170
10.3.3 Characterization of the Excess Electron ......................................... 171
10.4 Strategies for Designing Molecules and Clusters with Excess Electrons........172
10.4.1 Alkali-Metal-Based Excess Electron Compounds.......................... 173
10.4.2 Alkaline-Earth-Based Excess Electron Compounds ...................... 182
10.4.3 Transition Metal-Based Excess Electron Compounds .................... 185
10.4.4 Superalkali-Based Excess Electron Compounds ............................ 188
10.4.5 Clusters with Excess Electrons........................................................ 191
10.5 Concluding Remarks .....................................................................................194
10.5.1 Acknowledgment.............................................................................194
References ................................................................................................................194
Chapter 11 Organic Semiconducting Materials in Electronic Devices......................................205
Shamoon Ahmad Siddiqui, Ankit Kargeti, and Tabish Rasheed
11.1 Introduction ...................................................................................................205
11.2 Application of Organic Semiconducting Materials in Designing
Electronic Devices and Their Properties.......................................................206
11.2.1 Characteristic of the Single Molecular Diode.................................206
11.2.2 Characteristic of the Organic Field Effect Transistor .....................207
11.2.3 Characteristic of the Organic Solar Cells (Dye-Sensitized
Solar Cells) ......................................................................................207
11.2.4 Computational Methodology...........................................................207
11.3 Organic Molecular Diodes ............................................................................208
11.3.1 Analysis of Molecular System Taken from Figure 11.1: (a) S1
[p-Sexiphenyl-σ-TCNQ], (b) S2 [p-Sexiphenyl-σ-NTCDA] ...........208
11.3.2 Analysis of Molecular System Taken from Figure 11.2: (a)
S3 [TCNQ-σ-(TTF)], (b) S4 [TCNQ-σ-(DPh-BTBT)], (c) S5
[TCNQ-σ-(BEDT-TTF)].................................................................. 211
11.4 Organic Field Effect Transistors.................................................................... 213](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-16-320.jpg)
![1 DFT-Based Studies on
Thermodynamic, Electronic,
Optical, and Spectroscopic
Aspects of Liquid Crystals
An Overview
Dipendra Sharma, Gargi Tiwari, Abhishek Kumar, Neeraj Misra,
and Sugriva Nath Tiwari
1.1 INTRODUCTION
Conventionally, it is presumed that matter exists only in three states: solid, liquid, and gas. However,
this is not quite true: in particular, some of the organic substances do not undergo a single transition
from solid to liquid but rather a cascade of transitions involving new phases; the mechanical proper-
ties and the symmetry properties of these phases are intermediate between those of a liquid and those
of a crystal. For this reason, they have often been called liquid crystals, or mesogens. A more proper
name is “mesomorphic phases” (mesomorphic: of intermediate form). However, many crystals show
a transition from a strongly ordered state to a phase where each molecule commutes through several
equivalent orientations. The high-temperature phase is positionally ordered, but orientationally dis-
ordered. It is sometimes (loosely) called a plastic crystal. Examples of such rotational transitions are
solid hydrogen, ammonium halides, and also certain types of organic molecules. In the liquid crys-
talline phase, molecules of certain organic liquids are aligned preferentially along one direction or in
two dimensions at lower temperatures; they are positionally disordered but orientationally ordered
anisotropic liquids. At higher temperatures, they undergo a transition to a traditional (isotropic) liq-
uid phase.[1–3] A typical phase transformation for a thermotropic liquid crystal is shown in Figure 1.1.
The development of liquid crystal science has a long and colorful history. The frst research on
liquid crystals was discovered and published in 1888 by Austrian Botanist Friedrich Reinitzer from
FIGURE 1.1 Arrangements of molecules in thermotropic liquid crystalline phase transitions represented by
rod-like molecules.
DOI: 10.1201/9781003441328-1 1](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-26-320.jpg)
![2 Computational Studies
Karl-Ferdinands-Universität. He discussed the melting behavior of cholesteryl benzoate, which has
two melting points: at 145.5 °C, the compound changes into a murky fuid, and at 178.5 °C, it
becomes clear liquid.[4] German Physicist Otto Lehmann, a specialist in polarization microscopy,
was consulted by Reinitzer when he was unable to explain these data. Lehmann examined the opti-
cal characteristics of the compound, observed crystallites in the hazy fuid, and concluded that this
was an intermediate phase (or “mesophase”—from Ancient Greek, Îo (mésos) meaning “middle”)
between the liquid and solid phases. This transitional phase exhibited birefringence while simulta-
neously having a liquid-like fow.[5] Such intermediate (liquid crystal) phases can also be obtained
by mixing substances like sodium and potassium salts of higher fatty acids to suitable solvents.[1]
At present, liquid crystals have emerged as beautiful, mysterious, and soft condensed materials.
Since the topic of liquid crystal is very interesting and it encapsulates physics, chemistry, and, in
some aspect, also biology, it constitutes a very suitable content for an interdisciplinary integration
of the natural science studies.[6–12]
Depending upon the nature of the building blocks of molecules and upon external parameters
(temperature, solvents etc.), a wide variety of phenomena and transitions among liquid crystals can
be observed. To design a liquid crystal, one must use elongated objects. Presently, at least three
different ways are known to achieve this: with small organic molecules; with long helical rods that
either occur in nature or can be made artifcially; and with more complex units that are really associ-
ated structures of molecules and ions.Accordingly liquid crystals are classifed into various types.[13]
1.2 LIQUID CRYSTAL CLASSIFICATION
Liquid crystalline phases can be obtained either by heating and/or cooling the substances or by treat-
ing the substances with water or polar solvents (aqueous medium). Depending on the way mesomor-
phic phases are observed, liquid crystal materials are classifed as thermotropic or lyotropic. Further
subgroups of liquid crystals are made depending on the molecular architecture of constituent entities.
For instance, the molecules in the mesophases can be rod-like (or calamitic), disc-like (or dis-
cotic), amphiphilic, nonamphiphilic, polymeric, etc. There is no need of a solvent in case of ther-
motropic liquid crystalline substances. The concentration of the solvents, on the other hand, has an
impact on the behavior of the liquid crystals and aggregation in lyotropic liquid crystals.
1.3 THERMOTROPIC LCs
The order and orientation of molecular constituents in thermotropic mesophases can be used to
categorize them. Broadly, thermotropic LCs are classifed as nematic and smectic liquid crystals.
Cholesterics are treated as a special class of nematic liquid crystals.[14] Salient features of liquid
crystals are very briefy described here.
1.3.1 Nematic Lcs
The nematic phase is the most straightforward mesophase that has ever been observed; there is no short-
range positional order but rather long-range orientational order between mesogens. Mesogens are ran-
domly dispersed in space, yet they can freely translate and rotate along the director feld (Figure 1.2a).
“Nematic” is derived from the Ancient Greek word vεμα (“nema”) meaning thread. Since thread-like
molecular structures are seen under a microscope, they are referred to as nematic structures.[14]
1.3.2 choLesteric Lcs
The cholesteric phase is identical to the nematic phase, with the exception that the mesogens change
their orientation in a helical direction with respect to the director feld. In the cholesteric phase, the
director feld reverses course and faces the helix in the other direction. Each layer of the helix that the](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-27-320.jpg)
![3
DFT-Based Studies on Aspects of Liquid Crystals
molecules form, which is nonsuperimposable, gives rise to the chirality. This is why cholesteric LCs
are mostly referred to as chiral nematics. The gap between two mesogenic layers that have rotated 180°
to the director feld is known as the half of the pitch within the cholesteric mesophase (Figure 1.2b).
Further, cholesteric LCs exhibit emission of blue-violet radiations with decreasing temperature from
the isotropic phase and hence give rise to a new class of LCs, commonly known as blue phase LCs.[15–17]
1.3.3 Discotic Lcs
Numerous compounds made up of molecules with a disc shape have been shown in recent investiga-
tions to have stable thermotropic liquid crystalline phases. The name “discotic liquid crystals” is now
used to describe them. Most of them can be divided structurally into two groups: columnar and discotic
FIGURE 1.2 Different subphase alignments of molecular confgurations: (a) nematic, (b) cholesteric,
(c) discotic nematic, (d) discotic columnar phase, (e) smectic A, and (f) smectic C.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-28-320.jpg)
![4 Computational Studies
FIGURE 1.3 General classifcation of thermotropic liquid crystals.
nematic (Figures 1.2c and 1.2d). In its most basic form, the columnar phase is an orientationally ordered
arrangementofdiscswithoutanylong-rangetranslationalorder,whilethenematicphaseexhibitsliquid-
like disorder in the third dimension and long-range translational periodicity in the second.
1.3.4 smectic Lcs
The word “smectic” is derived from the Ancient Greek word σμεκτoσ (“smektos”) meaning soap-
like). This phase was frst identifed in liquid crystals made up of amphiphilic molecules. The term
“smectic” is now used to describe liquid crystals where the molecules are organized in layers in
addition to having an orientational order. The organized layers’ ability to slide past one another adds
to the liquid nature of the mesomorphic phase. Numerous smectic stages have been discovered,
and each of them varies in the position and orientation of the mesogens. Smectics are further des-
ignated as SmA, SmB, SmC, etc. To differentiate between the smectic phases, we may look at the
molecular orientation inside the layers (Figures 1.2e and 1.2f). The smectic A phase has molecules
aligned along a director feld (n) and parallel to the layer normal, whereas the smectic C phase has
molecules tilted at an angle away from the layer normal. Figure 1.3 shows a general classifcation of
the various polymorphs of thermotropic liquid crystals.[2, 18] Substances that display smectic LCs are
occasionally referred to as two-dimensional liquids.[10, 19]
In addition to these categories, ferroelectric and antiferroelectric liquid crystals, as well as many
other mesogenic substances, constitute separate classes because of their potential applications and
future prospects.[11, 12]
1.4 LYOTROPIC LCs
A lyotropic liquid crystal, on the other hand, is created when amphiphilic molecules melt in a certain
type of solvents under proper pressure, temperature, and concentration conditions. By adjusting the
solvent concentration, one can control the lyotropic liquid crystal combination. According to the
concentration of the amphiphilic species, lyotropic liquid crystals (LLCs), which are self-assembled
surfactant-solvent systems, can form a variety of mesophases, including micelles, micellar cubic,
bicontinuous cubic, hexagonal, lamellar structures, and cell membrane bilayer (Figure 1.4).[6, 20, 21]
Further, liquid crystalline properties in polymers, biopolymers (like protein, nucleic acids, blood cells,
viruses, etc.) and other bioactive substances are well established, and they constitute another class of
liquid crystals and help to mediate many living processes and biomolecular recognitions.[7, 8, 21]](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-29-320.jpg)
![5
DFT-Based Studies on Aspects of Liquid Crystals
FIGURE 1.4 Representation of molecular form and the architecture of different types of lyotropic liquid
crystal phases.
Theorderparameteriscrucialfordistinguishingbetweendifferentliquidcrystalphases.Figure1.5
shows the order parameter (S) and an nOCB LC molecule exhibiting different phases. Molecular
orientation research is one of the most important and inescapable concerns since the degree of order
determines the anisotropy of the physical characteristics of liquid crystal substances.[1, 22]
Over the past few decades, mesogens or liquid crystals (LCs) have attracted a lot of scientifc
interest in the feld of soft condensed matter due to their distinctive anisotropic properties, fuidity,
and wide range of applications, including spatial light modulators, sensors, optical antennas, fat
panel displays, and beam steering devices.[6, 23–38] The length of the aliphatic chain is one of the
key molecular structure factors that affects mesomorphic behavior. Since the beginning of the LC
investigation, its variation has been the simplest molecular method of regulating the capacity of
mesogenic materials to self-organize. Comparing different properties (electrical, optical, and meso-
morphic) of the members in a homologous series is a well established tool for gathering information
on the relationship between structure and properties. Beginners in the liquid crystalline feld can
easily see the strong odd-even effect dependent on the length of the terminal chain or chains, etc.
The spontaneous molecular ordering that is a characteristic of liquid crystalline phases has long
been used in many technical applications, such as electro-optic displays. Since the beginning of
display device technology, cyanobiphenyl liquid crystals have been used extensively due to their
mesomorphic behavior near the room temperature.[2, 29]
In view of these facts, this chapter presents the thermodynamic, electronic, optical, and spectro-
scopic aspects of the members of nCB and nOCB LC homologous series that have been investigated
using the DFT method.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-30-320.jpg)
![6 Computational Studies
FIGURE 1.5 Order parameter (S) and dependence of order parameter on director angle (θ) defning different
phases of LC material.
1.5 COMPUTATIONAL METHOD
The density functional theory (DFT) based B3LYP/6–31G(d,p) and B3LYP/6–311+G(d,p) schemes
developed in the GAUSSIAN 16W program[39] were employed as the computational tool in this
study. The total electronic energy of a molecular system[40] is expressed as:
EDFT ˜ En ° ˛
˙ ˝ Ee ° ˛
˙ ˝ ECR ° ˛
˙ ˝ EX ° ˛
˙ ˝ EC ° ˛
˙ (1.1)
where E stands for the energy functional and the subscripts n, e, CR, X, and C, respectively, refer to
the nuclear repulsion energy, one electron’s (kinetic + potential) energy, coulomb repulsion energy,
exchange energy, and correlation energy. For EC = 0, this equation is reduced to Hartree–Fock (HF)
form. The electron density function (ρ) and its gradient are represented as conventional integrals of
DFT functionals in equation (1.1):
E[ ]
˜ ° f ( ( ),
˜ r ˛˜ r
( ))dr (1.2)
˝
Equation (1.2) leads to integrals that must be assessed using numerical integration because they are
not directly solvable. The one aspect of DFT methods that differs between EX [ρ] and EC [ρ] is the
function f that is used.
The hybrid functional B3LYP has shown to be a good trade-off between computing cost, cov-
erage, and result correctness. It was initially developed to study circular dichroism and vibrational
absorption.[41] Analyzing organic molecules in the gas phase with this method is increasingly wide-
spread. The exchange correlation functional produced by this B3LYP method includes the param-
eterized exchange term of A. D. Becke[42] and the correlation term developed by Y. Lee, W. Yang,](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-31-320.jpg)
![ˇ
7
DFT-Based Studies on Aspects of Liquid Crystals
and R. G. Parr.[43] B3LYP is a hybrid functional with three parameters that includes a combination
of Becke’s exchange term, HF exchange, and Lee–Yang and Parr’s correlation term. The fnal two
elements of equation (1.1) are typically stated in B3LYP[44] as:
Slater HF Becke local non˙local
. ˝ ˙
1 ˝ ˆ
°
˜ E ( ˜).E . E ˝ E ˝ ˆ
˛. E (1.3)
X X X C C
where the three parameters α, β, and γ are determined by ftting to a diverse set of molecules.
A number of organic compounds have already adopted this widely used method.[45–50] There are
many functionals. e.g. B3PW91,[51] ωB97XD,[52] LC-ωHPBE,[53] CAM-B3LYP,[54] M062X,[55] etc.
have been used in recent years due to their quantum computational accuracy.
Vibrational infrared frequencies are computed using harmonic approximation:
3N 3N ˛ 2 ˆ
° E
E ˜
1
˙ ˘ q q (1.4)
2 ˙ ˘ i j
i j ˇ
i1 j1 ° °
q q
˝ o
where
o
q ˜ m (q q ) (1.5)
°
i i i i
Here mi is the mass of atom i, and qi represents the x-, y-, and z-coordinates for each of the
N atoms in a molecule. Once vibrational frequencies are obtained, vibrational contribution
(which is the most significant) of thermodynamic parameters are computed using following
relations:
3N˛6
˝hc hc
ˇ
H U
˜ ˜ R
i
° k T
i
(1.6)
ˆ hc
i˜1 2k k e
( ˛1)
˙ B B
i B
˘
3N°6
ˆ
˛ hc
i °hc
i B
S R ° ln(1° e k T
) (1.7)
˜ ˙ hc
k T ˘
B
ˇ
i˜1 k T(e °1)
˝ B
i
where H, U, and S denote enthalpy, internal energy, and entropy, respectively. Other parameters are
calculated using standard thermodynamic relations.
Numerical differentiation can be used to determine the dipole moment (μ), mean polariz-
ability (α), and anisotropy in polarizability (Δα) with an electric feld magnitude of 0.001 au
accordingly as:
2
˜ ° ˜
( x
2
˛ ˜y
1
2 2
˛ ˜ )
z
(1.8)
˜ °
˜xx ˛ ˜yy
3
˛ ˜zz
(1.9)
1
˜° ˛
ˆ(°xx
˘
ˇ
˘
2
˝ ° )
yy ˙ (°yy
2
˝ ° )
zz
2
˙ °
( zz
2
˝ ° )
xx
2
(1.10)
˜ ° ˝
˙ ˜
( xxx ˛˜xyy
2
˛˜ )
xzz ˛ ˜
( yyy ˛˜xxy
2
˛˜ )
yzz ˛ ˜
( zzz ˛˜xxz
1 2
/
2
˛˜ ) ˆ
yyz ˇ (1.11)](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-32-320.jpg)
![8 Computational Studies
Molar refractivity (MR) can be determined by the Lorenz-Lorentz formula:
2
°1 MW
n
MR ˜ ˜ 1 333 N (1.12)
.
2
˝
ˆ
˙n ˛ 2
ˇ
˘
The molar volume (MW/ρ), the Avogadro number (N), the refractive index (n), and the polarizability
of the molecular system (α) are all present in this equation. For α, 1 au = 0.1482 × 10−24 esu.
Further, Koopmans theorem has been used to determine the electronic and global properties
like ionization potential (I), electron affnity (A), electronegativity (χ), global hardness (η), and
softness (S).[56]
According to Parr et al.,[57] the relationship between chemical potential (φ) and electronegativity
(χ) is provided by the relation:
ˆ ˙E
˜ ˝ ˝ ˛ (1.13)
˘
ˇ ˙N °
r
where the terms denoted by v(r) and μ are the exterior and electronic chemical potentials, respec-
tively. The values of the electron affnity (A) and ionization potential (I) are given as:[58]
A ˜°E and I ˜ ° E (1.14)
LUMO HOMO
The I and A values can be used to calculate the molecule’s global hardness (η)[59] and electronegativ-
ity (χ)[65]:
I A
˝ ˙
I A
˜ ˛ and ° ˛ (1.15)
2 2
The electrophilicity index (ω), introduced by Parr et al.,[60] and chemical softness (S)[61] are given as:
1 ˝2
S ˜ and ˛ ˜ (1.16)
° 2°
The following equations can be used to calculate the molecules’ electron donating capability (ω−)
and electron accepting capability (ω+):
°
˜ ˝
2
(3 ˛ )
I A
(
16 ° )
I A
and ˛
˜ ˝
2
(I ˛ 3 )
A
(
16 ° )
I A
(1.17)
1.6 RESULTS AND DISCUSSION
1.6.1 4-aLkyL-4ʹ-cyaNobipheNyL series
It has been observed that there is an odd-even effect in the transition temperature for the nCB
LC homologous series in the nematic region. Additionally, the odd-even effect was exclusively
explored for the nematic zone.[29] Previously, the odd-even effect was not observed in smectic
liquid crystals, and the transition temperature is almost linearly related to the number of carbon
atoms in the alkyl chain. In this section, we discuss the electro-optical and electronic proper-
ties of the nCB series, which were studied theoretically for nematic and smectic phases of the
homologues.[62–65]](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-33-320.jpg)
![9
DFT-Based Studies on Aspects of Liquid Crystals
1.6.2 optimizeD parameter aNaLysis
Figure 1.6 depicts the equilibrium geometries of the nCB liquid crystal series. The frst methylene
group’s carbon (-CH2) along the extended molecular axis lengthens the molecule but has no effect
on its width, as in the case of 1CB, while the second methylene group’s carbon increases the length
and simultaneously widens the molecule, as in the case of 2CB. This applies to nCB molecules
having an alkyl chain at the terminal end. As a result, the carbon in the second methylene group, that
is the carbon in the odd position, increases the length but not by the same amount as the carbon of
the frst methylene group.[66] Depending on whether the terminal chain has an even or odd number
of methyl(ene) groups, the dimensions of the nCB members change as the chain grows. This phe-
nomenon, called the odd-even effect, was clearly seen in the case of the nCB series homologues.[29]
1.6.3 eLectroNic aND GLobaL parameter aNaLysis
The trend of some electronic characteristics, including electron affnity (A), ionization potential (I),
chemical hardness (η), and absolute-electronegativity (χ), has also been examined. These variables,
often known as reactivity descriptors, describe how chemically reactive molecular systems are or
how they interact with other species. Figure 1.7 displays how these parameters can vary with a
homologous number of nCB series. In both nematic and smectic zones, it is evident that the ioniza-
tion potential (Figure 1.7a) and global hardness (Figure 1.7d) vary with the number of carbon atoms
and refect the phenomena of odd-even effect; i.e., these variables are affected by the n parity value.
