Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

TLDR

The paper presents a general theory for numerically obtaining electronic wave functions of atoms and molecules. It investigates a general method that yields a convergent sequence of solutions toward the accurate electronic state. The method builds complete Gaussian‑based function sets, evaluates all necessary integrals explicitly, and applies them within molecular orbital, localized bond, or multi‑determinant variational frameworks. The study shows that computational effort is the sole barrier to achieving any desired accuracy, and introduces a highly practical atomic modification of the method.

Abstract

This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.