The properties of the unrestricted Hartree-Fock (UHF) wave function are discussed with particular attention to the vicinity of the "critical point" where the UHF wave function starts to differ from the restricted Hartree-Fock (RHF) one. By considering the simplest analytically solvable model, the origin of the critical point is analysed, based on the decomposition of the DODS determinant in terms of the full CI wave functions. It is shown that the UHF energy curve departs from the RHF one by exhibiting a discontinuity of the second derivative. (The first derivative of the UHF energy is continuous for any system.) The wave function obtained by subsequent spin projection of the UHF wave function (i.e. without performing orbital reoptimization) gives a discontinuity already for the first derivative of the energy, showing that this procedure is inapplicable to calculate potential curves.
ASJC Scopus subject areas
- Physics and Astronomy(all)