On convergence difficulties in the iterative Hartree-Fock procedure

Abstract

Different procedures for solving the nonlinear Hartree-Fock problem are analyzed. The classical iterative procedure involving recalculation of the one-electron density matrix in each step does not depend only on local properties of the one-electron density matrix in the previous step. Convergence difficulties arising from this fact are exhibited and analyzed for a diatomic molecule. There can result oscillation of atomic charges for larger internuclear distances. The resulting bond-order matrix does not correspond to any extremum of the expectation value of the Hamiltonian. Illustrative numerical examples are presented. Calculations for the PPP model of polyatomic chains show that the same effect can occur even for configurations slightly different from equilibrium ones.