Virtual orbitals for obtaining rapid convergence in configuration interaction calculations

A perturbational method is used to generate virtual orbitals intended to yield rapid convergence in configuration interaction calculations. It is shown that the problem of finding the orbitals and pair functions which maximize the interaction with the Hartree-Fock wavefunction can be solved exactly. The resulting first-order semi-internal virtual orbitals are determined by a simple closed expression. All further semi-internal excitations vanish to first order. As an example, the method of this work is applied to the semi-internal orbitals of the ground state of the carbon +1 ion. The resulting first order orbitals compare very well to corresponding variational virtual orbitals.