Self-consistent molecular orbital methods. XVI. Numerically stable direct energy minimization procedures for solution of Hartree–Fock equations

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Abstract
Direct energy minimization methods are examined for solution of the Hartree–Fock equations in a basis expansion. Given a set of trial spin– orbitals, an initial direction for a univariate search of spin–orbital space is specified using general energy-weighted coordinates. The first energy minimum in such a search then provides an initial point for the next iterative step. Techniques are proposed for the maintenance of spin–orbital continuity during this process. Comparison of various energy-weighted coordinates indicates that most effective convergence is achieved if the search path is chosen to pass through the point corresponding to the classical procedure involving the construction of successive approximations to the Fock matrix. The utility of the new method is illustrated by the completion of a previous systematic study of Hartree–Fock energies for small organic species.