Nonorthogonal molecular orbital method: single-determinant theory.

Using the variational principle, we have derived a variant of the Adams-Gilbert equation for nonorthogonal orbitals of a single-determinant wave function, which we name the modified Adams-Gilbert equation. If we divide the molecular system into several subsystems, such as bonds, lone pairs, and residues, we can solve the equations for the subsystems one by one. Thus, this procedure has linear scaling. We have presented a practical procedure for solving the equations that is also applicable to macromolecular calculations. The numerical examples show that the procedure yields, with reasonable effort, results comparable with those of the Hartree-Fock-Roothaan method for orthogonal orbitals. To resolve the convergence difficulty in the self-consistent-field iterations, we have found that virtual molecular-orbital shifts are very effective.