Further studies in configuration interaction methods
The combined configuration interaction (CI)-perturbation approximations of Gershgorn and Shavitt and the orbitally ordered CI method of Cooper and Pounder (on its own or including a modification implied by Roos, Taylor and Siegbahn) are applied to the calculation of the electron spin resonance hyperfine coupling constants of two small doublet state radicals BeH and NH2. On the one hand, it is found that, despite the absence of variational upper bounds to the resultant energies effectively nullifying the selection of the optimum expansion from several alternatives on the basis of the criterion of least eigenvalue, generally acceptable calculated values for the BeH hyperfine coupling constants can be obtained using no more orbitals to construct the active space of the wave function than that number normally employed in a minimal basis set calculation. On the other hand, it is shown that, although the method to correctly order the orbitals is much more complicated for open-shell systems, indeed, the concept of an orbital order may be lost, over 80% of the correlation energy can be recovered besides closely reproducing the isotropic hyperfine coupling constants of, e. g., the NH2 full single and double replacement CI calculation using of only one-tenth of the configurations. Of the four distinguishable methods to generate modified virtual orbitals (MVO's) considered, in addition, the modified Hartree-Fock operator is shown to be the best (i. e., in terms of optimum convergence properties of the corresponding MVO's for least computational effort). The optimum values of the variable associated parameter are found to lie close to ɤ= -15 for both singlet and doublet state molecules which is significant if the method is to have wide generality.