Simple Theorems, Proofs and Derivations in Quantum Chemistry Book

1	The Born-Oppenheimer Hamiltonian	1
1	Separating the center of mass motion in quantum mechanics	1
2	The Born-Oppenheimer approximation	12
2	General Theorems and Principles	19
1	The variation principle	19
2	The Hellmann-Feynman theorem	26
3	The virial theorem in quantum mechanics	32
3	The Linear Variational Method and Lowdin's Orthogonalization Schemes	45
1	The linear variational method (Ritz method)	45
2	Lowdin's symmetric orthogonalization	52
3	Linear independence of the basis of Lowdin's canonic orthogonalization	62
4	Perturbational Methods	69
1	Nondegenerate Rayleigh-Schrodinger perturbation theory	69
2	Variational-perturbational method: The Hylleraas functional	88
3	Degenerate Rayleigh-Schrodinger perturbation theory	93
4	Brillouin-Wigner perturbation theory	95
5	Size consistency of the Rayleigh-Schrodiger perturbation theory	100
6	Lowdin's partitioning method	115
5	Determinant Wave Functions	121
1	Spin orbitals	121
2	Many-electron spin states	124
3	Slater determinants	126
4	The antisymmetrizing operator	129
5	Invariance of the determinant wave function with respect to "mixing" the occupied orbitals	137
6	Matrix elements between determinant wave functions: Lowdin's general formulae for nonorthogonal orbitals	140
7	Lowdin's pairing theorem and its generalization	153
8	Theorem about the existence of orbitals of special structure	160
6	The Hartree-Fock Method	165
1	The variation principle for single determinant wave functions: The Brillouin theorem	166
2	The Hartree-Fock equations	170
3	Koopmans theorem	182
4	The RHF method	187
5	Finite basis Hartree-Fock theory	198
6	Restricted open-shell Hartree-Fock method	209
7	The gradient of the energy	216
7	Population Analysis, Bond Orders, and Valences	227
1	Mulliken's population analysis	228
2	Bond orders and valences	235
8	The Electron Correlation	251
1	The CI expansion	251
2	The correlation energy and Nesbet's theorem	253
3	Methods of electron correlation calculations	260
9	Miscellaneous	281
1	The 1/Z expansion	281
2	The cusp condition	283
3	The asymptotical behavior of the wave function at very large distances	286
4	Basis functions: The Gaussian product theorem	287
5	The integral transformation problem	290
	Appendices	293
App. I	Separating the motion of the center of mass in classical mechanics	295
App. II	Reducing the two-body problem to two one-body ones in classical mechanics	299
App. III	Analogy between differentials and variations	303
App. IV	Euler's theorem for homogenous functions	305
App. V	The virial theorem in classical mechanics	307
App. VI	The electronic Schrodinger equation in atomic units	309
App. VII	The "bra-ket" formalism	311
App. VIII	Collection of formulas for Rayleigh-Schrodinger perturbation theory (nondegenerate case)	323
App. IX	Direct products of matrices	325
App. X	Permutations	329
App. XI	An orthogonalization algorithm	331
	Index	333