The molecule’s propensity to donate an electron or to become an electron donor and yield a cation
is measured by the ionization potential. Chemical hardness gives a clear indication of how stable a
molecule’s electronic state is; in general, odd-number carbon chain molecules are more stable than
even-number ones. Chemical hardness and electronegativity are indicators of a molecular system’s
stability and chemical reactivity.[67] The electron affnity of a molecule evaluates its propensity to
absorb an electron, transform into an electron acceptor, and produce an anion, in contrast to ioniza-
tion potential.
Strong electron affnity exists for n = 2 and decreases with the number of carbon atoms in an alkyl
chain in the nematic zone, but it increases with the number of carbon atoms in the smectic zone, as
FIGURE 1.6 Optimized geometries of nCB liquid crystalline series calculated at the B3LYP/6–311++
G(d,p) level.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-34-320.jpg)
![10 Computational Studies
FIGURE 1.7 Variation of (a) ionization potential, (b) electron affnity, (c) electronegativity, and (d) chemical
hardness with regard to the number of carbon atoms in the alkyl chain of the nCB liquid crystalline series.
shown in Figure 1.7b. This is the key characteristic that explains the liquid crystalline behavior of
the nCB series. In the same way as that of the chemical hardness and ionization potential, the nCB’s
electronegativity demonstrates that this parameter is quite high for n = 2 and that it goes down with
the increase of the number of carbon atoms in the alkyl chain (Figure 1.7c). All of the estimated
characteristics, with the exception of electron affnity, indicate that the odd-even effect in the nCB
family members persists beyond the nematic range and spreads into the smectic region. Table 1.1
provides values for various global parameters.
1.6.4 eLectro-opticaL parameter aNaLysis
We have examined a number of electro-optical parameters, including dipole moment, mean polar-
izability, anisotropy in polarizability, and hyperpolarizability, to observe the odd-even effect in nCB
liquid crystalline series. Table 1.2 contains the values of these parameters. An indication of the
shape and charge distribution of a molecule can be found in its dipole moment. There is an odd-even
effect in the dipole moment depicted in Figure 1.8a, which may be seen as the dipole moment of an
even-number carbon atom molecule and which is greater than the dipole moment of an odd-number
carbon atom of the methylene group. Moreover, as previously described[63] this variance extends
into the smectic zone in addition to the nematic region. Clearly, it has to do with the molecular
design and charge distribution, putting aside the intermolecular interactions that exist in bulk liquid](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-35-320.jpg)
![11
DFT-Based Studies on Aspects of Liquid Crystals
TABLE 1.1
Electronic and Global Reactivity Descriptor Parameters of the nCB (n = 1 to 12) Series
Homologous No. (n) I (eV) A (eV) χ(eV) η(eV)
1 6.677 1.986 4.331 2.345
2 6.677 1.987 4.332 2.344
3 6.661 1.982 4.321 2.339
4 6.644 1.974 4.309 2.334
5 6.647 1.971 4.309 2.338
6 6.642 1.970 4.306 2.336
7 6.642 1.968 4.305 2.336
8 6.640 1.968 4.304 2.335
9 6.639 1.967 4.303 2.335
10 6.633 1.971 4.302 2.331
11 6.636 1.971 4.304 2.332
12 6.635 1.971 4.303 2.331
TABLE 1.2
Electro-Optical Parameters of the nCB (n = 1 to 12) Series
Anisotropy in
Dipole Moment Mean Polarizability Polarizability Hyperpolarizability
Homologous No. (n) (Debye) (α) (Bohr3) (∆α) (Bohr3) (β) (Bohr5)
1 6.110 183.170 181.402 1511.922
2 6.131 191.823 195.274 1364.240
3 6.180 204.395 209.518 1699.821
4 6.305 211.953 222.328 1918.433
5 6.283 222.531 235.840 1926.032
6 6.376 227.689 248.500 2042.674
7 6.338 237.322 261.775 2057.229
8 6.402 238.314 274.594 2104.940
9 6.364 246.241 287.589 2112.702
10 6.426 248.307 300.581 2169.996
11 6.378 255.610 313.439 2139.265
12 6.436 256.127 326.261 2183.852
crystals. The homologous number of the alkyl chain is directly related to the anisotropy in polariz-
ability, as seen in Figure 1.8c. It is widely acknowledged that torsional angle has the greater impact
on the anisotropy in polarizability values[68] The torsional angle alters as the carbon atoms are added
to the alkyl chain; which, in turn, also increases the anisotropy in polarizability. For even and odd
numbers of carbon atoms, the mean polarizability and hyperpolarizability values are somewhat dif-
ferent (Figures 1.8b and 1.8d). The odd-even effect has been observed for n ≥ 7 in the case of mean
polarizability, and below this, polarizability grows essentially linearly. In addition to the negligible
contribution from acoustic phonons, it is typically considered that the frst-order hyperpolarizability
of organic molecules is entirely of pure electrical origin.[69] Although the hyperpolarizability values
do indeed exhibit an odd-even effect, this impact becomes less pronounced as the number of carbon
atoms increases. It is anticipated that changes to the dihedral angle or deviations from planarity
will cause a decrease in hyperpolarizability. It seems pertinent to note that the planarity require-
ment must be met for a molecule to be nonlinearly optically active. Thus the polarizabilities and](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-36-320.jpg)
![12 Computational Studies
FIGURE 1.8 Variations in the (a) dipole moment, (b) mean polarizability, (c) anisotropic polarizability, and
(d) hyperpolarizability of the homologues of the nCB liquid crystalline series with regard to the number of
carbon atoms in the alkyl chain.
hyperpolarizabilities control the system’s nonlinear optical (NLO) properties in addition to the cross
sections of various scattering and collision processes and the strength of molecular interactions.[70]
1.7 4-N-ALKOXY-4ʹ-CYANOBIPHENYL LIQUID CRYSTAL SERIES
This section covers the theoretically explored Raman spectra, UV-vis spectra, electro-optical, global
(electronic), and thermal features of the nOCB LC series.[71] The homologues of 4-n-alkoxy-4ʹ-
cynobiphenyl series (nOCB; n = 1 to 12) are optimized by the DFT/B3LYP method and are shown
in Figure 1.9. The behavior of nOCB LC molecules is nematic for n = 1 to 7 and smectic up to 12.
The main difference between the homologous nOCB and nCB series is that the nOCB molecules
have an oxygen atom between the biphenyl ring and the alkyl unit. Hence it becomes interesting to
see how the extra oxygen atom affects the quantities of the nOCB LC series.
1.7.1 thermaL parameter VariatioN with homoLoGous Number
Vibrational frequency calculations at the B3LYP/6–31G(d,p) level have been done for procuring
thermal parameters after the optimization operations. Figure 1.10a shows the correlation between
the number of carbon atoms present in an alkoxy chain and thermal properties such as Gibbs free](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-37-320.jpg)
![15
DFT-Based Studies on Aspects of Liquid Crystals
TABLE 1.4
Orbital Energy Gap (∆E), HOMO Energy, and LUMO Energy of the nOCB (n = 1 to 12)
Series
Homologous No. (n) EHOMO (eV) ELUMO (eV) ∆E (eV)
1 −5.987 −1.529 4.458
2 −5.953 −1.511 4.442
3 −5.942 −1.506 4.436
4 −5.935 −1.503 4432
5 −5.932 −1.501 4.431
6 −5.930 −1.499 4.431
7 −5.930 −1.498 4432
8 −5.929 −1.497 4.432
9 −5.928 −1.497 4.431
10 −5.928 −1.497 4.431
11 −5.927 −1.497 4.430
12 −5.926 −1.496 4.430
the values of HOMO, LUMO, and ΔE are poorly changed. As the homologous number increases,
all these quantities descend gradually (Table 1.4). These molecules occupy the region of ultraviolet
transparency, according to the energy gaps (ΔE) of the nOCB series.
The variation of global parameters for the nOCB (n = 1 to 12) series with homologous numbers is
also shown in Figure 1.12. Their respective values are given in Table 1.5. These variables are known
as reactivity descriptors because they describe the chemical reactivity of molecular systems. These
global descriptors are followed by orbital energy gaps (ΔE), and they decrease as the homologous
number increases. According to global hardness variation, lower homologues are likely to be more
stable than higher ones. Similarly, the variation in electron affnities suggests that lower homologues
can readily take electrons to transform themselves into electron acceptors in order to generate anions.
1.7.3 eLectro-opticaL parameter VariatioN with homoLoGous Number
Figure 1.13 shows the total energy, dipole moment, mean polarizability, anisotropy in polarizability,
and molar refractivity. Table 1.6 provides the values of electro-optical parameters. The addition of
carbon atoms in the alkoxy chain linearly increases the total molecular energy of the nOCB homo-
logues (Figure 1.13a). Thus, it can be inferred that the confgurational stability of the homologues
of nOCB (n = 1 to 12) refects ascending values with the increase of alkoxy chain length. That is,
higher homologues are more stable as compared to their lower homologues; thus 12OCB poses the
most stable confguration among all the chosen molecules. Similarly, as the homologous number
rises, the dipole moment also increases (Figure 1.13b). The occurrence of the odd-even effect in
the dipole moment was explored by similar investigations on nCB series[63] Figure 1.13c illustrates
the dependence of mean polarizability and anisotropic polarizability on the homologous number.
Hence, anisotropic polarizability is largely infuenced by the torsional angles.[68]
Due to the addition of carbon atoms in the alkoxy chain, the torsion angle of the homologues
changes, leading to an increment in the value of the anisotropy in polarizability. A linear relation-
ship for the homologous number is also indicated by the molar refractivity plot, which is depicted
in Figure 1.13d. Figures 1.14a, and 1.14b, respectively, demonstrate the comparison between esti-
mated mean polarizability and anisotropy in polarizability values of nOCB (n = 9 to 12) molecules
with experimental data.[72] In Figure 1.13c, the components of α and Δα are reported in atomic units
(Bohr3), while the same (calculated values) are converted into cm3 (1 Bohr3 = 0.1482 × 10−24 cm3)
in Figures 1.14a and 1.14b.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-40-320.jpg)
![19
DFT-Based Studies on Aspects of Liquid Crystals
1.7.4 ramaN aND absorptioN spectra aNaLysis
The DFT/B3LYP/6–31G(d,p) approach has been used to examine the Raman spectra of the mem-
bers of the nOCB LC series. Figure 1.15 displays the Raman spectra of the 8OCB LC molecule in
the 400 cm−1 to 3500 cm−1 regions. The 8OCB, 9OCB, 10OCB, 11OCB, and 12OCB molecules all
have six distinct strong vibrational peaks. Table 1.7 compares the calculated Raman frequencies of
relevant vibrational modes for the 8OCB molecule and shows that they are in good agreement with
the experimental data.[73, 74] At the wave number of 3111.19 cm−1 and 3037.40 cm−1, peak one and
peak two are connected to asymmetric and symmetric CH3 mode stretching, respectively. Peak three
is due to CN stretching, which is seen at 2344.11 cm−1, and peak four is caused by C-C stretching of
the biphenyl ring, which is seen at 1671.22 cm−1. The ffth peak, at a wavelength of 1316.89 cm−1, is
a band of perpendicular deformations that combines symmetrical and asymmetrical deformations of
FIGURE 1.15 Raman spectrum of the 8OCB LC compound. The letters in Table 1.7 refer to distinct
vibrations.
TABLE 1.7
Raman Spectrum of 8OCB LC Molecule
Raman Frequency (cm−1)
Calculated by
B3YP/6–31G(d,p) Experimental[69, 70] Peaks
Assignment of the Raman
Peaks Shown in Figure 1.2
3111.19
3037.40
2344.11
1671.22
1316.89
2962∼2988
2878
2234
1522
1284
a
b
c
d
e
Asymmetric CH stretch
of CH3
Symmetric CH stretch of CH3
CN stretching
Ring C-C stretching
Combinational band of
1206.49 1185 f
symmetric and asymmetric
perpendicular deformations
of CH2 groups in the
aliphatic chain
In-plane deformation of CH
bonds of the biphenyl moiety](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-44-320.jpg)
![DFT-Based Studies on Aspects of Liquid Crystals 21
TABLE 1.8 (Continued)
Molecule Excited State Oscillator Strength (f) Excitation Energy (eV) λmax (nm)
5OCB 1 0.8485 4.126 300.52
2 0.0239 4.297 288.50
3 0.0014 4.352 284.90
6OCB 1 0.8496 4.126 300.50
2 0.0239 4.297 288.50
3 0.0014 4.352 284.89
7OCB 1 0.8501 4.127 300.44
2 0.0240 4.298 288.49
3 0.0014 4.352 284.87
8OCB 1 0.8508 4.127 300.45
2 0.0240 4.298 288.49
3 0.0014 4.352 284.87
9OCB 1 0.8514 4.126 300.47
2 0.0240 4.298 288.50
3 0.0014 4.352 284.88
10OCB 1 0.8519 4.126 300.50
2 0.0240 4.297 288.50
3 0.0014 4.352 284.88
11OCB 1 0.8526 4.125 300.55
2 0.0240 4.297 288.51
3 0.0013 4.352 284.90
12OCB 1 0.8489 4.115 301.28
2 0.0250 4.288 289.23
3 0.0009 4.349 285.04
CH2 groups in the aliphatic chain, while the last one, at a wavelength of 1206.49 cm−1, is connected
to an in-plane deformation of CH bonds of the biphenyl moiety. Further, it is important to mention
that all the fve homologues (n = 8 to 12) of nOCB LC series furnish almost identical spectra and
hence similar values of Raman frequencies.
The ZINDO technique was used to study electronic absorption spectra. The similar nature of
absorption spectra is rendered by the homologues of nOCB (n = 1 to 12). The UV-vis spectra of only
four homologues of the nOCB (n = 1, 4, 8, and 12) series have been shown in Figure 1.16. Table 1.8
provides a list of the excited states, oscillator strength (f), excitation energy (E), and excitation
wavelength (λmax). At 299.61 nm (4.138 eV) with oscillator strength of 0.8324, 1OCB experiences
one strong electronic transition from HOMO to LUMO (MO contribution 86.5%). Corresponding
to 288.23 nm (4.302 eV) and 284.68 nm (4.355 eV), two more electronic transitions take place, with
oscillator strengths of 0.0233 and 0.0015, respectively. At a wavelength of 300.52 nm, the 4OCB
molecule exhibits a strong absorption band. With 86.5% of the MO contribution, the transition
from HOMO to LUMO occurs at this wavelength. The oscillator strength and the related excitation
energy correspond to 4.126 eV and 0.8470, respectively. Moreover, the strong electronic transitions
in the 8OCB and 12OCB molecules occur at 300.45 nm (HOMO to LUMO with MO contribution
of 86.4%) and at 300.55 nm (HOMO to LUMO with MO contribution of 86.2%), respectively. The
experimental values of molar absorptivity (ε) and wavelength of maximum absorption (λmax) for the
8OCB LC molecule are reported to be 20.1 × 103 M−1 cm−1and 297 nm, respectively,[75] whereas in
this study, the molar absorptivity and maximum wavelength for the 8OCB molecule are found to be
35.3 × 103 M−1 cm−1 and 300.45 nm, respectively.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-46-320.jpg)
![22 Computational Studies
1.8 CONCLUSIONS AND VIEWPOINTS
This chapter discussed various aspects of thermodynamic, electronic, optical, and spectroscopic
aspects of alkyl and alkoxy cyanobiphenyls. Both the homologous series possess odd-even effect.
This investigation demonstrated the presence of phenomena of the odd-even effect in the case of
the nCB series only, which is in conformity with experimental observations. The plots of the ther-
mal, electronic, and electro-optical properties for the nOCB series elucidate a linear dependence on
homologous number. While ascending the homologous series, there exists a linear increase in the
values of the dipole moment, mean polarizability, anisotropy in polarizability, and molar refractivity.
In both LC series, the global parameters indicate that lower homologues are more prone to anionic
behavior. The higher homologues appear to be more disordered. For further research and applica-
tions of these homologues of the nCB and nOCB liquid crystalline series in fabrications of NLO
materials, electro-optical parameters can offer improved insights and auxiliary information.
1.8.1 ackNowLeDGmeNt
Dipendra Sharma is thankful to UGC, New Delhi, India, for providing the start-up grant.
1.8.2 coNfLict of iNterests
The authors declare no confict of interest.
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dispersion corrections. Phys Chem Chem Phys [Internet]. 2008 [cited 2021 Aug 26];10:6615–6620.
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[53] Henderson TM, Izmaylov AF, Scalmani G, et al. Can short-range hybrids describe long-range-dependent
properties? J Chem Phys [Internet]. 2009 [cited 2023 Jun 19];131. Available from: https://pubs.aip.org/
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[54] Yanai T, Tew DP, Handy NC. A new hybrid exchange–correlation functional using the Coulomb-
attenuating method (CAM-B3LYP). Chem Phys Lett. 2004;393:51–57.
[55] Zhao Y, Truhlar DG. The M06 suite of density functionals for main group thermochemistry, thermo-
chemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals
and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Accounts
2007 1201 [Internet]. 2007 [cited 2021 Aug 26];120:215–241. Available from: https://link.springer.com/
article/10.1007/s00214-007-0310-x.
[56] Geerlings P, De Proft F, Langenaeker W. Conceptual density functional theory. Chem Rev [Internet]. 2003
[cited 2023 Apr 1];103:1793–1873. Available from: https://pubs.acs.org/doi/abs/10.1021/cr990029p.
[57] Parr RG, Donnelly RA, Levy M, et al. Electronegativity: The density functional viewpoint. J Chem
Phys [Internet]. 1977 [cited 2021 May 28];68:3801–3807. Available from: https://aip.scitation.org/doi/
abs/10.1063/1.436185.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-49-320.jpg)
![25
DFT-Based Studies on Aspects of Liquid Crystals
[58] Foresman JB, Frisch Æ. Exploring Chemistry with Electronic Structure Methods [Internet] (2nd ed.).
