# Accession Number:

## AD0636548

# Title:

## THE PROJECTED HARTREE - FOCK METHOD, AN EXTENSION OF THE INDEPENDENT-PARTICLE SCHEME.

# Descriptive Note:

# Corporate Author:

## UPPSALA UNIV (SWEDEN) QUANTUM CHEMISTRY GROUP

# Personal Author(s):

# Report Date:

## 1966-03-01

# Pagination or Media Count:

## 45.0

# Abstract:

The symmetry dilemma in the ordinary Hartree-Fock schemes based on a single Slater determinant D is discussed, and it is shown that the symmetry requirements form a constraint which raises the energy and that any lowering of the energy is possible only at the expense of loss of symmetry. This phenomenon depends on the fact that the variation principle applied to a single determinant does not automatically lead to results which are compatible with the requirements resulting from the existence of constants of motion associated with the Hamiltonian of the system. In order to treat this problem, the projection operators 0 associated with a single constant of motion and with finite groups are derived, and it is shown that they form a resolution of the identity which renders a unique component analysis of any trial wave function, which may both restore the symmetry and lower the energy. In the projected Hartree-Fock scheme, the total wave function is approximated by a specific projection OD, in the component analysis of D, to which the variation principle is then applied. It is shown that the wave function is directly connected with the independent-particle model in the sense that it is uniquely determined by a set of N spin-orbitals, where N is the number of particles. The properties of this scheme are discussed in some detail, and references to applications are given. Author

# Descriptors:

# Subject Categories:

- Atomic and Molecular Physics and Spectroscopy
- Nuclear Physics and Elementary Particle Physics
- Quantum Theory and Relativity