Hartree–Fock density matrix equation

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Abstract
An equation for the Hartree–Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree–Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does.