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1. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Development of Theoretical Tools to Accurately Determine Spectroscopic Properties Using Advanced Electronic Structure Methods Andy Van Yperen-De Deyne Center for Molecular Modeling, Ghent University Promotors: prof. dr. ir. V. Van Speybroeck, prof. dr. ir. K. Hemelsoet, prof. dr. M. Waroquier September 16, 2014 1 / 49

2. Spectroscopy ? 2 / 49

3. Spectroscopy 3 / 49

4. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Electromagnetic radiation 4 / 49

13. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Electromagnetic radiation Wavelength Energy 4 / 49

14. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Length scale 5 / 49

20. Welcome in the quantum world 6 / 49

21. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Welcome in the quantum world At the nanoscale: Quantum Mechanics Uncertainty principle of Heisenberg xpx ~=2 Classical Mechanics deterministic Quantum Mechanics probabilities 7 / 49

22. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Welcome in the quantum world Classical position and momentum well de

23. ned electron is particle orbits around nucleus Quantum position and momentum well de

24. ned electron described by wave electron density 8 / 49

25. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Welcome in the quantum world Classical position and momentum well de

26. ned electron is particle orbits around nucleus Quantum position and momentum well de

27. ned electron described by wave electron density 8 / 49

28. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Energy quantization for atoms and molecules E6 E5 E4 E3 E2 E1 Energy 9 / 49

29. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Energy quantization for atoms and molecules E6 E5 E4 E3 E2 E1 Energy E6 E5 E4 E3 E2 E1 Energy Absorption Emission 9 / 49

30. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spectroscopy and the nanoscale 10 / 49

31. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spectroscopy and the nanoscale Energy 10 / 49

32. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spectroscopy: top-down or bottom-up approach? Physical interaction with the system ~E Studied Sample Experiment Calculation i¯h @ @t = ˆH Molecular structure 11 / 49

33. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Basis of this work: Computational Spectroscopy Calculate the spectrum of a system Use of quantum mechanical concepts Development to increase accuracy Requirements High Performance Computing (HPC) 15496 processors available up to 2048 processors used simultaniously 12 / 49

34. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Quantum or Classical description for molecules? Born-Oppenheimer Electrons Quantum Mechanics (post-) Hartree-Fock Density Functional Theory Nuclei Classical Mechanics Forces determined by nuclei and electrons 13 / 49

35. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Electronic structure: Density Functional Theory (DFT) Hohenberg-Kohn theorem Electron density of the system determines the external potential of the system. Kohn-Sham scheme Pratical implementation, requiring approximations for the XC functional 14 / 49

36. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Electronic Structure: Advanced Methods Limitations of DFT Dissociation of molecules not well described Combination with relativistic eects (heavy atoms) Degeneracy can be problematic Advanced Electronic Structure Methods: CASSCF, MRCI No parametrization Solves problems for DFT Much more complex 15 / 49

37. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Molecules expected in the cover gas of LBE? Van Yperen-De Deyne et al., J. Nucl. Mat., submitted Polonium molecules can evaporate Ab initio calculations indicate which molecules can be expected Very stable compounds: PoO, PoO2, PoPb, PoPbO 16 / 49

38. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Quantum or Classical description for molecules? Born-Oppenheimer Electrons Quantum Mechanics (post-) Hartree-Fock Density Functional Theory Nuclei Classical Mechanics Forces determined by nuclei and electrons 17 / 49

39. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Energy Landscape for Nuclear Con

40. gurations 18 / 49

42. gurations Draw the molecule for initial guess 18 / 49

44. gurations Calculation of forces to

45. nd optimum 18 / 49

47. gurations Optimized Minimum of the Potential Energy Surface 18 / 49

48. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Potential Energy Surface 18 / 49

49. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Potential Energy Surface PES 0 18 / 49

50. Molecular Dynamics 19 / 49

51. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Molecular Dynamics (MD) Very low temperature: at bottom of the valley Still some zero-point vibrations present 20 / 49

52. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Molecular Dynamics (MD) Normal working conditions Need for Molecular Dynamics 20 / 49

53. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Molecular Dynamics (MD) Setup Forces from Quantum Mechanics (QM) or Classical Mechanics (MM) Solution of Newton's equation of Motion Inclusion of Temperature Result Positions as function of time xi (t) Velocities as function of time vi (t) Forces as function of time fi (t) . . . as function of time i (t) 21 / 49

54. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Vibrational Spectroscopy Energy 22 / 49

55. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Infrared Region: Molecular Vibrations PES 0 Vibrational energy quantized Infrared spectroscopy Raman spectroscopy Each vibration has a characteristic frequency 23 / 49

56. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Vibrations from Molecular Dynamics PES 0 Time Time 24 / 49

57. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Fourier Tranform to decompose signals Time + + + Total MD mode 1 mode 2 mode 3 ... 25 / 49

58. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Power Spectra Velocity Power Spectrum IVPS(!) = X3N i=1 jFFT(vi (t))j2 Measure for Vibrational Motions Related to IR/Raman spectrum 26 / 49

59. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Characterization of materials through vibrational spectroscopy Lezcano-Gonzalez et al., PCCP, 16, pp. 1639, 2014 Reduction of NOx from car exhaust Characterization of catalyst in the Selective Catalytic Reduction 27 / 49

60. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Process: Selective Catalytic Reduction (SCR) Lezcano-Gonzalez et al., PCCP, 16, pp. 1639, 2014 4NO + 4NH3 + O2 ! 4N2 + 6H2O Zeolite Various topologies Nanoporous SiO2 Activation through Protonation Transition metals 28 / 49

61. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Vibrational spectra of Cu-SSZ-13 Lezcano-Gonzalez et al., PCCP, 16, pp. 1639, 2014 Experimental IR spectrum Velocity Power Spectrum 1 0.8 0.6 0.4 0.2 0 H-SSZ-13 Cu-SSZ-13 2200 2000 1800 1600 1400 1200 Intensity wavenumbers [1/cm] EFAl 29 / 49

62. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Application: SCR Lezcano-Gonzalez et al., PCCP, 16, pp. 1639 Ammonia adsorbed on proton or copper Copper mobile when ammonia is adsorbed 30 / 49

63. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion UV/Vis Spectroscopy Energy 31 / 49

64. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion UV/Vis region: Electron Transitions PES 1 PES 0 determines the color of matter useful for dyes, tracking chemical processes, ligand information 32 / 49

65. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion UV/Vis region: Electron Transitions PES 1 PES 0 In uence of vibrations? Vibration selectivity? In uence of temperature? 32 / 49

66. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Molecular Dynamics: vibrational

67. ngerprint Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 7.9 7.8 7.7 7.6 7.5 7.4 7.3 0 50 100 150 200 250 Excitation Energy e [eV] time [fs] e0 33 / 49

69. ngerprint Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 33 / 49

71. ngerprint Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 7.9 7.8 7.7 7.6 7.5 7.4 7.3 0 50 100 150 200 250 Excitation Energy e [eV] time [fs] e0 e e(t) 33 / 49

73. ngerprint Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 IPS =

77. Z (t) exp(i!t)dt

81. 2 IVPS(!) = X N;r

85. Z +1 1 vN;r (t) exp(i!t)dt

89. 2 33 / 49

90. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion PS vs VPS Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 I PS Normal Mode 1 Normal Mode 2 wavenumber [cm−1] VPS 34 / 49

91. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Vibrational

92. ngerprint: linear modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Linear 8.2 8.1 8 7.9 7.8 7.7 0.2 0.1 0 e0 −0.4 −0.2 0 0.2 0.4 Q6 [Å] PES0 7.6 E [eV] PES1 35 / 49

94. ngerprint: linear modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Linear 8.2 8.1 8 7.9 7.8 7.7 0.2 0.1 0 e0 −0.4 −0.2 0 0.2 0.4 Q6 [Å] PES0 7.6 E [eV] PES1 8.2 8 7.8 7.6 7.4 7.2 −0.4 −0.2 0 0.2 0.4 ε [eV] Q6 [Å] ε(Q6) ε0 ε Q6 Equilibrium 35 / 49

96. ngerprint: linear modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Linear: PS = VPS 8.2 8 7.8 7.6 7.4 7.2 −0.4 −0.2 0 0.2 0.4 ε [eV] Q6 [Å] ε(Q6) ε0 ε Q6 Equilibrium Same wavelength 35 / 49

98. ngerprint: linear modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Linear: PS = VPS 8.2 8 7.8 7.6 7.4 7.2 −0.4 −0.2 0 0.2 0.4 ε [eV] Q6 [Å] ε(Q6) ε0 ε Q6 Equilibrium 1.2 1 0.8 0.6 0.4 0.2 0 11,12 0 500 1000 1500 2000 2500 3000 3500 Intensity wavenumbers [1/cm] 1 2,3 4 5 6 7 8 9 10 VPS ePS 35 / 49

100. ngerprint: quadratic modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Quadratic 7.8 7.7 7.6 7.5 7.4 7.3 0.2 0.1 0 −0.4 −0.2 0 0.2 0.4 Q4 [Å] PES0 7.2 E [eV] e0 PES1 7.8 7.7 7.6 7.5 7.4 7.3 7.2 7.1 7 ε0 ε Q4 −0.4 −0.2 0 0.2 0.4 ε [eV] Q4 [Å] ε(Q4) Equilibrium 36 / 49

