The relationship between the unrestricted and projected Hartree–Fock methods in a simple three‐electron model system

Abstract

AbstractVarious forms of the unrestricted Hartree–Fock (UHF) scheme are studied for a simple three‐electron model system, represented by the PPP (Pariser–Parr–Pople) π‐electron model of the allyl radical. Both spin and space symmetry are violated in the UHF trial wave function, either individually or simultaneously. A comparison with the projected Hartree–Fock (PHF) schemes studied earlier is made and the effect of the order in which various symmetries are broken in both UHF and PHF schemes is studied. The effectiveness of various schemes follows from a comparison of the correlation energy and the wave function is obtained by various UHF (or projected UHF) and PHF schemes, in the whole range of the coupling constant, with the corresponding quantities given by the exact solution of the model. Finally, the implications of the stability of the restricted HF solutions for the behavior of various single‐ and multiparameter UHF and PHF schemes are briefly outlined and exemplified on the studied model.