STABILITY OF HARTREE-FOCK STATES
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. lntroducing spin explicitly into the equations, it is found that there are two classes of variational functions that are particularly suitable in investigations of stability. One variation is related to the alternate orbital transformation, while the other is connected with Hund's rule and the conditions for ferromagnetism. The first of these variations is used in numerical examples. In the first example the stability of a restricted Hartree-Fock wave function for LiH relative to an unrestricted one is investigated. It is found that for the chosen basis set, the restricted Hartree-Fock wave function is stable at the equilibrium internuclear distance (3.0 a.u.), but that at 4.0 a.u. it becomes unstable. A second example investigates the relative stability of the restricted and unrestricted HartreeFock 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. (auth)
- Research Organization:
- Univ. of Uppsala
- NSA Number:
- NSA-16-033637
- OSTI ID:
- 4780279
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 127; ISSN PHRVA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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