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

Abstract

A Hartree-Fock single determinant wave function is calculated for the normal state (1)Sigma(+)g 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)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0658447

Entities

People

  • Howard S. Taylor
  • Roger L. Wilkins

Organizations

  • The Aerospace Corporation

Tags

DTIC Thesaurus Topics

  • California
  • Cooperation
  • Electrons
  • Equations
  • Functions (Mathematics)
  • Harmonics
  • Hydrogen
  • Integral Equations
  • Integrals
  • Mathematics
  • Molecules
  • Spherical Harmonics
  • Wave Functions

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Quantum Chemistry

Technology Areas

  • Microelectronics
  • Space