Direct calculation of the one-electron density matrix for closed-shell systems

It has been found that independent parameters in the variation of a one-electron density matrix (DM) for closed-shell systems are elements of its unitary transformed matrix and, in a special case, reduce to the rotation parameters that connect the occupied and virtual orbital spaces in the exponential transformed self-consistent field method. To obtain the unitary matrix of transformation, a simpler method of orthogonalizing the column vectors of the DM has been proposed instead of its diagonalization. An iterative method has been formulated to determine these independent parameters. Several test calculations using this method reproduced the results using the Hartree–Fock–Roothaan method.