# Accession Number:

## AD0658447

# Title:

## A NUMERICAL SINGLE-CENTER SELF-CONSISTENT FIELD FUNCTION FOR THE HYDROGEN MOLECULE,

# Descriptive Note:

# Corporate Author:

## AEROSPACE CORP EL SEGUNDO CALIF LABS DIV

# Personal Author(s):

# Report Date:

## 1967-06-01

# Pagination or Media Count:

## 43.0

# Abstract:

A Hartree-Fock single determinant wave function is calculated for the normal state 1Sigmag of the hydrogen molecule. The one-electron molecular orbitals in this determinant are expanded up to fourth-order terms as a product of a series of spherical harmonics and radial wave functions about the molecular midpoint of the molecule. The potential field caused by the nuclei is expanded in spherical harmonics up to eighth-order terms, and the complete Hartree-Fock equations are set up and solved numerically for the three radial functions occurring in one-electron molecular orbitals. The numerical technique used to solve the three coupled second-order differential-integral equations differs from that usually used in atomic calculations. The total molecular energy obtained from this numerical approximation is -1.14100 a. u., which is a small improvement over the total analytic self-consistent energy of -1.13363 a. u. obtained by Kolos and Roothaan using nine-term orbitals. This calculation shows that the best Hartree-Fock Roothaan self-consistent field SCF molecular wave function must be very close indeed to the true Hartree-Fock SCF molecular wave function. Author

# Descriptors:

# Subject Categories:

- Atomic and Molecular Physics and Spectroscopy
- Quantum Theory and Relativity