Simple Theorems, Proofs, and Derivations in Quantum Chemistry
Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibl...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer US
2003, 2003
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| Edition: | 1st ed. 2003 |
| Series: | Mathematical and Computational Chemistry
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. The Born-Oppenheimer Hamiltonian
- 2. General Theorems and Principles
- 3. The Linear Variational Method and Löwdin’s Orthogonalization Schemes
- 4. Perturbational Methods
- 5. Determinant Wave Functions
- 6. The Hartree-Fock Method
- 7. Population Analysis, Bond Orders, and Valences
- 8. The Electron Correlation
- 9. Miscellaneous
- Appendices
- I. Separating the motion of the center of mass in classical mechanics
- II. Reducing the two-body problem to two one-body ones in classical mechanics
- III. Analogy between differentials and variations
- IV. Euler’s theorem for homogenous functions
- V. The virial theorem in classical mechanics
- VI. The electronic Schrödinger equation in atomic units
- VII. The “bra-ket” formalism
- 1. Dirac’s “bra” and “ket” vectors
- 2. Analogy with the matrix formalism
- 3. The use of an overlapping basis
- 4. Example of using the bra-ket formalism: The hypervirial theorem
- 5. Projection operators
- 6. Resolution of identity
- 7. Spectral resolution of Hermitian operators
- 8. The case of non-Hermitian operators—biorthogonal sets of functions
- 9. The trace of the projector
- VIII. Collection of formulas for Rayleigh-Schrödinger perturbation theory (nondegenerate case)
- IX. Direct products of matrices
- X. Permutations
- XI. An orthogonalization algorithm