THE STABILITY OF HARTREE-FOCK STATES
Abstract
The condition that must be satisfied by a Hartree-Fock wave function if it is to give an absolute minimum of the energy, is derived by variation of the one-electron density matrix. If the energy is not an absolute minimum, the state is unstable. Introducing spin explicitly into the equations, there are two classes of variational functions which are particularly suitable in investigations of stability. The one variation is related to the alternate orbital transformation, while the other is connected with Hund's rule and the conditio s for ferromagnetism. The first of these variations is used in two numerical examples. In the first example the stability of a restricted Hartree-Fock wave function for LiH relative to an unstricted one is investigated. For the chosen basis set, he restricted Hartree-Fock wave function is stable at the equilibrium internuclear distance (3.0 au), but that at 4.0 au it becomes unstable. The second example investigates the relative stability of the restricted and unrestricted Hartr eFock approximations for the electron gas. It is shown that at a sufficiently low density, the unrestricted Hartree-Fock method gives a lower energy. The resulting state has a nonzero spin density. The importance of the stability condition in atomic, molecular and solid state problems is emphasized. Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 15, 1961
- Accession Number
- AD0278504
Entities
People
- William H. Adams
Organizations
- Uppsala University