Accession Number : AD0424520

Title :   APPLICATION OF VARIANCE MINIMIZATION TO THE CALCULATION OF ELECTRONIC ENERGIES,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH

Personal Author(s) : Carlson,Charles M.

Report Date : SEP 1963

Pagination or Media Count : 26

Abstract : Three general types of approaches are outlined for calculating electronic energies in atoms and molecules. Each of these methods is based upon the same type of procedure which forms the basis for the local energy method successfully developed by A. A. Frost and co-workers. The first step in the procedure is the derivation of an approximate expression for the energy which when varied in a particular manner exhibits a variance from the mean. The variance is minimized with respect to the adjustable parameters in the wave function and the values of these parameters corresponding to the minimum are substituted back into the expression for the mean energy to obtain the optimum value of the energy. The particular form of expression derived for the approximate energy and the manner in which it is varied to derive the expression for the variance distinguishes each of the three types of approaches from one another. For the last two approaches it is discussed how summation over a finite number of points as opposed to integration may be employed without loss of generality. Finally specific approaches are suggested which will not encounter computational difficulties and are likely to exhibit optimum convergence properties. (Author)

Descriptors :   (*ELECTRON TRANSITIONS, ENERGY), ATOMIC ORBITALS, ELECTRONS, VALENCE, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, STATISTICAL DISTRIBUTIONS, POLYATOMIC MOLECULES, QUANTUM THEORY, CORRELATION TECHNIQUES

Distribution Statement : APPROVED FOR PUBLIC RELEASE