Pittsburgh, PA: Gaussian, Inc., 1996 [cited 2022 Nov 15]. Available from: www.csus.edu/indiv/g/gher-
manb/research_foo/g03_man/g_ur/refs/ref_308.htm.
[59] Senet P. Chemical hardnesses of atoms and molecules from frontier orbitals. Chem Phys Lett.
1997;275:527–532.
[60] Pauling L. The Nature of Chemical Bond (3rd ed.). Ithaca, NY: Cornell University Press, 1960. [Internet].
[cited 2021 May 28]. Available from: www.sciepub.com/reference/7634.
[61] Parr RG, Szentpaly LV, Liu S. Electrophilicity index. J Am Chem Soc [Internet]. 1999 [cited 2021
May 28];121:1922–1924. Available from: https://pubs.acs.org/doi/abs/10.1021/ja983494x.
[62] Lakshmi Praveen P, Ojha DP. Molecular Structure and Conformational Behavior of a Nematogen—A
Statistical Approach. http://dx.doi.org/101080/154214062011556455 [Internet]. 2011 [cited 2023 Apr 2];
537:64–75. Available from: www.tandfonline.com/doi/abs/10.1080/15421406.2011.556455.
[63] Kumar A, Srivastava AK, Tiwari SN, et al. Evolution of anisotropy, frst order hyperpolarizability and elec-
tronic parameters in p-alkyl-p’-cynobiphenyl series of liquid crystals: Odd-even effect revisited. Mol Cryst
Liq Cryst [Internet]. 2019;681:23–31. Available from: https://doi.org/10.1080/15421406.2019.1641987.
[64] Mishra M, Dwivedi MK, Shukla R, et al. Study of molecular ordering in liquid crystals: EBBA. Prog
Cryst Growth Charact Mater. 2006;52:114–124.
[65] Chaturvedi S, Chaturvedi N, Dwivedi MK, et al. Theoretical study of nematogenic behaviour of para-
hexyl-p’-cyanobiphenyl. Indian J Phys [Internet]. 2013 [cited 2023 Apr 2];87:263–269. Available from:
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[66] Marčelja S. Chain ordering in liquid crystals. I. Even-odd effect. J Chem Phys [Internet]. 2003 [cited
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[68] Alyar H, Bahat M. Torsional energy and nonlinear optical properties of 2-, 3-R-4-phenylpyridine
(R = CH3, NH2 and NO2). Asian J Chem [Internet]. 2012 [cited 2023 Apr 2];24:5319–5323. Available
from: https://asianjournalofchemistry.co.in/user/journal/viewarticle.aspx?ArticleID=24_11_119.
[69] Bosshard C, Spreiter R, Degiorgi L, et al. Infrared and Raman spectroscopy of the organic crystal
DAST: Polarization dependence and contribution of molecular vibrations to the linear electro-optic
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[70] Sun Y, Chen X, Sun L, et al. Nanoring structure and optical properties of Ga8As8. Chem Phys Lett.
2003;381:397–403.
[71] Sharma D, Sahu TK, Tiwari SN. DFT study of electro-optical, electronic and thermal properties of 4-n-
alkoxy-4′-cynobiphenyl liquid crystal series. Phase Transitions [Internet]. 2021;1–11. Available from:
https://doi.org/10.1080/01411594.2021.1944628.
[72] Mitra M, Gupta S, Paul R, et al. Determination of Orientational Order Parameter from Optical Studies
for a Homologous Series of Mesomorphic Compounds. http://dx.doi.org/101080/00268949108030937
[Internet]. 2006 [cited 2023 Apr 2];199:257–266. Available from: www.tandfonline.com/doi/abs/
10.1080/00268949108030937.
[73] Yu Y, Lin K, Zhou X, et al. New C−H Stretching Vibrational spectral features in the Raman Spectra
of gaseous and liquid ethanol†. J Phys Chem C [Internet]. 2007 [cited 2023 Apr 2];111:8971–8978.
Available from: https://pubs.acs.org/doi/abs/10.1021/jp0675781.
[74] Ghosh S, Roy A. Crystal polymorphism of 8OCB liquid crystal consisting of strongly polar rod-like
molecules. RSC Adv [Internet]. 2021 [cited 2023 Apr 2];11:4958–4965. Available from: https://pubs.rsc.
org/en/content/articlehtml/2021/ra/d0ra08543j.
[75] Özgan Ş, Okumuş M. Thermal and Spectrophotometric Analysis of Liquid Crystal 8CB/8OCB Mixtures.
Brazilian J Phys 2011 412 [Internet]. 2011 [cited 2023 Apr 2];41:118–122. Available from: https://link.
springer.com/article/10.1007/s13538-011-0034-1.
[76] Tiwari SN, Dwivedi MK, Sharma D. Physico-chemical properties, frontier orbitals and spectral study
of a nematogen: 4-n-ethoxy-4’-cyanobiphenyl and its two constituents. Mater Today Proc [Internet].
2020;29:987–992. Available from: https://doi.org/10.1016/j.matpr.2020.04.512.
[77] Sharma D, Tiwari G, Tiwari SN. Electronic structure and thermodynamic properties of 4-n-heptyl-4′-
cyanobiphenyl: A computational study. Mater Today Proc [Internet]. 2019;15:409–415. Available from:
https://doi.org/10.1016/j.matpr.2019.04.101 [53]
[78] Tiwari A, Palepu J, Choudhury A, et al. Theoretical analysis of the NH3, NO, and NO2 adsorption
on boron-nitrogen and boron-phosphorous co-doped monolayer graphene—A comparative study.
FlatChem. 2022;34:100392.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-50-320.jpg)
![26 Computational Studies
[79] Tiwari A, Chauhan MS, Sharma D. Fluorination of 2,5-diphenyl-1,3,4-oxadiazole enhances the electron
transport properties for OLED devices: A DFT analysis. https://doi.org/101080/0141159420222129051
[Internet]. 2022 [cited 2023 Jun 26];95:888–900. Available from: www.tandfonline.com/doi/abs/10.108
0/01411594.2022.2129051.
[80] Pandey AK, Kumar A, Srivastava AK, et al. Infuence of electric feld on the electro-optical and
electronic properties of 4-n-alkoxy-4′-cyanobiphenyl liquid crystal series: An application of DFT.
Pramana—J Phys [Internet]. 2023 [cited 2023 Jun 26];97:1–10. Available from: https://link.springer.
com/article/10.1007/s12043-023-02570-9.](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-51-320.jpg)
![2 Spectroscopic Signatures of
Some Organic Compounds
Theory Meets Experiment
Abhishek Kumar, Ambrish Kumar Srivastava,
Ratnesh Kumar, and Neeraj Misra
2.1 INTRODUCTION
The biological importance of the derivatives of hexahydroacridine-1,8-diones, similar to the octahy-
droacridine-1,8-diones cannot be disputed not only for their rich and wide-ranging chemistry but
also for a number of other characteristics. Anti-infammatory and hypertensive,[1] potassium chan-
nel opener,[2] and anti-microbial-like[3] properties have been reported in the literature. Depending
upon the type and placement of a substituent on the acridine core, there are a number of activities
against tumor,[4] parasites,[5] and bacteria.[6] It should be mentioned that the biological activities of
the acridines are mainly due to the ability of the acridine moiety to intercalate between base pairs
of double-stranded DNA through π–π interactions.[7] Acridine-1,8-dione dyes have been the focus of
studies due to their special photophysical and photochemical properties. The structure of these dyes
is similar to that of 1,4-dihydropyridine.
An extensive quantum chemical study has been carried out on 9,10-bis(4-fuorophenyl)-3,3,6,6-
tetramethyl-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione (FTHD) and 10-(4-fuorophenyl)-3,3,
6,6-tetramethyl-9-(3,4,5-trimethoxyphenyl)-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione
(FTMPHD) with the main aim of exploring their geometrical, vibrational, and electronic properties.
For the sake of a comparative study, theoretical work has also been done on 3,3,6,6-tetramethyl-9-
(4-nitrophenyl)-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (TNHXD) and 9-(benzo[d][1,3]
dioxol-5-yl)-3,3,6,6-tetramethyl-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (BDTHXD). To
perform quantum chemical calculations and to calculate important properties, rigorous implementation
of the DFT-based method has been carried out with a focus on those properties that are not easily obtain-
able via experimental methods. These properties include molecular geometry, vibrational frequencies,
dipole moments and higher-order moments, thermochemical properties, etc. In the standard literature,
several forms of DFT are available whose applications depend on the nature of the molecular systems
under investigation and characteristics to be explored. In numerous publications, it has been mentioned
that,[8–10] DFT offers a better trade-off between computational cost and accuracy for medium-sized
molecules, and hence it has been justifably implemented. A piece of inclusive information about the
density functional theory and the methods based on it can be accessed from contemporary literature.[11]
This chapter involves a comprehensive comparison of different properties of 9,10-bis
(4-fluorophenyl)-3,3,6,6-tetramethyl-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione
(FTHD) and 10-(4-fuorophenyl)-3,3,6,6-tetramethyl-9-(3,4,5-trimethoxyphenyl)-3,4,6,7,9,10-
hexahydroacridine-1,8(2H,5H)-dione(FTMPHD)withthatof3,3,6,6-tetramethyl-9-(4-nitrophenyl)-
3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (TNHXD) and 9-(benzo[d][1,3]dioxol-5-yl)-
3,3,6,6-tetramethyl-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (BDTHXD) as suggested
by density functional theory. In this chapter, the geometrical and some spectroscopic features of
these compounds are discussed.
Theoretical molecular modeling is a powerful tool for studying the physical, chemical, and bio-
logical properties of chemical compounds.[12, 13] Molecular modeling has different levels of theories
DOI: 10.1201/9781003441328-2 27](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-52-320.jpg)
![28 Computational Studies
utilized for studying chemical compounds and reactions’ properties.[14, 15] One of the most accurate
theoretical approaches is density function theory (DFT), which studies the properties of compounds
and provides indications close to those of an experiment.[16, 17] Moreover, molecular structure can be
studied and provided with signifcant information about compounds and their interactions by calcu-
lating the infrared (IR) spectrum theoretically, which confrms the expressed value IR result.[18, 19]
2.2 TOOLS OF STUDY: COMPUTATIONAL DETAILS
It has been observed that for a variety of systems of biological relevance, the combination of Becke’s
three-parameterhybridexchangefunctional[20] withtheLee–Yang–Parrcorrelationfunctional[21] (B3LYP)
functional is quite consistent. The B3LYP functional is a gradient-corrected hybrid functional and is
immensely popular for studying a variety of systems of biological interest.[22–25] Apart from the popular
functional, the standard split-valence basis set, combined with diffuse as well as polarization functions
6–311++G(d,p), has also been employed in the calculations. The computational work has been carried
out by employing the Gaussian 09 suite of code[26] using different keywords for different types of jobs.
The objective of geometry optimization is to fnd an atomic arrangement that makes the molecule
most stable. Molecules are most stable when their energy attains the lowest possible value. The
most stable structures of molecules are obtained by geometry optimization, necessarily followed by
frequency calculations. The sole purpose of geometry optimization is to predict a three-dimensional
arrangement of atoms that makes the molecule most stable, i.e., having minimum energy. Positive
real values of frequencies further ensure that the optimized structure is really the lowest possible
energy structure. The optimized geometries of dione-derivative compounds are shown in Figure 2.1.
The calculated geometrical parameters show a good proximity when compared with the experi-
mental results. The average value for C-C bonds in rings is found to be in the range of 1.515–1.567
FIGURE 2.1 Optimized geometry of (a) FTHD, (b) FTMPHD, (c) TNHXD, and (d) BDTHXD.
Source: Regenerated from Ref. [8, 9].](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-53-320.jpg)
![29
Spectroscopic Signatures of Some Organic Compounds
Å and that for C-H bonds in the range of 1.090–1.100 Å, which are in good agreement with those
reported for similar structures.[27, 28] The C-O bond length of 1.43 Å is also in good agreement with
the literature data.[29, 30]
2.3 RESULTS AND DISCUSSION
2.3.1 VibratioNaL aNaLyses
Frequency calculations yield some of the most important information discussed in this thesis. IR
and Raman spectra of molecules can be predicted for any optimized molecular structure. The posi-
tion and relative intensity of vibrational bands can be gathered from the output of a frequency
calculation. This information is independent of the experiment and can therefore be used as a tool
to confrm peak positions in experimental spectra or to predict peak positions and intensities when
experimental data is not available. Calculated frequencies are based on the harmonic model, while
real vibrational frequencies are anharmonic. This partially explains discrepancies between calcu-
lated and experimental frequencies.
The total energy of a molecule comprising N atoms near its equilibrium structure may be
written as:
3˛ 3˛ 3˛ 2
1 2
ˇ ˆ V
˜ ° V q ˙V ˙
˝ ˙ ˝ q q (2.1)
i eq i j
2 i˝ i 1 j 1 ˘ ˆ ˆ
i j eq
1 ˝ ˝ q q
Here the mass-weighted Cartesian displacements, qi, are defned in terms of the locations Xi of the
nuclei relative to their equilibrium positions Xi’eq and their masses Mi:
qi ˜ ˙1 2
˛ˆ ° ˆ ˝ (2.2)
i i ieq
Veq is the potential energy at the equilibrium nuclear confguration.
For such a system, the classical mechanical equation of motion takes the form:
3˛
q ˜ ° f q j = 1, 2, 3 ˝3N (2.3)
i ij i
i˜1
The fij term quadratic force constants are the second derivatives of the potential energy with respect
to mass-weighted Cartesian displacement, evaluated at the equilibrium nuclear confguration:
2
˛ ° V ˆ
f ˜ ˙ ˘ (2.4)
ij ˙ ˘
° °
i j
˝ q q ˇeq
The fij may be evaluated by numerical second differentiation:
V
˜2
V ˙ ˙
˛ ˝
£
° (2.5)
˜ ˜
q q q Vq
˙ ˙
i j i j
By numerical frst differentiation of analytical frst derivatives:
˜2
V ˙˛˜ ˜
V q ˝
°
j
(2.6)
˜ ˜ ˙q
q q
i j i](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-54-320.jpg)
![This ebook is for the use of anyone anywhere in the United
States and most other parts of the world at no cost and with
almost no restrictions whatsoever. You may copy it, give it away
or re-use it under the terms of the Project Gutenberg License
included with this ebook or online at www.gutenberg.org. If you
are not located in the United States, you will have to check the
laws of the country where you are located before using this
eBook.
Title: Poems of Giosuè Carducci, Translated with two
introductory essays
Author: Giosuè Carducci
Contributor: Frank Sewall
Release date: March 9, 2018 [eBook #56711]
Language: English
Credits: Produced by ellinora, Bryan Ness, Barbara Magni and
the
Online Distributed Proofreading Team at
http://www.pgdp.net
(This file was produced from images generously made
available by The Internet Archive/American Libraries.)
*** START OF THE PROJECT GUTENBERG EBOOK POEMS OF
GIOSUÈ CARDUCCI, TRANSLATED WITH TWO INTRODUCTORY
ESSAYS ***](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-60-320.jpg)
![It is only to the Latin nations of Europe, sprung from Hellenic stock
and having a continuous literary history covering a period of from
two to three thousand years, that we may look for the example of a
people undergoing these radical religious changes and preserving
meanwhile a living record of them in a contemporaneous literature.
Such a nation we find in Italy.
So thorough is the reaction exhibited during the last half of the
present century in that country against the dogma and the authority
of the Church of Rome that we are led to inquire whether, not the
church alone, as Mr. Symonds says,[1] but Christianity itself has ever
“imposed on the Italian character” to such an extent as to obliterate
wholly the underlying Latin or Hellenic elements, or prevent these
from springing again into a predominating influence when the
foreign yoke is once removed.
To speak of Christianity coming and going as a mere passing episode
in the life of a nation, and taking no deep hold on the national
character, is somewhat shocking to the religious ideas which prevail
among Christians, but not more so than would have been to a
Roman of the time of the Cæsars the suggestion that the Roman
Empire might itself one day pass away, a transient phase only in the
life of a people whose history was to extend in unbroken line over a
period of twenty-five hundred years.
In the work just referred to Mr. Symonds also briefly hints at another
idea of profound significance,—namely, whether there is not an
underlying basis of primitive race character still extant in the various
sections of the Italian people to which may be attributed the variety
in the development of art and literature which these exhibit. In his
Studii Letterari (Bologna, 1880), Carducci has made this idea a
fundamental one in his definition of the three elements of Italian
literature. These are, he says, the church, chivalry, and the national
character. The first or ecclesiastical element is superimposed by the
Roman hierarchy, but is not and never was native to the Italian
people. It has existed in two forms. The first is Oriental, mystic, and
violently opposed to nature and to human instincts and appetites,](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-72-320.jpg)
![1871, in the collection entitled Decennali. Even through the
burdensome guise of a metrical translation, something of the
splendid fire of the original can hardly fail to make itself felt. [I]
The movement for the revival of Italian literature may be said to
have begun with Alfieri, at the close of the last and the beginning of
the present century. It was contemporary with the breaking up of
the political institutions of the past in Europe, the dissolution of the
Holy Roman Empire, the brief existence of the Italian Republic, the
revival for a short joyous moment of the hope of a restored Italian
independence. Again a thrill of patriotic ardour stirs the measures of
the languid Italian verse. Alfieri writes odes on America Liberata,
celebrating as the heroes of the new age of liberty Franklin,
Lafayette, and Washington. Still more significant of the new life
imparted to literature at this time is the sober dignity and strength of
Alfieri's sonnets, and the manly passion that speaks in his dramas
and marks him as the founder of Italian tragedy.
But the promise of those days was illusory. With the downfall of
Napoleon and the return of the Austrian rule, the hope of the Italian
nationality again died out. Alfieri was succeeded by Vincenzo Monti
and his fellow-classicists, who sought to console a people deprived
of future hope with the contemplation of the remote past. This
school restored rather than revived the ancient classics. They gave
Italians admirable translations of Homer and Virgil, and turned their
own poetic writing into the classical form. But they failed to make
these dead forms live. These remained in all their beauty like
speechless marble exhumed and set up in the light and stared at. If
they spoke at all, as they did in the verses of Ugo Foscolo and
Leopardi, it was not to utter the joyous emotions, the godlike
freedom and delight of living which belonged to the world's youthful
time; it was rather to give voice to an all-pervading despair and
brooding melancholy, born, it is true, of repeated disappointments
and of a very real sense of the vanity of life and the emptiness of
great aspirations, whether of the individual or of society. This
melancholy, itself repugnant to the primitive Italian nature, opened
the way for the still more foreign influence of the romanticists, which](https://image.slidesharecdn.com/29026240-250522204305-c8eeb274/85/Computational-Studies-From-Molecules-To-Materials-Ambrish-Kumar-Srivastava-75-320.jpg)
Computational Studies From Molecules To Materials Ambrish Kumar Srivastava
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- 6. Computational Studies The book covers a diverse range of topics based on computational studies, including modeling and simulations based on quantum chemical studies and molecular dynamics (MD) simulations. It contains quantum chemical studies on several molecules, including biologically relevant molecules and liquid crystals and various aspects of superatomic clusters including superalkalis and superhalogens. It gives an overview of MD simulations and their applications on biomolecular systems such as HIV-1 protease and integrase. Features: • Includes frst principle methods, density functional theory, as well as molecular dynamics simulations. • Explores quantum chemical studies on several molecules. • Gives readers an overview of the power of computation. • Discusses superatomic clusters, superalkalis, and superhalogens. • Covers themes from molecules, clusters, materials, as well as biophysical systems. This book is aimed at researchers and graduate students in materials science and computational and theoretical chemistry.
