General properties of the hartree-fock problem demonstrated on the frontier orbital model

The general Hartree-Fock energy in the frontier orbital model in the terms of independent variables is given. The existence conditions for extrema of this expression are derived and their relation with various types of solutions of the HF problem as RHF, UHF and complex wavefunctions is shown. The connection between overall properties of the energy surface and the local properties i.e. the stability and instability conditions of various kinds is demonstrated. The conditions for the occurrence of strange HF solutions are expressed in terms of quantities characterizing the correlation effects. This shows explicitly that the lack of respecting the electronic correlation is the reason for the occurrence of the strange HF solutions for the molecular configurations which exhibit a certain amount of diradical character.The summary of the results has been presented at the 6th Jerusalem Symposium on Quantum Chemistry and Biochemistry and at the I. Congress of Quantum Chemistry, Menton, July 1973.On leave of absence from Institute Rudjer Bokovi, Zagreb, Yugoslavia.