1 Quantum Chemistry ............................................ 1
1.1 History of Quantum Chemistry ............................ 1
1.2 History of Theoretical Chemistry Prior to the Advent
of Quantum Chemistry .................................... 6
1.3 Analytical Mechanics Underlying the Schrцdinger
Equation ............................................... 11
1.4 Schrцdinger Equation ................................... 15
1.5 Interpretation of the Wavefunction ..................... 17
1.6 Molecular Translational Motion ......................... 19
1.7 Molecular Vibrational Motion ........................... 22
1.8 Molecular Rotational Motion ............................ 25
1.9 Electronic Motion in the Hydrogen Atom ................. 29
References .................................................. 31
2 Hartree-Fock Method ......................................... 35
2.1 Hartree Method ......................................... 35
2.2 Molecular Orbital Theory ............................... 38
2.3 Slater Determinant ..................................... 42
2.4 Hartree-Fock Method .................................... 43
2.5 Roothaan Method ........................................ 47
2.6 Basis Function ......................................... 50
2.7 Coulomb and Exchange Integral Calculations ............. 53
2.8 Unrestricted Hartree-Fock Method ....................... 56
2.9 Electronic States of Atoms ............................. 59
References .................................................. 63
3 Electron Correlation ........................................ 65
3.1 Electron Correlation ................................... 65
3.2 Dynamical and Nondynamical Correlations ................ 67
3.3 Configuration Interaction .............................. 70
3.4 Brillouin Theorem ...................................... 73
3.5 Advanced Correlation Theories .......................... 75
References .................................................. 77
4 Kohn-Sham Method ............................................ 79
4.1 Thomas-Fermi Method .................................... 79
4.2 Hohenberg-Kohn Theorem ................................. 80
4.3 Kohn-Sham Method ....................................... 83
4.4 Generalized Kohn-Sham Method ........................... 85
4.5 Constrained Search Method for Constructing Kohn-Sham
Potentials ............................................. 87
4.6 Time-Dependent Kohn-Sham Method ........................ 90
4.7 Coupled Perturbed Kohn-Sham Method ..................... 94
References .................................................. 99
5 Exchange-Correlation Functionals ........................... 101
5.1 Classification of Exchange-Correlation Functionals .... 101
5.2 LDA and GGA Exchange Functionals ...................... 103
5.3 LDA and GGA Correlation Functionals ................... 107
5.4 Meta-GGA Functionals .................................. 114
5.5 Hybrid Functionals .................................... 118
5.6 Semiempirical Functionals ............................. 120
References ................................................. 123
6 Corrections for Functionals ................................ 125
6.1 Long-Range Correction ................................. 125
6.2 Self-interaction Correction ........................... 130
6.3 van der Waals Correction .............................. 134
6.4 Relativistic Corrections .............................. 144
6.5 Vector Potential Correction and Current Density ....... 152
References ................................................. 158
7 Orbital Energy ............................................. 161
7.1 Koopmans Theorem ...................................... 161
7.2 Janak's Theorem ....................................... 163
7.3 The Indispensability of Producing Accurate Orbital
Energies .............................................. 166
7.4 Electron Correlation Effects on Orbital Energies ...... 169
7.5 Optimized Effective Potential Method .................. 170
7.6 Highly Correlated Correlation Potentials .............. 172
7.7 Constrained Search for Exact Potentials ............... 175
7.8 Corrections for Orbital Energy Gaps in Solids ......... 176
7.9 Orbital Energy Reproduction by Long-Range Corrected
DFT ................................................... 180
References ................................................. 187
8 Appendix: Fundamental Conditions ........................... 189
References ................................................. 195
Index ......................................................... 197
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