- 7. Emerging Materials and Technologies Series Editor: Boris I. Kharissov The Emerging Materials and Technologies series is devoted to highlighting publications centered on emerging advanced materials and novel technologies. Attention is paid to those newly discovered or applied materials with potential to solve pressing societal problems and improve quality of life, corresponding to environmental protection, medicine, communications, energy, transportation, ad- vanced manufacturing, and related areas. The series takes into account that, under present strong demands for energy, material, and cost savings, as well as heavy contamination problems and worldwide pandemic conditions, the area of emerging materials and related scalable technologies is a highly interdisciplinary feld, with the need for researchers, professionals, and academics across the spectrum of engineering and technological disciplines. The main objective of this book series is to attract more attention to these materials and technologies and invite conversation among the international R&D community. Smart Micro- and Nanomaterials for Pharmaceutical Applications Edited by Ajit Behera, Arpan Kumar Nayak, Ranjan K. Mohapatra, and Ali Ahmed Rabaan Friction Stir-Spot Welding Metallurgical, Mechanical and Tribological Properties Edited by Jeyaprakash Natarajan and K. Anton Savio Lewise Phase Change Materials for Thermal Energy Management and Storage Fundamentals and Applications Edited by Hafz Muhammad Ali Nanofuids Fundamentals, Applications, and Challenges Shriram S. Sonawane and Parag P. Thakur MXenes From Research to Emerging Applications Edited by Subhendu Chakroborty Biodegradable Polymers, Blends and Biocomposites Trends and Applications Edited by A. Arun, Kunyu Zhang, Sudhakar Muniyasamy and Rathinam Raja Bioinspired Materials and Metamaterials A New Look at the Materials Science Edward Bormashenko Computational Studies From Molecules to Materials Edited by Ambrish Kumar Srivastava For more information about this series, please visit: www.routledge.com/Emerging-Materials-and-Technologies/book-series/ CRCEMT
- 8. Computational Studies From Molecules to Materials Edited by Ambrish Kumar Srivastava
- 9. First edition published 2025 by CRC Press 2385 NW Executive Center Drive, Suite 320, Boca Raton FL 33431 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2025 selection and editorial matter, Ambrish Kumar Srivastava; individual chapters, the contributors Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microflming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www. copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978–750–8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.co.uk Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identifcation and explanation without intent to infringe. ISBN: 978-1-032-52854-0 (hbk) ISBN: 978-1-032-57858-3 (pbk) ISBN: 978-1-003-44132-8 (ebk) DOI: 10.1201/9781003441328 Typeset in Times by Apex CoVantage, LLC
- 10. Dedicated to My Parents (whose sacrifces turned into my achievements)
- 12. Contents Preface..............................................................................................................................................xv About the Editor.............................................................................................................................xvii List of Contributors.........................................................................................................................xix Chapter 1 DFT-Based Studies on Thermodynamic, Electronic, Optical, and Spectroscopic Aspects of Liquid Crystals: An Overview.....................................1 Dipendra Sharma, Gargi Tiwari, Abhishek Kumar, Neeraj Misra, and Sugriva Nath Tiwari 1.1 Introduction .......................................................................................................1 1.2 Liquid Crystal Classifcation.............................................................................2 1.3 Thermotropic LCs .............................................................................................2 1.3.1 Nematic LCs........................................................................................2 1.3.2 Cholesteric LCs ...................................................................................2 1.3.3 Discotic LCs........................................................................................3 1.3.4 Smectic LCs.........................................................................................4 1.4 Lyotropic LCs....................................................................................................4 1.5 Computational Method......................................................................................6 1.6 Results and Discussion......................................................................................8 1.6.1 4-Alkyl-4ʹ-Cyanobiphenyl Series........................................................8 1.6.2 Optimized Parameter Analysis ...........................................................9 1.6.3 Electronic and Global Parameter Analysis..........................................9 1.6.4 Electro-Optical Parameter Analysis..................................................10 1.7 4-n-Alkoxy-4ʹ-Cyanobiphenyl Liquid Crystal Series .....................................12 1.7.1 Thermal Parameter Variation with Homologous Number ................12 1.7.2 Electronic and Global Parameter Variation with Homologous Number..............................................................................................13 1.7.3 Electro-Optical Parameter Variation with Homologous Number.....15 1.7.4 Raman and Absorption Spectra Analysis..........................................19 1.8 Conclusions and Viewpoints ...........................................................................22 1.8.1 Acknowledgment...............................................................................22 1.8.2 Confict of Interests ...........................................................................22 References ..................................................................................................................22 Chapter 2 Spectroscopic Signatures of Some Organic Compounds: Theory Meets Experiment .........................................................................................27 Abhishek Kumar, Ambrish Kumar Srivastava, Ratnesh Kumar, and Neeraj Misra 2.1 Introduction .....................................................................................................27 2.2 Tools of Study: Computational Details ...........................................................28 2.3 Results and Discussion....................................................................................29 2.3.1 Vibrational Analyses .........................................................................29 2.3.2 NMR Spectroscopic Analysis ...........................................................36 vii
- 13. viii Contents 2.4 Conclusion .......................................................................................................37 2.4.1 Acknowledgments .............................................................................37 References ..................................................................................................................37 Chapter 3 Exploring the Properties of Vincosamide-N-Oxide, a Biologically Active Natural Compound by Density Functional Theory.................................................... 41 Ashok Kumar Mishra and Satya Prakash Tewari 3.1 Introduction ..................................................................................................... 41 3.2 Investigations Based on DFT...........................................................................43 3.2.1 Computational Details and Molecular Structure ..............................43 3.2.2 Molecular Electrostatic Potential (MESP)........................................44 3.2.3 HOMO, LUMO, and Global Reactivity Descriptors.........................45 3.2.4 Nonlinear Optical Properties ............................................................45 3.2.5 Local Reactivity Descriptors.............................................................47 3.2.6 NBO Analysis....................................................................................49 3.3 Drug Properties ...............................................................................................49 3.4 Conclusion and Future Scope..........................................................................49 References ..................................................................................................................51 Chapter 4 Drugs, Drug–Biomolecule Interactions, and Drugs Delivery Systems: Quantum Chemical Approaches ................................................................................53 Soni Mishra and Abhishek Kumar Mishra 4.1 Introduction .....................................................................................................53 4.1.1 Novel Drug Delivery Systems...........................................................53 4.1.2 Nanoparticles and Drug Delivery......................................................53 4.2 Methodology....................................................................................................55 4.3 Result and Discussion......................................................................................56 4.3.1 Quantum Chemical Calculations of Drug Molecules .......................56 4.4 Quantum Chemical Calculation of DPPC with Drug Molecule ..................... 61 4.5 Quantum Chemical Calculation of DPPC with Functionalized CNTs ...........63 4.6 Conclusions......................................................................................................64 References ..................................................................................................................65 Chapter 5 Graphene-Based Nanomaterials (GBNs) and Their Biomedical Applications................................................................................................................68 Ruby Srivastava and Sravani Joshi 5.1 Introduction .....................................................................................................68 5.2 History of GBNs..............................................................................................68 5.3 Synthesis..........................................................................................................68 5.4 Structures and Properties ................................................................................69 5.4.1 Graphene............................................................................................69 5.4.2 Graphene Oxide (GO)........................................................................69 5.4.3 Reduced Graphene Oxide (rGO).......................................................69
- 14. ix Contents 5.4.4 Graphene Quantum Dots (GQDs) .....................................................69 5.4.5 Graphene Nanoribbons (GNRs) ........................................................70 5.5 Computational Studies on GBNs.....................................................................70 5.6 Functional Modifcation ..................................................................................72 5.7 Biomedical Applications ................................................................................. 74 5.7.1 Drug/Gene Delivery .......................................................................... 74 5.7.2 Biosensor ...........................................................................................75 5.7.3 Bioimaging ........................................................................................76 5.7.4 Tissue Engineering............................................................................77 5.7.5 Photothermal Therapy (PTT)............................................................78 5.7.6 Antibacteria .......................................................................................78 5.8 Health and Environmental Risks of GBNs .....................................................78 5.8.1 Impact on the Environment...............................................................79 5.8.2 Methods to Reduce Toxicity..............................................................79 5.9 Conclusions......................................................................................................79 5.9.1 Acknowledgments .............................................................................80 5.9.2 Competing Interests...........................................................................80 References ..................................................................................................................80 Chapter 6 Concept and Applications of Biomolecular Simulations ...........................................87 Vandana Kardam and Kshatresh Dutta Dubey 6.1 Introduction .....................................................................................................87 6.2 Molecular Dynamics Simulations ...................................................................88 6.2.1 Basic Principles of Molecular Dynamic Simulations........................88 6.2.2 Periodic Boundary Conditions .......................................................... 91 6.2.3 Simulation Protocols ......................................................................... 91 6.2.4 Applications of MD Simulations.......................................................96 6.2.5 Challenges and Limitations in Molecular Dynamics Simulations........99 6.3 QM/MM Calculations...................................................................................100 6.3.1 General Overview of QM/MM .......................................................100 6.4 Case Studies of MD and QM/MM Methods.................................................106 6.4.1 Investigation of Role of a Crucial Dyad and Mechanistic Elucidation of Hydroxylation Mechanism in CYP450 from Mint Family.....................................................................................106 6.4.2 Assessing the Impact of Various Water Models on the Structure and Function of Three Enzymes in CYP5450 ................................107 6.4.3 Effect of Allostery on the Capping Loop and Its Role in Catalysis in Dipeptide Epimerases of Enolase Family....................108 6.5 Conclusion ..................................................................................................... 110 References ................................................................................................................111 Chapter 7 Soft Computing Technique towards the Geometry Optimization of Atomic Clusters.................................................................................................... 116 Ranita Pal, Bhrigu Chakraborty, and Pratim Kumar Chattaraj 7.1 Introduction ................................................................................................... 116 7.2 Global Optimization (GO)............................................................................. 117
- 15. x Contents 7.2.1 Particle Swarm Optimization (PSO) ...............................................120 7.2.2 Firefy Algorithm (FA) .................................................................... 121 7.2.3 Artifcial Bee Colony (ABC) Algorithm.........................................122 7.2.4 Bonobo Optimizer (BO)..................................................................124 7.2.5 Artifcial Neural Network (ANN)...................................................125 7.2.6 Convolutional Neural Network (CNN)............................................128 7.2.7 Basin Hopping (BH)........................................................................130 7.2.8 Simulated Annealing (SA)............................................................... 131 7.2.9 Genetic Algorithm (GA).................................................................. 132 7.3 Case Studies................................................................................................... 133 7.3.1 CNN and PSO in the Determination of GM Structures.................. 133 7.3.2 FA Integrated with DFT for the GO of Al4 2− Clusters....................134 7.3.3 ABC Algorithm in the Determination of GM Structures of Hypercoordinate Clusters................................................................134 7.4 Summary .......................................................................................................136 7.4.1 Acknowledgments ...........................................................................136 7.4.2 Confict of Interest...........................................................................136 References ................................................................................................................136 Chapter 8 17 Atoms Magnesium Nanoclusters for Purifcation of Air-Forming Gases .............................................................................................. 140 Sara Ahmadi and Mahmood Reza Dehghan 8.1 Introduction ................................................................................................... 140 8.2 Nanoclusters Chemistry ................................................................................ 140 8.3 Types of Nanoclusters.................................................................................... 142 8.4 Surface Absorption and Various Absorption Methods ................................. 145 8.5 Physical Adsorption....................................................................................... 145 8.6 Chemical Surface Adsorption ....................................................................... 146 8.7 Exchange Adsorption .................................................................................... 146 8.8 Factors Affecting Surface Absorption........................................................... 148 8.9 Examining Adsorption Behaviors through Theoretical Calculations........... 148 8.10 Computational Chemistry .............................................................................150 8.11 Magnesium Nanoclusters for Purifcation of Air-Forming Gases: A DFT Approach...........................................................................................150 8.12 Application of Mg17 (Mg16M; M=Be, Mg, and Ca) Nanocluster in Purifcation of N2 from Air........................................................................... 151 8.13 Application of Mg17 (Mg16M; M = Be, Mg, and Ca) Nanocluster in Purifcation of CO from Air.......................................................................... 152 8.14 Application of Mg17 (Mg16M; M = Be, Mg, and Ca) Nanocluster in Purifcation of O2 from Air ...........................................................................154 8.15 Conclusion .....................................................................................................154 References ................................................................................................................156 Chapter 9 Effect of Confnement in Bonding and Catalysis..................................................... 158 Ruchi Jha, Ranita Pal, and Pratim Kumar Chattaraj 9.1 Introduction ................................................................................................... 158 9.2 Different Types of Geometrical Confnement............................................... 159
- 16. xi Contents 9.2.1 Cucurbit[n]uril................................................................................. 159 9.2.2 Fullerene Cages Cn [n = 60, 70, 80, 90, etc.] ...................................160 9.3 Catalysis Using Cucurbituril Cavities ........................................................... 161 9.4 Catalysis Using Fullerene Cages ................................................................... 162 9.5 Bonding inside Fullerene Cages.................................................................... 163 9.6 Conclusion .....................................................................................................164 9.6.1 Acknowledgment............................................................................. 165 9.6.2 Confict of Interest........................................................................... 165 References ................................................................................................................165 Chapter 10 Computational Studies on the NLO Properties of Molecules and Clusters Containing Excess Electrons.................................................................................... 168 Wei‑Ming Sun 10.1 Introduction ................................................................................................... 168 10.2 Background of the Excess Electron............................................................... 168 10.3 Computational Methodology......................................................................... 169 10.3.1 Theoretical Background .................................................................. 169 10.3.2 Computational Methods .................................................................. 170 10.3.3 Characterization of the Excess Electron ......................................... 171 10.4 Strategies for Designing Molecules and Clusters with Excess Electrons........172 10.4.1 Alkali-Metal-Based Excess Electron Compounds.......................... 173 10.4.2 Alkaline-Earth-Based Excess Electron Compounds ...................... 182 10.4.3 Transition Metal-Based Excess Electron Compounds .................... 185 10.4.4 Superalkali-Based Excess Electron Compounds ............................ 188 10.4.5 Clusters with Excess Electrons........................................................ 191 10.5 Concluding Remarks .....................................................................................194 10.5.1 Acknowledgment.............................................................................194 References ................................................................................................................194 Chapter 11 Organic Semiconducting Materials in Electronic Devices......................................205 Shamoon Ahmad Siddiqui, Ankit Kargeti, and Tabish Rasheed 11.1 Introduction ...................................................................................................205 11.2 Application of Organic Semiconducting Materials in Designing Electronic Devices and Their Properties.......................................................206 11.2.1 Characteristic of the Single Molecular Diode.................................206 11.2.2 Characteristic of the Organic Field Effect Transistor .....................207 11.2.3 Characteristic of the Organic Solar Cells (Dye-Sensitized Solar Cells) ......................................................................................207 11.2.4 Computational Methodology...........................................................207 11.3 Organic Molecular Diodes ............................................................................208 11.3.1 Analysis of Molecular System Taken from Figure 11.1: (a) S1 [p-Sexiphenyl-σ-TCNQ], (b) S2 [p-Sexiphenyl-σ-NTCDA] ...........208 11.3.2 Analysis of Molecular System Taken from Figure 11.2: (a) S3 [TCNQ-σ-(TTF)], (b) S4 [TCNQ-σ-(DPh-BTBT)], (c) S5 [TCNQ-σ-(BEDT-TTF)].................................................................. 211 11.4 Organic Field Effect Transistors.................................................................... 213
