An Overview of Molecular Quantum Mechanics

Abstract

The fundamentals of molecular quantum mechanics have changed remarkably little since the 1930’s: the most commonly used methods of constructing molecular wave functions are still dominated by expansions in terms of Slater determinants, in which individual electrons are described by spin-orbitals; the spin-orbitals (one-electron wavefunctions) still usually refer to an independent-particle model (IPM) in which each electron ‘sees’ an average field due to the nuclei and to all its companion electrons — in the spirit of Hartree and Fock; and simple first approximations, in which the wavefunction is built up from a few configurations of ‘occupied’ orbitals, are still systematically refined by adding more and more configurational functions (CFs) in a typical configuration interaction (CI) calculation. It is true that the techniques have changed: Fock space, for example, is now more familiar to quantum chemists than it used to be; the simple self-consistent field (SCF) of Hartree and Fock is nowadays often replaced by its multi-configuration counterpart; and CI may be admitted by diagrammatic perturbation theory or by unitary group methods. But, beautiful as some of these techniques may be, they are simply sophisticated and clever ways of doing the same old things!