102. ngerprint: quadratic modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Quadratic: PS = 2VPS half the original wavelength 7.8 7.7 7.6 7.5 7.4 7.3 7.2 7.1 7 ε0 ε Q4 −0.4 −0.2 0 0.2 0.4 ε [eV] Q4 [Å] ε(Q4) 36 / 49

104. ngerprint: quadratic modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Quadratic: PS = 2VPS 7.8 7.7 7.6 7.5 7.4 7.3 7.2 7.1 7 ε0 ε Q4 −0.4 −0.2 0 0.2 0.4 ε [eV] Q4 [Å] ε(Q4) Equilibrium 1.2 1 0.8 0.6 0.4 0.2 0 11,12 0 500 1000 1500 2000 2500 3000 3500 Intensity wavenumbers [1/cm] 1 2,3 4 5 6 7 8 9 10 VPS ePS 36 / 49

106. ngerprint: quadratic modes Van Yperen-De Deyne et al., J. Chem. Phys. 140, pp. 134105, 2014 Quadratic 1.2 1 0.8 0.6 0.4 0.2 0 11,12 0 500 1000 1500 2000 2500 3000 3500 Intensity wavenumbers [1/cm] 1 2,3 4 5 6 7 8 9 10 VPS ePS 36 / 49

107. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion EPR Spectroscopy Energy 37 / 49

108. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spin - a quantum concept Atoms and electrons have spin Spin is quantized 38 / 49

109. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spin - a quantum concept Atoms and electrons have spin Spin is quantized 38 / 49

110. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Radiofrequency range: Magnetic Interactions NMR Nuclear Magnetic Resonance used in MRI EPR Electron Paramagnetic Resonance 39 / 49

111. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Electron Paramagnetic Resonance ~B = 0 ~B 0 Unpaired electrons essential role radicals transition metals Free electron ^H S = BgeSzB Environment Direction is important Introduction of tensor property 40 / 49

112. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Material Characterization through EPR Sakhabutdinova et al., J. Phys. Chem. A, 114, pp. 1721, 2011 Rh2+ defect in NaCl Cluster vs. Periodic Vacancy distribution g-tensor 41 / 49

113. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Cluster $ Periodic Cluster Periodic 42 / 49

114. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Cluster $ Periodic Cluster Periodic 42 / 49

115. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Cluster $ Periodic Cluster Structural information incorrect Problems at boundary Advanced models for EPR properties Periodic Correct structures No boundaries Room for improvement of EPR properties 43 / 49

116. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spin-Orbit Coupling Contribution to g-tensor Van Yperen-De Deyne et al., PCCP, 14, pp. 10690, 2012 g = gZKE + gSOC + ggauge ^H SO = X i 2 4g02 4 X A ZAsi riA pi riA 3 X j6=i 0 @g02 4 si rij pi rij 3 + X j6=i 2 4 si rji pj rij 3 1 A 3 5 44 / 49 A i j i i j

117. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion SOC: Exchange contribution 1(1)2(2) difference? 1(2)2(1) Pauli Principle (1)6= (2) Requires anti-symmetrical wavefunctions 1(1)2(2) 1(2)2(1) + Next to direct two-body interactions also exchange interactions 45 / 49

118. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion SOC: model development Van Yperen-De Deyne et al., PCCP, 14, pp. 10690, 2012 SOMF . VSOO 12

121. exchange = 2 VSSO 12

124. exchange can be exploited by Ve methods. X 2occ hhjVSOO 12 jpi6= 0 in literature this contribution is neglected. Implementation in CP2K Validation on a set of diatomic molecules Focus on transition metal containing systems 46 / 49 A i j i i j

125. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion EPR: Results Van Yperen-De Deyne et al., PCCP, 14, pp. 10690, 2012 g-values for diatomic molecules (expressed in ppt) In uence gSOO;Exchange Molecule exp. ref. old new BO -1.72 -1.75 -2.29 -1.81 BS -8.12 -9.07 -10.25 -9.21 ZnH -17.1 -16.03 -16.82 -16.18 YO -0.22 -0.69 -0.80 -0.60 CdH -49.9 -51.33 -53.27 -51.84 In uence gSOO;Direct Molecule exp. old new NCl 5.4 5.03 5.28 NBr 19.3 18.83 19.18 VO -21.9 -15.52 -19.25 CrN -5.6 -4.41 -5.02 MnH -1.3 -1.661 -1.35 47 / 49

126. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Spectroscopic techniques studied in this thesis ms = 12 ms =−12 PES 1 PES 0 Electronic transitions (UV/Vis) Vibrational transitions (IR, VPS) Magnetic transitions (EPR) 48 / 49

127. Introduction Vibrational Spectroscopy UV/Vis EPR Conclusion Acknowledgements 49 / 49

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