- 17. xii Contents 11.4.1 Analysis of Molecular System Taken from Figure 11.7: M1(2,2-bis(4-trifuoromethylphenyl)-5,5–bithiazole)...................... 214 11.4.2 Analysis of Molecular System Taken from Figures 11.8a and 11.8b.......................................................................................... 215 11.5 Dye-Sensitized Solar Cells............................................................................ 217 11.5.1 Photovoltaic Performance Analysis................................................. 218 11.5.2 Effect of Double Donor Moieties on the Performance of DSSC for Dyes 1–8 .....................................................................220 11.5.3 Effect of Double Acceptor Moieties on the Performance of DSSC for Dyes 9 and 10..................................................................223 11.6 Limitation of Organic Semiconducting Materials and Future Scope ...........224 11.7 Conclusion .....................................................................................................224 11.7.1 Acknowledgment.............................................................................225 References ................................................................................................................225 Chapter 12 Hydrogen Storage Effciency of Isomeric Cu(I)-Triazine Complexes: In Quest of New Hydrogen Storage Material..........................................................................228 Abhishek Bag, Mrinal Kanti Dash, Santanab Giri, Gobinda Chandra De, and Gourisankar Roymahapatra 12.1 Introduction ...................................................................................................228 12.2 Theory and Computational Details...............................................................229 12.3 Result and Discussion.................................................................................... 231 12.3.1 Mono- and Di-Cu(I)-Decorated Isomeric Triazine Systems .......... 231 12.3.2 H2 Adsorption on Mono- and Di-Cu(I)-Decorated Isomeric Triazine Systems .............................................................................232 12.3.3 ESP and NBO Analysis...................................................................235 12.4 Bonding Nature Analysis ..............................................................................236 12.4.1 Electron Localization Function (ELF)............................................236 12.4.2 Noncovalent Interaction (NCI)........................................................236 12.4.3 Energy Decomposition Analysis (EDA)..........................................236 12.4.4 Partial Density of State (PDOS) Analysis.......................................237 12.5 Effect of Temperature on H2 Adsorption.......................................................239 12.6 Conclusion .....................................................................................................240 12.6.1 Acknowledgments ...........................................................................241 References ................................................................................................................241 Chapter 13 Quantum Chemical Study on Pure and Silicon-Doped Activated Carbon Sheets........245 Ratnesh Kumar, Abhishek Kumar, Ambrish Kumar Srivastava, and Neeraj Misra 13.1 Introduction ...................................................................................................245 13.2 Computational Methods ................................................................................246 13.3 Results and Discussions.................................................................................247 13.3.1 Geometrical Properties....................................................................247 13.3.2 Electronic Properties.......................................................................249 13.4 Conclusions.................................................................................................... 251 References ................................................................................................................252
- 18. Contents xiii Chapter 14 Quantum Computing in Materials: A Perspective...................................................256 Ruby Srivastava and Sravani Joshi 14.1 Introduction ...................................................................................................256 14.2 Quantum Computation ..................................................................................257 14.3 Quantum Gates and Quantum-Circuit-Based Paradigm...............................258 14.4 Quantum Algorithms.....................................................................................259 14.4.1 Variational Quantum Eigensolver (VQE)........................................259 14.4.2 Quantum Phase Estimation (QPE) ..................................................259 14.5 Multiscale Quantum Computing................................................................... 261 14.5.1 Divide and Conquer (DC) Approach............................................... 261 14.5.2 Correlation Energy Decomposition.................................................262 14.6 Conclusion .....................................................................................................262 14.6.1 Acknowledgments ...........................................................................263 14.6.2 Confict of Interest...........................................................................263 References ................................................................................................................263 Index..............................................................................................................................................267
- 20. Preface Atoms form molecules, which form bulk materials. There is also an intermediate phase between molecules and materials, known as clusters. This book deals with the computational studies of mol- ecules to materials. Computational studies cover an important part of modern science, which plays a pivotal role in complementing experimental studies and explaining the experimental results in a very constructive way. In addition, the studies become a powerful tool in the absence of experiments. With the advent of powerful computers and advancement in theory and its implementation in the form of computer code or software, the scope of computational research expanded to a variety of felds and reached the next levels. This book, Computational Studies: From Molecules to Materials, aims to present readers with multidimensional forms of computational research. The book consists of 14 chapters contributed by leading and active researchers and experts in their respective felds. The chapters are based on computational studies with a variety of themes. Chapter 1 discusses various aspects of the molecules of liquid crystals. Chapter 2 compares the spectroscopic results of some organic compounds obtained by theory with experiments. Chapter 3 offers various properties of a biologically relevant molecule using density functional theory. Chap- ter 4 provides insight into drug interactions and drug delivery systems using quantum chemical methods. Chapter 5 discusses graphene oxide-based nanomaterials and their applications in biomed- icine. Chapter 6 details the concept of molecular dynamics and its role in biomolecular simulations. Chapter 7 offers a technique for the optimization of atomic clusters and related algorithms in detail. Chapter 8 discusses the role of a magnesium nanocluster in the purifcation of oxygen, nitrogen, and carbon monoxide gases. Chapter 9 reveals the effect of confnement on bonding and catalysis. Chapter 10 provides a comprehensive account of the nonlinear optical properties of molecules and clusters with excess electrons. Chapter 11 discusses the properties of molecules for various devices in organic electronics such as diodes, transistors, and solar cells. Chapter 12 presents the hydro- gen storage capacity of Cu(I)-triazine-based organometallic complexes. Chapter 13 discusses the properties of pure and doped activated carbon sheets using density functional theory. In the end, Chapter 14 sheds some light on the role of quantum computing in the study of materials. All in all, the book reveals various aspects of computational research along with the latest developments. I believe that this book will beneft young researchers and scientists working at the interface of physics, chemistry, and biology. It is particularly useful for researchers in theoretical chemistry, computational chemistry, computational materials science, biophysics, biochemistry, modeling, and simulations. Best wishes, Ambrish Kumar Srivastava Gorakhpur, India July 2023 xv
- 22. About the Editor Ambrish Kumar Srivastava is Assistant Professor at the Department of Physics in Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, India. He was Junior Research Fellow (with All India Rank 18) and Senior Research Fellow of the Council of Scientifc and Industrial Research (CSIR), India. He earned his PhD on the topic entitled “Computational Studies on Biologically Active Molecules and Small Clusters: DFT and TDDFT Approaches” from the University of Lucknow, India, and subsequently worked as National Postdoctoral Fellow of the Science & Engineering Research Board (SERB) at D.D.U. Gorakhpur University. He has published over 120 research papers in various journals of international repute with an h-index of 23 and a citation index of 1700. In addition, he has authored/edited 3 books, and 3 more books are currently in press. He is an active reviewer for various leading journals and has reviewed more than 40 research papers so far. He is an Associate Editor of Frontiers in Physics for the Chemical Physics and Physical Chemistry section and also serves on the Editorial Board of several journals. He is a member of various scientifc societies and organizations including the American Chemical Society, Royal Society of Chemistry, Indian Chemical Society, Materials Research Society of India, among others. He has recently received the prestigious NASI-Young Scientist Platinum Jubilee Award–2022 from the NationalAcademy of Sciences, India. His broad research interests include Superatomic Clusters, Computational Materials Science, and Biophysics. Laboratory website: https://cutt.ly/CMSLab xvii
- 24. Contributors Ahmadi, Sara Department of Chemistry Islamic Azad University Firoozabad, Iran Bag, Abhishek Department of Chemistry Cooch Behar Panchanan Barma University Cooch Behar, India Chakraborty, Bhrigu Department of Chemistry Indian Institute of Technology Kharagpur Kharagpur, India Chattaraj, Pratim Kumar Department of Chemistry Birla Institute of Technology Ranchi, India Dash, Mrinal Kanti School of Applied Sciences and Humanities Haldia Institute of Technology Haldia, India De, Gobinda Chandra Department of Chemistry Cooch Behar Panchanan Barma University Cooch Behar, India Dehghan, Mahmood Reza Department of Chemistry Islamic Azad University Firoozabad, Iran Dubey, Kshatresh Dutta Department of Chemistry Shiv Nadar Institution of Eminence Gautam Buddha Nagar, India Giri, Santanab School of Applied Sciences and Humanities Haldia Institute of Technology Haldia, India Jha, Ruchi Advanced Technology Development Centre Indian Institute of Technology Kharagpur Kharagpur, India Joshi, Sravani Bioinformatics Centre CSIR–Centre for Cellular and Molecular Biology Hyderabad, India Kardam, Vandana Department of Chemistry Shiv Nadar Institution of Eminence Gautam Buddha Nagar, India Kargeti, Ankit Department of Applied Sciences BML Munjal University Gurugram, India Kumar, Abhishek Department of Physics University of Lucknow Lucknow, India Kumar, Ratnesh Department of Physics University of Lucknow Lucknow, India Mishra, Abhishek Kumar Department of Physics University of Petroleum and Energy Studies Dehradun, India Mishra, Ashok Kumar Department of Physics Dr. Shakuntala Misra National Rehabilitation University Lucknow, India Mishra, Soni Department of Physics Graphic Era Hill University Dehradun, India xix
- 25. xx Contributors Misra, Neeraj Department of Physics University of Lucknow Lucknow, India Pal, Ranita Advanced Technology Development Centre Indian Institute of Technology Kharagpur Kharagpur, India Rasheed, Tabish Department of Applied Sciences BML Munjal University Gurugram, India Roymahapatra, Gourisankar School of Applied Sciences and Humanities Haldia Institute of Technology Haldia, India Sharma, Dipendra Department of Physics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur, India Siddiqui, Shamoon Ahmad Department of Physics Integral University Lucknow, India Srivastava, Ambrish Kumar Department of Physics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur, India Srivastava, Ruby Bioinformatics Centre CSIR–Centre for Cellular and Molecular Biology Hyderabad, India Sun, Wei-Ming Department of Basic Chemistry School of Pharmacy Fujian Medical University Fujian, China Tewari, Satya Prakash Department of Physics Dr. Shakuntala Misra National Rehabilitation University Lucknow, India Tiwari, Gargi Department of Physics Patna University Patna, India Tiwari, Sugriva Nath Department of Physics Deen Dayal Upadhyaya Gorakhpur University Gorakhpur, India
- 26. 1 DFT-Based Studies on Thermodynamic, Electronic, Optical, and Spectroscopic Aspects of Liquid Crystals An Overview Dipendra Sharma, Gargi Tiwari, Abhishek Kumar, Neeraj Misra, and Sugriva Nath Tiwari 1.1 INTRODUCTION Conventionally, it is presumed that matter exists only in three states: solid, liquid, and gas. However, this is not quite true: in particular, some of the organic substances do not undergo a single transition from solid to liquid but rather a cascade of transitions involving new phases; the mechanical proper- ties and the symmetry properties of these phases are intermediate between those of a liquid and those of a crystal. For this reason, they have often been called liquid crystals, or mesogens. A more proper name is “mesomorphic phases” (mesomorphic: of intermediate form). However, many crystals show a transition from a strongly ordered state to a phase where each molecule commutes through several equivalent orientations. The high-temperature phase is positionally ordered, but orientationally dis- ordered. It is sometimes (loosely) called a plastic crystal. Examples of such rotational transitions are solid hydrogen, ammonium halides, and also certain types of organic molecules. In the liquid crys- talline phase, molecules of certain organic liquids are aligned preferentially along one direction or in two dimensions at lower temperatures; they are positionally disordered but orientationally ordered anisotropic liquids. At higher temperatures, they undergo a transition to a traditional (isotropic) liq- uid phase.[1–3] A typical phase transformation for a thermotropic liquid crystal is shown in Figure 1.1. The development of liquid crystal science has a long and colorful history. The frst research on liquid crystals was discovered and published in 1888 by Austrian Botanist Friedrich Reinitzer from FIGURE 1.1 Arrangements of molecules in thermotropic liquid crystalline phase transitions represented by rod-like molecules. DOI: 10.1201/9781003441328-1 1
- 27. 2 Computational Studies Karl-Ferdinands-Universität. He discussed the melting behavior of cholesteryl benzoate, which has two melting points: at 145.5 °C, the compound changes into a murky fuid, and at 178.5 °C, it becomes clear liquid.[4] German Physicist Otto Lehmann, a specialist in polarization microscopy, was consulted by Reinitzer when he was unable to explain these data. Lehmann examined the opti- cal characteristics of the compound, observed crystallites in the hazy fuid, and concluded that this was an intermediate phase (or “mesophase”—from Ancient Greek, Îo (mésos) meaning “middle”) between the liquid and solid phases. This transitional phase exhibited birefringence while simulta- neously having a liquid-like fow.[5] Such intermediate (liquid crystal) phases can also be obtained by mixing substances like sodium and potassium salts of higher fatty acids to suitable solvents.[1] At present, liquid crystals have emerged as beautiful, mysterious, and soft condensed materials. Since the topic of liquid crystal is very interesting and it encapsulates physics, chemistry, and, in some aspect, also biology, it constitutes a very suitable content for an interdisciplinary integration of the natural science studies.[6–12] Depending upon the nature of the building blocks of molecules and upon external parameters (temperature, solvents etc.), a wide variety of phenomena and transitions among liquid crystals can be observed. To design a liquid crystal, one must use elongated objects. Presently, at least three different ways are known to achieve this: with small organic molecules; with long helical rods that either occur in nature or can be made artifcially; and with more complex units that are really associ- ated structures of molecules and ions.Accordingly liquid crystals are classifed into various types.[13] 1.2 LIQUID CRYSTAL CLASSIFICATION Liquid crystalline phases can be obtained either by heating and/or cooling the substances or by treat- ing the substances with water or polar solvents (aqueous medium). Depending on the way mesomor- phic phases are observed, liquid crystal materials are classifed as thermotropic or lyotropic. Further subgroups of liquid crystals are made depending on the molecular architecture of constituent entities. For instance, the molecules in the mesophases can be rod-like (or calamitic), disc-like (or dis- cotic), amphiphilic, nonamphiphilic, polymeric, etc. There is no need of a solvent in case of ther- motropic liquid crystalline substances. The concentration of the solvents, on the other hand, has an impact on the behavior of the liquid crystals and aggregation in lyotropic liquid crystals. 1.3 THERMOTROPIC LCs The order and orientation of molecular constituents in thermotropic mesophases can be used to categorize them. Broadly, thermotropic LCs are classifed as nematic and smectic liquid crystals. Cholesterics are treated as a special class of nematic liquid crystals.[14] Salient features of liquid crystals are very briefy described here. 1.3.1 Nematic Lcs The nematic phase is the most straightforward mesophase that has ever been observed; there is no short- range positional order but rather long-range orientational order between mesogens. Mesogens are ran- domly dispersed in space, yet they can freely translate and rotate along the director feld (Figure 1.2a). “Nematic” is derived from the Ancient Greek word vεμα (“nema”) meaning thread. Since thread-like molecular structures are seen under a microscope, they are referred to as nematic structures.[14] 1.3.2 choLesteric Lcs The cholesteric phase is identical to the nematic phase, with the exception that the mesogens change their orientation in a helical direction with respect to the director feld. In the cholesteric phase, the director feld reverses course and faces the helix in the other direction. Each layer of the helix that the
- 28. 3 DFT-Based Studies on Aspects of Liquid Crystals molecules form, which is nonsuperimposable, gives rise to the chirality. This is why cholesteric LCs are mostly referred to as chiral nematics. The gap between two mesogenic layers that have rotated 180° to the director feld is known as the half of the pitch within the cholesteric mesophase (Figure 1.2b). Further, cholesteric LCs exhibit emission of blue-violet radiations with decreasing temperature from the isotropic phase and hence give rise to a new class of LCs, commonly known as blue phase LCs.[15–17] 1.3.3 Discotic Lcs Numerous compounds made up of molecules with a disc shape have been shown in recent investiga- tions to have stable thermotropic liquid crystalline phases. The name “discotic liquid crystals” is now used to describe them. Most of them can be divided structurally into two groups: columnar and discotic FIGURE 1.2 Different subphase alignments of molecular confgurations: (a) nematic, (b) cholesteric, (c) discotic nematic, (d) discotic columnar phase, (e) smectic A, and (f) smectic C.
- 29. 4 Computational Studies FIGURE 1.3 General classifcation of thermotropic liquid crystals. nematic (Figures 1.2c and 1.2d). In its most basic form, the columnar phase is an orientationally ordered arrangementofdiscswithoutanylong-rangetranslationalorder,whilethenematicphaseexhibitsliquid- like disorder in the third dimension and long-range translational periodicity in the second. 1.3.4 smectic Lcs The word “smectic” is derived from the Ancient Greek word σμεκτoσ (“smektos”) meaning soap- like). This phase was frst identifed in liquid crystals made up of amphiphilic molecules. The term “smectic” is now used to describe liquid crystals where the molecules are organized in layers in addition to having an orientational order. The organized layers’ ability to slide past one another adds to the liquid nature of the mesomorphic phase. Numerous smectic stages have been discovered, and each of them varies in the position and orientation of the mesogens. Smectics are further des- ignated as SmA, SmB, SmC, etc. To differentiate between the smectic phases, we may look at the molecular orientation inside the layers (Figures 1.2e and 1.2f). The smectic A phase has molecules aligned along a director feld (n) and parallel to the layer normal, whereas the smectic C phase has molecules tilted at an angle away from the layer normal. Figure 1.3 shows a general classifcation of the various polymorphs of thermotropic liquid crystals.[2, 18] Substances that display smectic LCs are occasionally referred to as two-dimensional liquids.[10, 19] In addition to these categories, ferroelectric and antiferroelectric liquid crystals, as well as many other mesogenic substances, constitute separate classes because of their potential applications and future prospects.[11, 12] 1.4 LYOTROPIC LCs A lyotropic liquid crystal, on the other hand, is created when amphiphilic molecules melt in a certain type of solvents under proper pressure, temperature, and concentration conditions. By adjusting the solvent concentration, one can control the lyotropic liquid crystal combination. According to the concentration of the amphiphilic species, lyotropic liquid crystals (LLCs), which are self-assembled surfactant-solvent systems, can form a variety of mesophases, including micelles, micellar cubic, bicontinuous cubic, hexagonal, lamellar structures, and cell membrane bilayer (Figure 1.4).[6, 20, 21] Further, liquid crystalline properties in polymers, biopolymers (like protein, nucleic acids, blood cells, viruses, etc.) and other bioactive substances are well established, and they constitute another class of liquid crystals and help to mediate many living processes and biomolecular recognitions.[7, 8, 21]
- 30. 5 DFT-Based Studies on Aspects of Liquid Crystals FIGURE 1.4 Representation of molecular form and the architecture of different types of lyotropic liquid crystal phases. Theorderparameteriscrucialfordistinguishingbetweendifferentliquidcrystalphases.Figure1.5 shows the order parameter (S) and an nOCB LC molecule exhibiting different phases. Molecular orientation research is one of the most important and inescapable concerns since the degree of order determines the anisotropy of the physical characteristics of liquid crystal substances.[1, 22] Over the past few decades, mesogens or liquid crystals (LCs) have attracted a lot of scientifc interest in the feld of soft condensed matter due to their distinctive anisotropic properties, fuidity, and wide range of applications, including spatial light modulators, sensors, optical antennas, fat panel displays, and beam steering devices.[6, 23–38] The length of the aliphatic chain is one of the key molecular structure factors that affects mesomorphic behavior. Since the beginning of the LC investigation, its variation has been the simplest molecular method of regulating the capacity of mesogenic materials to self-organize. Comparing different properties (electrical, optical, and meso- morphic) of the members in a homologous series is a well established tool for gathering information on the relationship between structure and properties. Beginners in the liquid crystalline feld can easily see the strong odd-even effect dependent on the length of the terminal chain or chains, etc. The spontaneous molecular ordering that is a characteristic of liquid crystalline phases has long been used in many technical applications, such as electro-optic displays. Since the beginning of display device technology, cyanobiphenyl liquid crystals have been used extensively due to their mesomorphic behavior near the room temperature.[2, 29] In view of these facts, this chapter presents the thermodynamic, electronic, optical, and spectro- scopic aspects of the members of nCB and nOCB LC homologous series that have been investigated using the DFT method.
