Use of Molecular Quantum-Mechanical Approximations Exemplified in the Energy Calculation of the H3— System

Abstract

Certain approximations of molecular quantum mechanics are examined. The size of the resultant error due to approximate methods for specific multicenter integral evaluations are cited. Examination of the Sklar approximate multicenter electron repulsion formula together with the generalizations and extensions of Vroeland and Löwdin allow application of the underlying approximation principle to three center nuclear attraction integrals. Specific approximate formulation of these integrals is given. The accumulation of computational errors arising from the many individual integral approximations in the energy evaluation of the linear H₃^— system is specifically examined. The ground state energy of this system found from the Heitler‐London and Wang‐like treatments were — 70 kcal/mole and — 84 kcal/mole for the Sklar type approximations, — 1 kcal/mole and — 19 kcal/mole for the Mulliken type approximations, and — 26 kcal/mole and — 41 kcal/mole for exact integral evaluations. It is concluded that the Sklar type approximations, while preferable to the Mulliken type in a few specific evaluations lead like that formulation to considerable discrepancy between the over‐all energy obtained for a polyatomic system. The Sklar approximations have the further disadvantage of requiring two‐center integral evaluations not needed in the over‐all energy calculations. However, both the Sklar and the Mulliken approximations do give a rapid method for evaluating ``best'' distance and effective charge parameters for use with more extensive exact integral variational method calculations.