Simple Theorems, Proofs, and Derivations in Quantum Chemistry

by Istvan Mayer

Overview

Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chemistry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in preparation of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin­ ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex­ tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe­ cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.

Product Details

ISBN-13:	9780306474095
Publisher:	Springer US
Publication date:	03/31/2003
Series:	Mathematical and Computational Chemistry
Edition description:	2003
Pages:	337
Product dimensions:	7.01(w) x 10.00(h) x 0.03(d)

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.