- 31. 6 Computational Studies FIGURE 1.5 Order parameter (S) and dependence of order parameter on director angle (θ) defning different phases of LC material. 1.5 COMPUTATIONAL METHOD The density functional theory (DFT) based B3LYP/6–31G(d,p) and B3LYP/6–311+G(d,p) schemes developed in the GAUSSIAN 16W program[39] were employed as the computational tool in this study. The total electronic energy of a molecular system[40] is expressed as: EDFT ˜ En ° ˛ ˙ ˝ Ee ° ˛ ˙ ˝ ECR ° ˛ ˙ ˝ EX ° ˛ ˙ ˝ EC ° ˛ ˙ (1.1) where E stands for the energy functional and the subscripts n, e, CR, X, and C, respectively, refer to the nuclear repulsion energy, one electron’s (kinetic + potential) energy, coulomb repulsion energy, exchange energy, and correlation energy. For EC = 0, this equation is reduced to Hartree–Fock (HF) form. The electron density function (ρ) and its gradient are represented as conventional integrals of DFT functionals in equation (1.1): E[ ] ˜ ° f ( ( ), ˜ r ˛˜ r ( ))dr (1.2) ˝ Equation (1.2) leads to integrals that must be assessed using numerical integration because they are not directly solvable. The one aspect of DFT methods that differs between EX [ρ] and EC [ρ] is the function f that is used. The hybrid functional B3LYP has shown to be a good trade-off between computing cost, cov- erage, and result correctness. It was initially developed to study circular dichroism and vibrational absorption.[41] Analyzing organic molecules in the gas phase with this method is increasingly wide- spread. The exchange correlation functional produced by this B3LYP method includes the param- eterized exchange term of A. D. Becke[42] and the correlation term developed by Y. Lee, W. Yang,
- 32. ˇ 7 DFT-Based Studies on Aspects of Liquid Crystals and R. G. Parr.[43] B3LYP is a hybrid functional with three parameters that includes a combination of Becke’s exchange term, HF exchange, and Lee–Yang and Parr’s correlation term. The fnal two elements of equation (1.1) are typically stated in B3LYP[44] as: Slater HF Becke local non˙local . ˝ ˙ 1 ˝ ˆ ° ˜ E ( ˜).E . E ˝ E ˝ ˆ ˛. E (1.3) X X X C C where the three parameters α, β, and γ are determined by ftting to a diverse set of molecules. A number of organic compounds have already adopted this widely used method.[45–50] There are many functionals. e.g. B3PW91,[51] ωB97XD,[52] LC-ωHPBE,[53] CAM-B3LYP,[54] M062X,[55] etc. have been used in recent years due to their quantum computational accuracy. Vibrational infrared frequencies are computed using harmonic approximation: 3N 3N ˛ 2 ˆ ° E E ˜ 1 ˙ ˘ q q (1.4) 2 ˙ ˘ i j i j ˇ i1 j1 ° ° q q ˝ o where o q ˜ m (q q ) (1.5) ° i i i i Here mi is the mass of atom i, and qi represents the x-, y-, and z-coordinates for each of the N atoms in a molecule. Once vibrational frequencies are obtained, vibrational contribution (which is the most significant) of thermodynamic parameters are computed using following relations: 3N˛6 ˝hc hc ˇ H U ˜ ˜ R i ° k T i (1.6) ˆ hc i˜1 2k k e ( ˛1) ˙ B B i B ˘ 3N°6 ˆ ˛ hc i °hc i B S R ° ln(1° e k T ) (1.7) ˜ ˙ hc k T ˘ B ˇ i˜1 k T(e °1) ˝ B i where H, U, and S denote enthalpy, internal energy, and entropy, respectively. Other parameters are calculated using standard thermodynamic relations. Numerical differentiation can be used to determine the dipole moment (μ), mean polariz- ability (α), and anisotropy in polarizability (Δα) with an electric feld magnitude of 0.001 au accordingly as: 2 ˜ ° ˜ ( x 2 ˛ ˜y 1 2 2 ˛ ˜ ) z (1.8) ˜ ° ˜xx ˛ ˜yy 3 ˛ ˜zz (1.9) 1 ˜° ˛ ˆ(°xx ˘ ˇ ˘ 2 ˝ ° ) yy ˙ (°yy 2 ˝ ° ) zz 2 ˙ ° ( zz 2 ˝ ° ) xx 2 (1.10) ˜ ° ˝ ˙ ˜ ( xxx ˛˜xyy 2 ˛˜ ) xzz ˛ ˜ ( yyy ˛˜xxy 2 ˛˜ ) yzz ˛ ˜ ( zzz ˛˜xxz 1 2 / 2 ˛˜ ) ˆ yyz ˇ (1.11)
- 33. 8 Computational Studies Molar refractivity (MR) can be determined by the Lorenz-Lorentz formula: 2 °1 MW n MR ˜ ˜ 1 333 N (1.12) . 2 ˝ ˆ ˙n ˛ 2 ˇ ˘ The molar volume (MW/ρ), the Avogadro number (N), the refractive index (n), and the polarizability of the molecular system (α) are all present in this equation. For α, 1 au = 0.1482 × 10−24 esu. Further, Koopmans theorem has been used to determine the electronic and global properties like ionization potential (I), electron affnity (A), electronegativity (χ), global hardness (η), and softness (S).[56] According to Parr et al.,[57] the relationship between chemical potential (φ) and electronegativity (χ) is provided by the relation: ˆ ˙E ˜ ˝ ˝ ˛ (1.13) ˘ ˇ ˙N ° r where the terms denoted by v(r) and μ are the exterior and electronic chemical potentials, respec- tively. The values of the electron affnity (A) and ionization potential (I) are given as:[58] A ˜°E and I ˜ ° E (1.14) LUMO HOMO The I and A values can be used to calculate the molecule’s global hardness (η)[59] and electronegativ- ity (χ)[65]: I A ˝ ˙ I A ˜ ˛ and ° ˛ (1.15) 2 2 The electrophilicity index (ω), introduced by Parr et al.,[60] and chemical softness (S)[61] are given as: 1 ˝2 S ˜ and ˛ ˜ (1.16) ° 2° The following equations can be used to calculate the molecules’ electron donating capability (ω−) and electron accepting capability (ω+): ° ˜ ˝ 2 (3 ˛ ) I A ( 16 ° ) I A and ˛ ˜ ˝ 2 (I ˛ 3 ) A ( 16 ° ) I A (1.17) 1.6 RESULTS AND DISCUSSION 1.6.1 4-aLkyL-4ʹ-cyaNobipheNyL series It has been observed that there is an odd-even effect in the transition temperature for the nCB LC homologous series in the nematic region. Additionally, the odd-even effect was exclusively explored for the nematic zone.[29] Previously, the odd-even effect was not observed in smectic liquid crystals, and the transition temperature is almost linearly related to the number of carbon atoms in the alkyl chain. In this section, we discuss the electro-optical and electronic proper- ties of the nCB series, which were studied theoretically for nematic and smectic phases of the homologues.[62–65]
- 34. 9 DFT-Based Studies on Aspects of Liquid Crystals 1.6.2 optimizeD parameter aNaLysis Figure 1.6 depicts the equilibrium geometries of the nCB liquid crystal series. The frst methylene group’s carbon (-CH2) along the extended molecular axis lengthens the molecule but has no effect on its width, as in the case of 1CB, while the second methylene group’s carbon increases the length and simultaneously widens the molecule, as in the case of 2CB. This applies to nCB molecules having an alkyl chain at the terminal end. As a result, the carbon in the second methylene group, that is the carbon in the odd position, increases the length but not by the same amount as the carbon of the frst methylene group.[66] Depending on whether the terminal chain has an even or odd number of methyl(ene) groups, the dimensions of the nCB members change as the chain grows. This phe- nomenon, called the odd-even effect, was clearly seen in the case of the nCB series homologues.[29] 1.6.3 eLectroNic aND GLobaL parameter aNaLysis The trend of some electronic characteristics, including electron affnity (A), ionization potential (I), chemical hardness (η), and absolute-electronegativity (χ), has also been examined. These variables, often known as reactivity descriptors, describe how chemically reactive molecular systems are or how they interact with other species. Figure 1.7 displays how these parameters can vary with a homologous number of nCB series. In both nematic and smectic zones, it is evident that the ioniza- tion potential (Figure 1.7a) and global hardness (Figure 1.7d) vary with the number of carbon atoms and refect the phenomena of odd-even effect; i.e., these variables are affected by the n parity value. The molecule’s propensity to donate an electron or to become an electron donor and yield a cation is measured by the ionization potential. Chemical hardness gives a clear indication of how stable a molecule’s electronic state is; in general, odd-number carbon chain molecules are more stable than even-number ones. Chemical hardness and electronegativity are indicators of a molecular system’s stability and chemical reactivity.[67] The electron affnity of a molecule evaluates its propensity to absorb an electron, transform into an electron acceptor, and produce an anion, in contrast to ioniza- tion potential. Strong electron affnity exists for n = 2 and decreases with the number of carbon atoms in an alkyl chain in the nematic zone, but it increases with the number of carbon atoms in the smectic zone, as FIGURE 1.6 Optimized geometries of nCB liquid crystalline series calculated at the B3LYP/6–311++ G(d,p) level.
- 35. 10 Computational Studies FIGURE 1.7 Variation of (a) ionization potential, (b) electron affnity, (c) electronegativity, and (d) chemical hardness with regard to the number of carbon atoms in the alkyl chain of the nCB liquid crystalline series. shown in Figure 1.7b. This is the key characteristic that explains the liquid crystalline behavior of the nCB series. In the same way as that of the chemical hardness and ionization potential, the nCB’s electronegativity demonstrates that this parameter is quite high for n = 2 and that it goes down with the increase of the number of carbon atoms in the alkyl chain (Figure 1.7c). All of the estimated characteristics, with the exception of electron affnity, indicate that the odd-even effect in the nCB family members persists beyond the nematic range and spreads into the smectic region. Table 1.1 provides values for various global parameters. 1.6.4 eLectro-opticaL parameter aNaLysis We have examined a number of electro-optical parameters, including dipole moment, mean polar- izability, anisotropy in polarizability, and hyperpolarizability, to observe the odd-even effect in nCB liquid crystalline series. Table 1.2 contains the values of these parameters. An indication of the shape and charge distribution of a molecule can be found in its dipole moment. There is an odd-even effect in the dipole moment depicted in Figure 1.8a, which may be seen as the dipole moment of an even-number carbon atom molecule and which is greater than the dipole moment of an odd-number carbon atom of the methylene group. Moreover, as previously described[63] this variance extends into the smectic zone in addition to the nematic region. Clearly, it has to do with the molecular design and charge distribution, putting aside the intermolecular interactions that exist in bulk liquid
- 36. 11 DFT-Based Studies on Aspects of Liquid Crystals TABLE 1.1 Electronic and Global Reactivity Descriptor Parameters of the nCB (n = 1 to 12) Series Homologous No. (n) I (eV) A (eV) χ(eV) η(eV) 1 6.677 1.986 4.331 2.345 2 6.677 1.987 4.332 2.344 3 6.661 1.982 4.321 2.339 4 6.644 1.974 4.309 2.334 5 6.647 1.971 4.309 2.338 6 6.642 1.970 4.306 2.336 7 6.642 1.968 4.305 2.336 8 6.640 1.968 4.304 2.335 9 6.639 1.967 4.303 2.335 10 6.633 1.971 4.302 2.331 11 6.636 1.971 4.304 2.332 12 6.635 1.971 4.303 2.331 TABLE 1.2 Electro-Optical Parameters of the nCB (n = 1 to 12) Series Anisotropy in Dipole Moment Mean Polarizability Polarizability Hyperpolarizability Homologous No. (n) (Debye) (α) (Bohr3) (∆α) (Bohr3) (β) (Bohr5) 1 6.110 183.170 181.402 1511.922 2 6.131 191.823 195.274 1364.240 3 6.180 204.395 209.518 1699.821 4 6.305 211.953 222.328 1918.433 5 6.283 222.531 235.840 1926.032 6 6.376 227.689 248.500 2042.674 7 6.338 237.322 261.775 2057.229 8 6.402 238.314 274.594 2104.940 9 6.364 246.241 287.589 2112.702 10 6.426 248.307 300.581 2169.996 11 6.378 255.610 313.439 2139.265 12 6.436 256.127 326.261 2183.852 crystals. The homologous number of the alkyl chain is directly related to the anisotropy in polariz- ability, as seen in Figure 1.8c. It is widely acknowledged that torsional angle has the greater impact on the anisotropy in polarizability values[68] The torsional angle alters as the carbon atoms are added to the alkyl chain; which, in turn, also increases the anisotropy in polarizability. For even and odd numbers of carbon atoms, the mean polarizability and hyperpolarizability values are somewhat dif- ferent (Figures 1.8b and 1.8d). The odd-even effect has been observed for n ≥ 7 in the case of mean polarizability, and below this, polarizability grows essentially linearly. In addition to the negligible contribution from acoustic phonons, it is typically considered that the frst-order hyperpolarizability of organic molecules is entirely of pure electrical origin.[69] Although the hyperpolarizability values do indeed exhibit an odd-even effect, this impact becomes less pronounced as the number of carbon atoms increases. It is anticipated that changes to the dihedral angle or deviations from planarity will cause a decrease in hyperpolarizability. It seems pertinent to note that the planarity require- ment must be met for a molecule to be nonlinearly optically active. Thus the polarizabilities and
- 37. 12 Computational Studies FIGURE 1.8 Variations in the (a) dipole moment, (b) mean polarizability, (c) anisotropic polarizability, and (d) hyperpolarizability of the homologues of the nCB liquid crystalline series with regard to the number of carbon atoms in the alkyl chain. hyperpolarizabilities control the system’s nonlinear optical (NLO) properties in addition to the cross sections of various scattering and collision processes and the strength of molecular interactions.[70] 1.7 4-N-ALKOXY-4ʹ-CYANOBIPHENYL LIQUID CRYSTAL SERIES This section covers the theoretically explored Raman spectra, UV-vis spectra, electro-optical, global (electronic), and thermal features of the nOCB LC series.[71] The homologues of 4-n-alkoxy-4ʹ- cynobiphenyl series (nOCB; n = 1 to 12) are optimized by the DFT/B3LYP method and are shown in Figure 1.9. The behavior of nOCB LC molecules is nematic for n = 1 to 7 and smectic up to 12. The main difference between the homologous nOCB and nCB series is that the nOCB molecules have an oxygen atom between the biphenyl ring and the alkyl unit. Hence it becomes interesting to see how the extra oxygen atom affects the quantities of the nOCB LC series. 1.7.1 thermaL parameter VariatioN with homoLoGous Number Vibrational frequency calculations at the B3LYP/6–31G(d,p) level have been done for procuring thermal parameters after the optimization operations. Figure 1.10a shows the correlation between the number of carbon atoms present in an alkoxy chain and thermal properties such as Gibbs free
- 38. 13 DFT-Based Studies on Aspects of Liquid Crystals FIGURE 1.9 Equilibrium geometries of nOCB liquid crystal homologous series computed at the B3LYP/6– 31G(d,p) level. FIGURE 1.10 Variation of (a) thermal energy (ET), zero point energy (ZPE), Gibbs free energy (G), and enthalpy (H); (b) entropy with respect to homologous number for nOCB LC series. energy, zero-point energy, thermal energy, and enthalpy. Figure 1.10b depicts the variance in entropy. The addition of carbon atoms in the alkoxy chain causes an increase in all the thermal parameters. Figure 1.10a vividly refects that thermal energy (ET) and enthalpy (H) are in close proximity for each individual homologue of the nOCB (Table 1.3). Further, as evident from Figure 1.10b, with an increase in the number of carbon atoms in the alkoxy chain, entropy of the individual homologue increases, leading to the inference that disorder assumes a higher value for higher homologues. This means the higher the homologue is, greater will be the disorder in the molecular system. 1.7.2 eLectroNic aND GLobaL parameter VariatioN with homoLoGous Number Figures 1.11a–c depict the energy variation of the HOMO (EHOMO) and LUMO (ELUMO), as well as the associated energy gap between the HOMO-LUMO (ΔE) with the homologous number for nOCB (n =1 to 12) LC series. Table 1.4 contains the values of these quantities. With increasing n,
- 39. 14 Computational Studies TABLE 1.3 Thermal Parameters of the nOCB (n = 1 to 12) Series Thermal Gibbs Free Homologous ZPE Energy (Ethermal) Enthalpy Energy (G) Entropy No. (n) (kcal/mol) (kcal/mol) (H) (kcal/mol) (kcal/mol) (cal/mol-K) 1 133.588 141.951 142.544 108.030 115.761 2 151.337 160.589 161.181 124.414 123.318 3 169.228 179.352 179.945 140.961 130.754 4 187.133 198.113 198.704 157.532 138.093 5 205.041 216.874 217.466 174.081 145.515 6 222.926 235.618 236.211 190.641 152.842 7 240.818 254.371 254.963 207.111 160.499 8 258.692 273.106 273.699 223.644 167.886 9 276.542 291.828 292.421 239.946 176.002 10 294.408 310.558 311.151 256.452 183.458 11 312.241 329.271 329.864 271.927 194.320 12 330.254 348.017 348.609 289.496 198.266 FIGURE 1.11 (a) HOMO, (b) LUMO, and (c) orbital energy gap (ΔE) variation with the homologous number for nOCB LC series.
- 40. 15 DFT-Based Studies on Aspects of Liquid Crystals TABLE 1.4 Orbital Energy Gap (∆E), HOMO Energy, and LUMO Energy of the nOCB (n = 1 to 12) Series Homologous No. (n) EHOMO (eV) ELUMO (eV) ∆E (eV) 1 −5.987 −1.529 4.458 2 −5.953 −1.511 4.442 3 −5.942 −1.506 4.436 4 −5.935 −1.503 4432 5 −5.932 −1.501 4.431 6 −5.930 −1.499 4.431 7 −5.930 −1.498 4432 8 −5.929 −1.497 4.432 9 −5.928 −1.497 4.431 10 −5.928 −1.497 4.431 11 −5.927 −1.497 4.430 12 −5.926 −1.496 4.430 the values of HOMO, LUMO, and ΔE are poorly changed. As the homologous number increases, all these quantities descend gradually (Table 1.4). These molecules occupy the region of ultraviolet transparency, according to the energy gaps (ΔE) of the nOCB series. The variation of global parameters for the nOCB (n = 1 to 12) series with homologous numbers is also shown in Figure 1.12. Their respective values are given in Table 1.5. These variables are known as reactivity descriptors because they describe the chemical reactivity of molecular systems. These global descriptors are followed by orbital energy gaps (ΔE), and they decrease as the homologous number increases. According to global hardness variation, lower homologues are likely to be more stable than higher ones. Similarly, the variation in electron affnities suggests that lower homologues can readily take electrons to transform themselves into electron acceptors in order to generate anions. 1.7.3 eLectro-opticaL parameter VariatioN with homoLoGous Number Figure 1.13 shows the total energy, dipole moment, mean polarizability, anisotropy in polarizability, and molar refractivity. Table 1.6 provides the values of electro-optical parameters. The addition of carbon atoms in the alkoxy chain linearly increases the total molecular energy of the nOCB homo- logues (Figure 1.13a). Thus, it can be inferred that the confgurational stability of the homologues of nOCB (n = 1 to 12) refects ascending values with the increase of alkoxy chain length. That is, higher homologues are more stable as compared to their lower homologues; thus 12OCB poses the most stable confguration among all the chosen molecules. Similarly, as the homologous number rises, the dipole moment also increases (Figure 1.13b). The occurrence of the odd-even effect in the dipole moment was explored by similar investigations on nCB series[63] Figure 1.13c illustrates the dependence of mean polarizability and anisotropic polarizability on the homologous number. Hence, anisotropic polarizability is largely infuenced by the torsional angles.[68] Due to the addition of carbon atoms in the alkoxy chain, the torsion angle of the homologues changes, leading to an increment in the value of the anisotropy in polarizability. A linear relation- ship for the homologous number is also indicated by the molar refractivity plot, which is depicted in Figure 1.13d. Figures 1.14a, and 1.14b, respectively, demonstrate the comparison between esti- mated mean polarizability and anisotropy in polarizability values of nOCB (n = 9 to 12) molecules with experimental data.[72] In Figure 1.13c, the components of α and Δα are reported in atomic units (Bohr3), while the same (calculated values) are converted into cm3 (1 Bohr3 = 0.1482 × 10−24 cm3) in Figures 1.14a and 1.14b.
- 41. 16 Computational Studies FIGURE 1.12 Dependence of parameters like (a) ionization potential, (b) electron affnity, (c) electronegativ- ity, (d) global hardness, (e) chemical potential, (f) electrophilicity index, (g) electron donating capability, and (h) electron accepting capability upon the homologous number for nOCB LC series.
- 42. 17 DFT-Based Studies on Aspects of Liquid Crystals TABLE 1.5 Electronic and Global Parameters for the Homologues of nOCB (n = 1 to 12) LC Series Homologous No. (n) I (eV) A (eV) χ(eV) η(eV) S(eV) φ(eV) ω(eV) ω–(eV) ω+(eV) 1 5.987 1.529 3.758 2.229 0.448 −3.758 3.168 5.325 1.567 2 5.953 1.511 3.732 2.221 0.450 −3.732 3.135 5.279 1.547 3 5.942 1.506 3.724 2.218 0.451 −3.724 3.126 5.265 1.541 4 5.935 1.503 3.719 2.216 0.451 −3.719 3.121 5.257 1.538 5 5.932 1.501 3.716 2.215 0.451 −3.716 3.117 5.252 1.536 6 5.930 1.499 3.714 2.215 0.451 −3.714 3.114 5.248 1.533 7 5.930 1.498 3.714 2.216 0.451 −3.714 3.112 5.246 1.532 8 5.929 1.497 3.713 2.216 0.451 −3.713 3.111 5.244 1.531 9 5.928 1.497 3.712 2.215 0.451 −3.712 3.110 5.264 1.531 10 5.928 1.497 3.712 2.215 0.451 −3.712 3.110 5.264 1.531 11 5.927 1.497 3.712 2.215 0.451 −3.712 3.110 5.243 1.531 12 5.926 1.496 3.711 2.215 0.451 −3.711 3.109 5.241 1.530 FIGURE 1.13 Variation of electro-optical parameters: (a) total energy, (b) dipole moment, (c) polarizability (mean and anisotropic), and (d) molar refractivity with the homologous number of nOCB LC series.
