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Chapter 1 Introduction 1 Chapter 2 Theoretical Basis of Computational Simulation 7 2.1 Semi-empirical method 7 2.1.1 Introduction of semi-empirical method 7 2.1.2 The accuracy and applicable scale of the semi-empirical method 10 2.1.3 Mainstream software 11 2.2 Hartree-Fock method 16 2.3 Density functional theory 19 2.3.1 Difficulties in calculation of actual materials 19 2.3.2 Hohenberg-Kohn theorem 20 2.3.3 Exchange correlation functional 22 2.3.4 Selection of functional 24 2.3.5 How to change the functional 30 2.4 Basis sets 33 2.4.1 Selection of basis sets 33 2.4.2 Application of mixed basis set, custom basis set and pseudopotential basis set in Gaussian 48 2.4.3 Diffuse functions 61 Chapter 3 Calculation and Analysis of Electron Transition Spectra 69 3.1 Calculation method of excited states 69 3.1.1 Introduction 69 3.1.2 TDDFT 71 3.1.3 Other calculation methods excited states 77 3.1.4 Appendix: list of HF components of different DFT functionals 82 3.2 Analysis method of excited states 84 3.2.1 Hole-electron analysis 84 3.2.2 Quantitative description 86 3.2.3 Exciton binding energy 88 3.2.4 Ghost-Hunter index 89 Chapter 4 Vibration Spectrum Calculation and Analysis 91 4.1 IR spectra 91 4.2 Raman spectra 98 4.3 Calculation of vibration-resolved electronic spectra 100 4.3.1 Principles 100 4.3.2 Calculation methods 103 4.3.3 Additional parameters 107 4.4 Vibration mode 108 Chapter 5 Calculation of Nonlinear Optical Properties 112 5.1 Two-photon absorption 112 5.1.1 Calculation method of TPA cross-section 115 5.1.2 Application of TPA calculation 118 5.2 Second order Harmonic wave generate 120 5.2.1 Sum-of-states 120 5.2.2 Calculation of SHG 124 Chapter 6 Calculation and Analysis of Molecular Chiral Spectra 127 6.1 Chirality 127 6.2 Chiral spectroscopy 131 6.2.1 Electron circular dichroism 131 6.2.2 Raman optical activity 135 Chapter 7 First Principles Calculation of Optical Properties of Solids 138 7.1 Optical properties of solids 138 7.2 Light absorption of inorganic solids 139 7.3 Optical properties of semiconductor 140 7.3.1 Intrinsic semiconductor light absorption 140 7.3.2 Extrinsic semiconductor light absorption 141 7.4 Calculation of solid optical properties in common software 142 7.5 Application of solid optical properties in surface plasmon 146 Chapter 8 Application of Electronic Structure Method in Optical Calculation and Analysis 149 8.1 Energy band theory 149 8.1.1 Fundamental assumption 151 8.1.2 Conduction band 151 8.1.3 Valence and forbidden band 152 8.2 Density of states 153 8.3 Effective mass 155 8.4 Application of electronic structure method 157 Bibliography 164