- 43. 18 Computational Studies TABLE 1.6 Electro-Optical Parameters of the nOCB (n = 1 to 12) Series Mean Anisotropy in Homologous Total Energy Dipole Moment Polarizability (α) Polarizability Molar Refractivity No. (n) (eV) (Debye) (Bohr3) (∆σ) (Bohr3) (MR) in e.s.u. 1 −18234.068 6.496 167.786 208.671 62.677 2 −19304.099 6.763 181.447 221.755 67.806 3 −20373.956 6.903 193.753 230.265 72.377 4 −21443.810 6.981 205.977 239.894 76.944 5 −22513.669 7.072 217.811 246.538 81.364 6 −23583.527 7.072 229.583 254.825 85.762 7 −24653.384 7.103 241.177 260.764 90.093 8 −25723.242 7.117 252.786 268.681 94.429 9 −26793.098 7.138 264.316 274.711 98.737 10 −27862.956 7.143 275.836 282.426 103.040 11 −28932.812 7.159 287.332 288.626 107.334 12 −30002.611 7.194 298.202 295.691 111.395 FIGURE 1.14 (a) Mean polarizability (α) and (b) molecular polarizability anisotropy (Δα) of the nOCB (n = 9 to 12) as computed by B3LYP/6–31G(d,p) method.
- 44. 19 DFT-Based Studies on Aspects of Liquid Crystals 1.7.4 ramaN aND absorptioN spectra aNaLysis The DFT/B3LYP/6–31G(d,p) approach has been used to examine the Raman spectra of the mem- bers of the nOCB LC series. Figure 1.15 displays the Raman spectra of the 8OCB LC molecule in the 400 cm−1 to 3500 cm−1 regions. The 8OCB, 9OCB, 10OCB, 11OCB, and 12OCB molecules all have six distinct strong vibrational peaks. Table 1.7 compares the calculated Raman frequencies of relevant vibrational modes for the 8OCB molecule and shows that they are in good agreement with the experimental data.[73, 74] At the wave number of 3111.19 cm−1 and 3037.40 cm−1, peak one and peak two are connected to asymmetric and symmetric CH3 mode stretching, respectively. Peak three is due to CN stretching, which is seen at 2344.11 cm−1, and peak four is caused by C-C stretching of the biphenyl ring, which is seen at 1671.22 cm−1. The ffth peak, at a wavelength of 1316.89 cm−1, is a band of perpendicular deformations that combines symmetrical and asymmetrical deformations of FIGURE 1.15 Raman spectrum of the 8OCB LC compound. The letters in Table 1.7 refer to distinct vibrations. TABLE 1.7 Raman Spectrum of 8OCB LC Molecule Raman Frequency (cm−1) Calculated by B3YP/6–31G(d,p) Experimental[69, 70] Peaks Assignment of the Raman Peaks Shown in Figure 1.2 3111.19 3037.40 2344.11 1671.22 1316.89 2962∼2988 2878 2234 1522 1284 a b c d e Asymmetric CH stretch of CH3 Symmetric CH stretch of CH3 CN stretching Ring C-C stretching Combinational band of 1206.49 1185 f symmetric and asymmetric perpendicular deformations of CH2 groups in the aliphatic chain In-plane deformation of CH bonds of the biphenyl moiety
- 45. 20 Computational Studies FIGURE 1.16 UV-vis spectra of nOCB (n = 1, 4, 8, and 12) liquid crystal molecules computed by the ZINDO technique. TABLE 1.8 Oscillator Strength, Excitation Energy and Wavelength of nOCB LC Molecules as Computed by ZINDO Method Molecule Excited State Oscillator Strength (f) Excitation Energy (eV) λmax (nm) 1OCB 1 0.8324 4.138 299.61 2 0.0233 4.302 288.23 3 0.0015 4.355 284.68 2OCB 1 0.8396 4.131 300.13 2 0.0238 4.298 288.41 3 0.7965 4.031 307.61 3OCB 1 0.8444 4.126 300.45 2 0.0239 4.298 288.48 3 0.0014 4.352 284.89 4OCB 1 0.8470 4.126 300.52 2 0.0239 4.297 288.49 3 0.0013 4.352 284.90 (Continued)
- 46. DFT-Based Studies on Aspects of Liquid Crystals 21 TABLE 1.8 (Continued) Molecule Excited State Oscillator Strength (f) Excitation Energy (eV) λmax (nm) 5OCB 1 0.8485 4.126 300.52 2 0.0239 4.297 288.50 3 0.0014 4.352 284.90 6OCB 1 0.8496 4.126 300.50 2 0.0239 4.297 288.50 3 0.0014 4.352 284.89 7OCB 1 0.8501 4.127 300.44 2 0.0240 4.298 288.49 3 0.0014 4.352 284.87 8OCB 1 0.8508 4.127 300.45 2 0.0240 4.298 288.49 3 0.0014 4.352 284.87 9OCB 1 0.8514 4.126 300.47 2 0.0240 4.298 288.50 3 0.0014 4.352 284.88 10OCB 1 0.8519 4.126 300.50 2 0.0240 4.297 288.50 3 0.0014 4.352 284.88 11OCB 1 0.8526 4.125 300.55 2 0.0240 4.297 288.51 3 0.0013 4.352 284.90 12OCB 1 0.8489 4.115 301.28 2 0.0250 4.288 289.23 3 0.0009 4.349 285.04 CH2 groups in the aliphatic chain, while the last one, at a wavelength of 1206.49 cm−1, is connected to an in-plane deformation of CH bonds of the biphenyl moiety. Further, it is important to mention that all the fve homologues (n = 8 to 12) of nOCB LC series furnish almost identical spectra and hence similar values of Raman frequencies. The ZINDO technique was used to study electronic absorption spectra. The similar nature of absorption spectra is rendered by the homologues of nOCB (n = 1 to 12). The UV-vis spectra of only four homologues of the nOCB (n = 1, 4, 8, and 12) series have been shown in Figure 1.16. Table 1.8 provides a list of the excited states, oscillator strength (f), excitation energy (E), and excitation wavelength (λmax). At 299.61 nm (4.138 eV) with oscillator strength of 0.8324, 1OCB experiences one strong electronic transition from HOMO to LUMO (MO contribution 86.5%). Corresponding to 288.23 nm (4.302 eV) and 284.68 nm (4.355 eV), two more electronic transitions take place, with oscillator strengths of 0.0233 and 0.0015, respectively. At a wavelength of 300.52 nm, the 4OCB molecule exhibits a strong absorption band. With 86.5% of the MO contribution, the transition from HOMO to LUMO occurs at this wavelength. The oscillator strength and the related excitation energy correspond to 4.126 eV and 0.8470, respectively. Moreover, the strong electronic transitions in the 8OCB and 12OCB molecules occur at 300.45 nm (HOMO to LUMO with MO contribution of 86.4%) and at 300.55 nm (HOMO to LUMO with MO contribution of 86.2%), respectively. The experimental values of molar absorptivity (ε) and wavelength of maximum absorption (λmax) for the 8OCB LC molecule are reported to be 20.1 × 103 M−1 cm−1and 297 nm, respectively,[75] whereas in this study, the molar absorptivity and maximum wavelength for the 8OCB molecule are found to be 35.3 × 103 M−1 cm−1 and 300.45 nm, respectively.
- 47. 22 Computational Studies 1.8 CONCLUSIONS AND VIEWPOINTS This chapter discussed various aspects of thermodynamic, electronic, optical, and spectroscopic aspects of alkyl and alkoxy cyanobiphenyls. Both the homologous series possess odd-even effect. This investigation demonstrated the presence of phenomena of the odd-even effect in the case of the nCB series only, which is in conformity with experimental observations. The plots of the ther- mal, electronic, and electro-optical properties for the nOCB series elucidate a linear dependence on homologous number. While ascending the homologous series, there exists a linear increase in the values of the dipole moment, mean polarizability, anisotropy in polarizability, and molar refractivity. In both LC series, the global parameters indicate that lower homologues are more prone to anionic behavior. The higher homologues appear to be more disordered. For further research and applica- tions of these homologues of the nCB and nOCB liquid crystalline series in fabrications of NLO materials, electro-optical parameters can offer improved insights and auxiliary information. 1.8.1 ackNowLeDGmeNt Dipendra Sharma is thankful to UGC, New Delhi, India, for providing the start-up grant. 1.8.2 coNfLict of iNterests The authors declare no confict of interest. REFERENCES [1] de Gennes P-G, Prost J. The Physics of Liquid Crystals [Internet] (2nd ed.). Oxford Sci. Publ. New York: Oxford University Press, 1995 [cited 2023 Apr 1]. Available from: https://global.oup.com/academic/ product/the-physics-of-liquid-crystals-9780198517856. [2] Chandrasekhar S. Liquid Crystals [Internet] (2nd ed.). Cambridge University Press, 1992 [cited 2023 Apr 1]. Available from: www.cambridge.org/core/books/liquid-crystals/7972CBEB90A0F90F0D23C9 B83B6A46D2. [3] Priestley EB, Wojtowicz PJ, Sheng P, eds. Introduction to Liquid Crystals. New York, NY: Springer, 1975. [4] Reinitzer F. Beiträge zur Kenntniss des cholesterins. Monatshefte für Chemie [Internet]. 1888 [cited 2023 Jun 6];9:421–441. Available from: https://link.springer.com/article/10.1007/BF01516710. [5] Lehmann O. Über fiessende krystalle. Zeitschrift für Phys Chemie [Internet]. 1889 [cited 2023 Jun 6];4U:462–472. Available from: www.degruyter.com/document/doi/10.1515/zpch-1889-0434/html? lang=en. [6] Khoo I-C. Liquid Crystals. New Jersey, NJ: John Wiley Sons, Inc., 2022. [7] Petrov AG. The Lyotropic State of Matter: Molecular Physics and Living Matter Physics. Boca Raton, FL: CRC Press, 1999. [8] Neto AMF, Salinas SRA, Press OU. Physics of Lyotropic Liquid Crystals: Phase Transitions and Structural Properties. Oxford: Oxford University Press, 2005. [9] Collings PJ, Patel SJ. Handbook of Liquid Crystal Research [Internet]. Patel, SJ. and Collings PJ, (eds.). New York: Oxford University Press, 2006 [cited 2023 Jun 6]. Available from: www.tandfonline.com/ doi/abs/10.1080/10587250008024819. [10] Jakli A, Saupe A. One- and Two-Dimensional Fluids : Properties of Smectic, Lamellar and Columnar Liquid Crystals [Internet]. London: CRC Press; 2006 [cited 2023 Jun 6]. Available from: www.routledge. com/One-and-Two-Dimensional-Fluids-Properties-of-Smectic-Lamellar-and-Columnar/Jakli-Saupe/p/ book/9780367390761. [11] Bahadur B. Liquid Crystals—Applications and Uses. Bahadur B, (ed.). Singapore: World Scientifc, 1990. [12] Lagerwall S. Ferroelectric and Antiferroelectric Liquid Crystals, Weinheim: Wiely-VCH, 1999. [13] Singh S. Liquid Crystals. Singapore: World Scientifc, 2002. [14] Vertogen G, de Jeu, WH. Thermotropic Liquid Crystals, Fundamentals [Internet]. Heidelberg: Springer, 1988 [cited 2023 Apr 1]. Available from: http://link.springer.com/10.1007/978-3-642-83133-1.
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- 51. 26 Computational Studies [79] Tiwari A, Chauhan MS, Sharma D. Fluorination of 2,5-diphenyl-1,3,4-oxadiazole enhances the electron transport properties for OLED devices: A DFT analysis. https://doi.org/101080/0141159420222129051 [Internet]. 2022 [cited 2023 Jun 26];95:888–900. Available from: www.tandfonline.com/doi/abs/10.108 0/01411594.2022.2129051. [80] Pandey AK, Kumar A, Srivastava AK, et al. Infuence of electric feld on the electro-optical and electronic properties of 4-n-alkoxy-4′-cyanobiphenyl liquid crystal series: An application of DFT. Pramana—J Phys [Internet]. 2023 [cited 2023 Jun 26];97:1–10. Available from: https://link.springer. com/article/10.1007/s12043-023-02570-9.
- 52. 2 Spectroscopic Signatures of Some Organic Compounds Theory Meets Experiment Abhishek Kumar, Ambrish Kumar Srivastava, Ratnesh Kumar, and Neeraj Misra 2.1 INTRODUCTION The biological importance of the derivatives of hexahydroacridine-1,8-diones, similar to the octahy- droacridine-1,8-diones cannot be disputed not only for their rich and wide-ranging chemistry but also for a number of other characteristics. Anti-infammatory and hypertensive,[1] potassium chan- nel opener,[2] and anti-microbial-like[3] properties have been reported in the literature. Depending upon the type and placement of a substituent on the acridine core, there are a number of activities against tumor,[4] parasites,[5] and bacteria.[6] It should be mentioned that the biological activities of the acridines are mainly due to the ability of the acridine moiety to intercalate between base pairs of double-stranded DNA through π–π interactions.[7] Acridine-1,8-dione dyes have been the focus of studies due to their special photophysical and photochemical properties. The structure of these dyes is similar to that of 1,4-dihydropyridine. An extensive quantum chemical study has been carried out on 9,10-bis(4-fuorophenyl)-3,3,6,6- tetramethyl-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione (FTHD) and 10-(4-fuorophenyl)-3,3, 6,6-tetramethyl-9-(3,4,5-trimethoxyphenyl)-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione (FTMPHD) with the main aim of exploring their geometrical, vibrational, and electronic properties. For the sake of a comparative study, theoretical work has also been done on 3,3,6,6-tetramethyl-9- (4-nitrophenyl)-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (TNHXD) and 9-(benzo[d][1,3] dioxol-5-yl)-3,3,6,6-tetramethyl-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (BDTHXD). To perform quantum chemical calculations and to calculate important properties, rigorous implementation of the DFT-based method has been carried out with a focus on those properties that are not easily obtain- able via experimental methods. These properties include molecular geometry, vibrational frequencies, dipole moments and higher-order moments, thermochemical properties, etc. In the standard literature, several forms of DFT are available whose applications depend on the nature of the molecular systems under investigation and characteristics to be explored. In numerous publications, it has been mentioned that,[8–10] DFT offers a better trade-off between computational cost and accuracy for medium-sized molecules, and hence it has been justifably implemented. A piece of inclusive information about the density functional theory and the methods based on it can be accessed from contemporary literature.[11] This chapter involves a comprehensive comparison of different properties of 9,10-bis (4-fluorophenyl)-3,3,6,6-tetramethyl-3,4,6,7,9,10-hexahydroacridine-1,8(2H,5H)-dione (FTHD) and 10-(4-fuorophenyl)-3,3,6,6-tetramethyl-9-(3,4,5-trimethoxyphenyl)-3,4,6,7,9,10- hexahydroacridine-1,8(2H,5H)-dione(FTMPHD)withthatof3,3,6,6-tetramethyl-9-(4-nitrophenyl)- 3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (TNHXD) and 9-(benzo[d][1,3]dioxol-5-yl)- 3,3,6,6-tetramethyl-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione (BDTHXD) as suggested by density functional theory. In this chapter, the geometrical and some spectroscopic features of these compounds are discussed. Theoretical molecular modeling is a powerful tool for studying the physical, chemical, and bio- logical properties of chemical compounds.[12, 13] Molecular modeling has different levels of theories DOI: 10.1201/9781003441328-2 27
- 53. 28 Computational Studies utilized for studying chemical compounds and reactions’ properties.[14, 15] One of the most accurate theoretical approaches is density function theory (DFT), which studies the properties of compounds and provides indications close to those of an experiment.[16, 17] Moreover, molecular structure can be studied and provided with signifcant information about compounds and their interactions by calcu- lating the infrared (IR) spectrum theoretically, which confrms the expressed value IR result.[18, 19] 2.2 TOOLS OF STUDY: COMPUTATIONAL DETAILS It has been observed that for a variety of systems of biological relevance, the combination of Becke’s three-parameterhybridexchangefunctional[20] withtheLee–Yang–Parrcorrelationfunctional[21] (B3LYP) functional is quite consistent. The B3LYP functional is a gradient-corrected hybrid functional and is immensely popular for studying a variety of systems of biological interest.[22–25] Apart from the popular functional, the standard split-valence basis set, combined with diffuse as well as polarization functions 6–311++G(d,p), has also been employed in the calculations. The computational work has been carried out by employing the Gaussian 09 suite of code[26] using different keywords for different types of jobs. The objective of geometry optimization is to fnd an atomic arrangement that makes the molecule most stable. Molecules are most stable when their energy attains the lowest possible value. The most stable structures of molecules are obtained by geometry optimization, necessarily followed by frequency calculations. The sole purpose of geometry optimization is to predict a three-dimensional arrangement of atoms that makes the molecule most stable, i.e., having minimum energy. Positive real values of frequencies further ensure that the optimized structure is really the lowest possible energy structure. The optimized geometries of dione-derivative compounds are shown in Figure 2.1. The calculated geometrical parameters show a good proximity when compared with the experi- mental results. The average value for C-C bonds in rings is found to be in the range of 1.515–1.567 FIGURE 2.1 Optimized geometry of (a) FTHD, (b) FTMPHD, (c) TNHXD, and (d) BDTHXD. Source: Regenerated from Ref. [8, 9].
- 54. 29 Spectroscopic Signatures of Some Organic Compounds Å and that for C-H bonds in the range of 1.090–1.100 Å, which are in good agreement with those reported for similar structures.[27, 28] The C-O bond length of 1.43 Å is also in good agreement with the literature data.[29, 30] 2.3 RESULTS AND DISCUSSION 2.3.1 VibratioNaL aNaLyses Frequency calculations yield some of the most important information discussed in this thesis. IR and Raman spectra of molecules can be predicted for any optimized molecular structure. The posi- tion and relative intensity of vibrational bands can be gathered from the output of a frequency calculation. This information is independent of the experiment and can therefore be used as a tool to confrm peak positions in experimental spectra or to predict peak positions and intensities when experimental data is not available. Calculated frequencies are based on the harmonic model, while real vibrational frequencies are anharmonic. This partially explains discrepancies between calcu- lated and experimental frequencies. The total energy of a molecule comprising N atoms near its equilibrium structure may be written as: 3˛ 3˛ 3˛ 2 1 2 ˇ ˆ V ˜ ° V q ˙V ˙ ˝ ˙ ˝ q q (2.1) i eq i j 2 i˝ i 1 j 1 ˘ ˆ ˆ i j eq 1 ˝ ˝ q q Here the mass-weighted Cartesian displacements, qi, are defned in terms of the locations Xi of the nuclei relative to their equilibrium positions Xi’eq and their masses Mi: qi ˜ ˙1 2 ˛ˆ ° ˆ ˝ (2.2) i i ieq Veq is the potential energy at the equilibrium nuclear confguration. For such a system, the classical mechanical equation of motion takes the form: 3˛ q ˜ ° f q j = 1, 2, 3 ˝3N (2.3) i ij i i˜1 The fij term quadratic force constants are the second derivatives of the potential energy with respect to mass-weighted Cartesian displacement, evaluated at the equilibrium nuclear confguration: 2 ˛ ° V ˆ f ˜ ˙ ˘ (2.4) ij ˙ ˘ ° ° i j ˝ q q ˇeq The fij may be evaluated by numerical second differentiation: V ˜2 V ˙ ˙ ˛ ˝ £ ° (2.5) ˜ ˜ q q q Vq ˙ ˙ i j i j By numerical frst differentiation of analytical frst derivatives: ˜2 V ˙˛˜ ˜ V q ˝ ° j (2.6) ˜ ˜ ˙q q q i j i
- 55. Random documents with unrelated content Scribd suggests to you:
- 59. The Project Gutenberg eBook of Poems of Giosuè Carducci, Translated with two introductory essays
- 60. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: Poems of Giosuè Carducci, Translated with two introductory essays Author: Giosuè Carducci Contributor: Frank Sewall Release date: March 9, 2018 [eBook #56711] Language: English Credits: Produced by ellinora, Bryan Ness, Barbara Magni and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) *** START OF THE PROJECT GUTENBERG EBOOK POEMS OF GIOSUÈ CARDUCCI, TRANSLATED WITH TWO INTRODUCTORY ESSAYS ***
- 64. POEMS O F GIOSUÈ CARDUCCI TRANSLATED WITH TWO INTRODUCTORY ESSAYS I GIOSUÈ CARDUCCI AND THE HELLENIC REACTION IN ITALY II CARDUCCI AND THE CLASSIC REALISM BY FRANK SEWALL
- 65. “Le secret de l'art grec réside là, dans cette finesse à dégager la ligne unique et nécessaire qui évoque la vie et en détermine du coup comme le type éternel” PAUL BOURGET
- 66. LONDON OSGOOD, McILVAINE CO. 45 ALBEMARLE ST., W. 1893
- 67. The De Vinne Press, New-York, U. S. A.
- 68. CONTENTS PAGE Preface vii Essays i. Giosuè Carducci and the Hellenic Reaction in Italy 1 ii. Carducci and the Classic Realism 29 Translations i. Roma 57 ii. Hymn to Satan 58 iii. Homer 66 iv. Virgil 67 v. Invocation to the Lyre 68 vi. Sun and Love 70 vii. To Aurora 71 viii. Ruit Hora 76 ix. The Ox 77 x. To Phœbus Apollo 78 xi. Hymn to the Redeemer 81 xii. Outside the Certosa 84 xiii. Dante—Sonnet 85 xiv. In a Gothic Church 86
- 69. xv. Innanzi, innanzi! 88 xvi. Sermione 89 xvii. To a Horse 93 xviii. A Dream in Summer 94 xix. On a Saint Peter's Eve 97 xx. The Mother 99 xxi. “Passa la nave mia, sola, tra il pianto” 101 xxii. Carnival. Voice from the Palace 102 Voice from the Hovel 103 Voice from the Banquet 105 Voice from the Garret 106 Voice from Beneath 107 xxiii. Sonnet to Petrarch 109 xxiv. Sonnet to Goldoni 110 xxv. Sonnet to Alfieri 111 xxvi. Sonnet to Monti 112 xxvii. Sonnet to Niccolini 113 xxviii. In Santa Croce 114 xxix. Voice of the Priests 115 xxx. Voice of God 116 xxxi. On my Daughter's Marriage 117 xxxii. At the Table of a Friend 119 xxxiii. Dante 120 xxxiv. On the Sixth Centenary of Dante 126 xxxv. Beatrice 127 xxxvi. “A questi dí prima io la vidi. Uscia” 130 xxxvii. “Non son quell'io che già d'amiche cene” 131 xxxviii. The Ancient Tuscan Poetry 132 xxxix. Old Figurines 133 xl. Madrigal 134 xli. Snowed Under 135
- 70. PREFACE n endeavouring to introduce Carducci to English readers through the following essays and translations, I would not be understood as being moved to do so alone by my high estimate of the literary merit of his poems, nor by a desire to advocate any peculiar religious or social principles which they may embody. It is rather because these poems seem to me to afford an unusually interesting example of the survival of ancient religious motives beneath the literature of a people old enough to have passed through a succession of religions; and also because they present a form of realistic literary art which, at this time, when realism is being so perverted and abused, is eminently refreshing, and sure to impart a healthy impetus to the literature of any people. For these reasons I have thought that, even under the garb of very inadequate translations, they would constitute a not unwelcome contribution to contemporary literary study. I am indebted to the courtesy of Harper Brothers for the privilege of including here, in an amplified form, the essay on Giosuè Carducci and the Hellenic Reaction in Italy, which appeared first in Harper's Magazine for July, 1890. F. S. Washington, D. C., June, 1892.
- 71. I GIOSUÈ CARDUCCI AND THE HELLENIC REACTION IN ITALY he passing of a religion is at once the most interesting and the most tragic theme that can engage the historian. Such a record lays bare what lies inmostly at the heart of a people, and has, consciously or unconsciously, shaped their outward life. The literature of a time reveals, but rarely describes or analyses, the changes that go on in the popular religious beliefs. It is only in a later age, when the religion itself has become desiccated, its creeds and its forms dried and parcelled for better preservation, that this analysis is made of its passing modes, and these again made the subject of literary treatment. Few among the existing nations that possess a literature have a history which dates back far enough to embrace these great fundamental changes, such as that from paganism to Christianity, and also a literature that is coeval with those changes. The Hebrew race possess indeed their ancient Scriptures, and with them retain their ancient religious ideas. The Russians and Scandinavians deposed their pagan deities to give place to the White Christ within comparatively recent times, but they can hardly be said to have possessed a literature in the pre-Christian period. Our own saga of Beowulf is indeed a religious war-chant uttering the savage emotions of our Teutonic ancestors, but not a work of literary art calmly reflecting the universal life of the people.
- 72. It is only to the Latin nations of Europe, sprung from Hellenic stock and having a continuous literary history covering a period of from two to three thousand years, that we may look for the example of a people undergoing these radical religious changes and preserving meanwhile a living record of them in a contemporaneous literature. Such a nation we find in Italy. So thorough is the reaction exhibited during the last half of the present century in that country against the dogma and the authority of the Church of Rome that we are led to inquire whether, not the church alone, as Mr. Symonds says,[1] but Christianity itself has ever “imposed on the Italian character” to such an extent as to obliterate wholly the underlying Latin or Hellenic elements, or prevent these from springing again into a predominating influence when the foreign yoke is once removed. To speak of Christianity coming and going as a mere passing episode in the life of a nation, and taking no deep hold on the national character, is somewhat shocking to the religious ideas which prevail among Christians, but not more so than would have been to a Roman of the time of the Cæsars the suggestion that the Roman Empire might itself one day pass away, a transient phase only in the life of a people whose history was to extend in unbroken line over a period of twenty-five hundred years. In the work just referred to Mr. Symonds also briefly hints at another idea of profound significance,—namely, whether there is not an underlying basis of primitive race character still extant in the various sections of the Italian people to which may be attributed the variety in the development of art and literature which these exhibit. In his Studii Letterari (Bologna, 1880), Carducci has made this idea a fundamental one in his definition of the three elements of Italian literature. These are, he says, the church, chivalry, and the national character. The first or ecclesiastical element is superimposed by the Roman hierarchy, but is not and never was native to the Italian people. It has existed in two forms. The first is Oriental, mystic, and violently opposed to nature and to human instincts and appetites,
- 73. and hence is designated the ascetic type of Christianity. The other is politic and accommodating, looking to a peaceful meeting-ground between the desires of the body and the demands of the soul, and so between the pagan and the Christian forms of worship. Its aim is to bring into serviceable subjection to the church those elements of human nature or of natural character which could not be crushed out altogether. This element is represented by the church or the ecclesiastical polity. It becomes distinctly Roman, following the eclectic traditions of the ancient empire, which gave the gods of all the conquered provinces a niche in the Pantheon. It transformed the sensual paganism of the Latin races and the natural paganism of the Germanic into a religion which, if not Christianity, could be made to serve the Christian church. In the same way that the church brought in the Christian element, both in its ascetic and its Roman or semi-pagan form, so did feudalism and the German Empire bring in that of chivalry. This, again, was no native development of the Italian character. It came with the French and German invaders; it played no part in the actions of the Italians on their own soil. “There never was in Italy,” says Carducci, “a true chivalry, and therefore there never was a chivalrous poetry.” With the departure of a central imperial power the chivalrous tendency disappeared. There remained the third element, that of nationality, the race instinct, resting on the old Roman, and even older Latin, Italic, Etruscan, Hellenic attachments in the heart of the people. Witness during all the Middle Ages, even when the power of the church and the influence of the empire were strongest, the reverence everywhere shown by the Italian people for classical names and traditions. Arnold of Brescia, Nicola di Rienzi, spoke to a sentiment deeper and stronger in the hearts of their hearers than any that either pope or emperor could inspire. The story is told of a schoolmaster of the eleventh century, Vilgardo of Ravenna, who saw visions of Virgil, Horace, and Juvenal, and rejoiced in their commendation of his efforts to preserve the ancient literature of the people. The national principle also exists in two forms, the Roman and the Italian—the aulic or learned, and the
- 74. popular. Besides the traditions of the great days of the republic and of the Cæsars, besides the inheritance of the Greek and Latin classics, there are also the native instincts of the people themselves, which, especially in religion and in art, must play an important part. Arnold of Brescia cried out, “Neither pope nor emperor!” It was then the people, as the third estate, made their voices heard—“Ci sono anch'io!” (Here am I too!). After the elapse of three hundred years from the downfall of the free Italian municipalities and the enslavement of the peninsula under Austrio-Spanish rule, we have witnessed again the achievement by Italians of national independence and national unity. The effect of this political change on the free manifestations of the Italian character would seem to offer another corroboration of Carducci's assertion that “Italy is born and dies with the setting and the rising of the stars of the pope and the emperor.” (Studii Letterari, p. 44.) Not only with the withdrawal of the Austrian and French interference has the pope's temporal power come to an end, but in a large measure the religious emancipation of Italy from the foreign influences of Christianity in every way has been accomplished. The expulsion of the Jesuits and the secularisation of the schools and of the monastic properties were the means of a more real emancipation of opinion, of belief, and of native impulse, which, free from restraint either ecclesiastical or political, could now resume its ancient habit, lift from the overgrowth of centuries the ancient shrines of popular worship, and invoke again the ancient gods. The pope remains, indeed, and the Church of Rome fills a large space in the surface life of the people of Italy; and so far as in its gorgeous processions and spectacles, its joyous festivals and picturesque rites, and especially in its sacrificial and vicarious theory of worship, the church has assimilated to itself the most important feature of the ancient pagan religion, it may still be regarded as a thing of the people. But the real underlying antagonism between the ancient national instinct, both religious and civil, and that habit of Christianity which has been imposed upon it, finds its true expression in the strong lines of a sonnet of Carducci's, published in
- 75. 1871, in the collection entitled Decennali. Even through the burdensome guise of a metrical translation, something of the splendid fire of the original can hardly fail to make itself felt. [I] The movement for the revival of Italian literature may be said to have begun with Alfieri, at the close of the last and the beginning of the present century. It was contemporary with the breaking up of the political institutions of the past in Europe, the dissolution of the Holy Roman Empire, the brief existence of the Italian Republic, the revival for a short joyous moment of the hope of a restored Italian independence. Again a thrill of patriotic ardour stirs the measures of the languid Italian verse. Alfieri writes odes on America Liberata, celebrating as the heroes of the new age of liberty Franklin, Lafayette, and Washington. Still more significant of the new life imparted to literature at this time is the sober dignity and strength of Alfieri's sonnets, and the manly passion that speaks in his dramas and marks him as the founder of Italian tragedy. But the promise of those days was illusory. With the downfall of Napoleon and the return of the Austrian rule, the hope of the Italian nationality again died out. Alfieri was succeeded by Vincenzo Monti and his fellow-classicists, who sought to console a people deprived of future hope with the contemplation of the remote past. This school restored rather than revived the ancient classics. They gave Italians admirable translations of Homer and Virgil, and turned their own poetic writing into the classical form. But they failed to make these dead forms live. These remained in all their beauty like speechless marble exhumed and set up in the light and stared at. If they spoke at all, as they did in the verses of Ugo Foscolo and Leopardi, it was not to utter the joyous emotions, the godlike freedom and delight of living which belonged to the world's youthful time; it was rather to give voice to an all-pervading despair and brooding melancholy, born, it is true, of repeated disappointments and of a very real sense of the vanity of life and the emptiness of great aspirations, whether of the individual or of society. This melancholy, itself repugnant to the primitive Italian nature, opened the way for the still more foreign influence of the romanticists, which
- 76. tended to the study and love of nature from the subjective or emotional side, and to a more or less morbid dwelling upon the passions and the interior life. With a religion whose life-sap of a genuine faith had been drained away for ages, and a patriotism enervated and poisoned by subserviency to foreign rule and fawning for foreign favour, naught seemed to remain for Italian writers who wished to do something else than moan, but to compose dictionaries and cyclopædias, to prepare editions of the thirteenth-century classics, with elaborate critical annotations, and so to keep the people mindful of the fact that there was once an Italian literature, even if they were to despair of having another. The decay of religious faith made the external forms of papal Christianity seem all the more a cruel mockery to the minds that began now to turn their gaze inward, and to feel what Taine so truly describes as the Puritan melancholy, the subjective sadness which belongs peculiarly to the Teutonic race. The whole literature of the romantic school, whether in Italy or throughout Europe, betrayed a certain morbidness of feeling which, says Carducci, belongs to all periods of transition, and appears alike in Torquato Tasso, under the Catholic reaction of the sixteenth century, and in Châteaubriand, Byron, and Leopardi, in the monarchical restoration of the nineteenth. The despair which furnishes a perpetual undertone to the writing of this school is that which is born of the effort to keep a semblance of life in dead forms of the past, while yet the really living motives of the present have found neither the courage nor the fitting forms for their expression. In many respects the present revival of Italian literature is a reawakening of the same spirit that constituted the Renaissance of the fourteenth and fifteen centuries, and disappeared under the subsequent influences of the Catholic reaction. Three hundred years of papal supremacy and foreign civic rule have, however, tempered the national spirit, weakened the manhood of the people, and developed a habit of childlike subserviency and effeminate dependence. While restraining the sensuous tendency of pagan religion and pagan art within the channels of the church ritual, Rome has not meanwhile rendered the Italian people more, but, if
- 77. anything, less spiritual and less susceptible of spiritual teaching than they were in the days of Dante or even of Savonarola. The new Italian renaissance, if we may so name the movement witnessed by the present century for the re-establishment of national unity and the building up of a new Italian literature, lacks the youthful zeal, the fiery ardour which characterised the age of the Medici. The glow is rather that of an Indian summer than that of May. The purpose, the zeal, whatever shall be its final aim, will be the result of reflection and not of youthful impulse. The creature to be awakened and stirred to new life is more than a mere animal; it is a man, whose thinking powers are to be addressed, as well as his sensuous instincts and amatory passion. Such a revival is slow to be set in motion. When once fairly begun, provided it have any really vital principle at bottom, it has much greater promise of permanence than any in the past history of the Italian people. A true renascence of a nation will imply a reform or renewal of not one phase alone of the nation's life, but of all; not only a new political life and a new poetry, but a new art, a new science, and, above all, a new religious faith. The steps to this renewal are necessarily at the beginning oftener of the nature of negation of the old than of assertion of the new. The destroyer and the clearer-away of the débris go before the builder. It will not be strange, therefore, if the present aspect of the new national life of Italy should offer us a number of conspicuous negations rather than any positive new conceptions; that the people's favorite scientist, Mantegazza,—the ultra-materialist,— should be the nation's chosen spokesman to utter in the face of the Vatican its denial of the supernatural; and that Carducci, the nation's foremost and favourite poet, should sing the return of the ancient worship of nature, of beauty, and of sensuous love, and seek to drown the solemn notes of the Christian ritual in a universal jubilant hymn to Bacchus. These are the contradictions exhibited in all great transitions. They will not mislead if the destroyer be not confounded with the builder who is to follow, and the temporary ebullition of pent-up passion be not mistaken for the after-thought of a reflecting, sobered mind. No one has recognized this more truly than Carducci:
- 78. Or destruggiam. Dei secoli Lo strato è sul pensiero: O pochi e forti, all'opera, Chè nei profundi è il vero. Now we destroy. Of the ages The highway is built upon thinking. O few and strong, to the work! For truth 's at the bottom. It was in the year 1859, when once more the cry for Italian independence and Italian unity was raised, that the newly awakened nation found its laureate poet in the youthful writer of a battle hymn entitled “Alla Croce Bianca di Savoia”—The White Cross of Savoy. Set to music, it became very popular with the army of the revolutionists, and the title is said to have led to the adoption of the present national emblem for the Italian flag. As a poem it is not remarkable, unless it be for the very conventional commingling of devout, loyal, and valorous expressions, like the following, in the closing stanza: Dio ti salvi, o cara insegna, Nostro amore e nostra gioja, Bianca Croce di Savoja, Dio ti salvi, e salvi il Re! But six years later, in 1865, there appeared at Pistoja a poem over the signature Enotrio Romano, and dated the “year MMDCXVIII from the Foundation of Rome,” which revealed in a far more significant manner in what sense its author, Giosuè Carducci, then in his thirtieth year, was to become truly the nation's poet, in giving utterance again to those deeply hidden and long-hushed ideas and emotions which belonged anciently to the people, and which no exotic influence had been able entirely to quench. This poem was called a “Hymn to Satan.” The shock it gave to the popular sense of propriety is evident not only from the violence and indignation with
- 79. which it was handled in the clerical and the conservative journals, one of which called it an “intellectual orgy,” but from the number of explanations, more or less apologetic, which the poet and his friends found it necessary to publish. One of these, which appeared over the signature Enotriofilo in the Italian Athenæum of January, 1886, has been approvingly quoted by Carducci in his notes to the Decennali. We may therefore regard it as embodying ideas which are, at least, not contrary to what the author of the poem intended. From this commentary it appears that we are to look here “not for the poetry of the saints but of the sinners,—of those sinners, that is, who do not steal away into the deserts to hide their own virtues, so that others shall not enjoy them, who are not ashamed of human delights and human comforts, and who refuse none of the paths that lead to these. Not laudes or spiritual hymns, but a material hymn is what we shall here find. “Enotrio sings,” says his admiring apologist, “and I forget all the curses which the catechism dispenses to the world, the flesh, and the devil. Asceticism here finds no defender and no victim. Man no longer goes fancying among the vague aspirations of the mystics. He respects laws, and wills well, but to him the sensual delights of love and the cup are not sinful, and in these, to him, innocent pleasures Satan dwells. It was to the joys of earth that the rites of the Aryans looked; the same joys were by the Semitic religion either mocked or quenched. But the people did not forget them. As a secretly treasured national inheritance, despite both Christian church and Gothic empire, this ancient worship of nature and of the joys of the earth remains with the people. It is this spirit of nature and of natural sensuous delights, and lastly of natural science, that the poet here addresses as Satan. As Satan it appears in nature's secret powers of healing and magic, in the arts of the sorcerer and of the alchemist. The anchorites, who, drunk with paradise, deprived themselves of the joys of earth, gradually began to listen to these songs from beyond the gratings of their cells— songs of brave deeds, of fair women, and of the triumph of arms. It is Satan who sings, but as they listen they become men again, enamoured of civil glory. New theories arise, new masters, new ideals of life. Genius awakes, and the cowl of the Dominican falls to
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