A comparison of different methods in determining energies and geometries of open-shell systems

Abstract

Three methods of obtaining eigenvectors for open-shell systems, namely the Roothaan restricted open-shell method, the “half-electron” method, and the use of ground state orbitals, are compared with each other both on a formal basis, and by contrasting theab initio energies predicted by these schemes for a series of radicals and triplets. The r.m.s. improvement in the energy of eight radicals by use of the Roothaan method rather than the half-electron approximation amounts to 4.8 kcal mole⁻¹, whereas the r.m.s. improvement for nineteen triplet states is 8.2 kcal mole⁻¹. Optimum geometries predicted by these two methods do not differ appreciably. The use of closed-shell eigenvectors rather than those of the half-electron method leads to very large errors for triplet states whose electron density distributions differ appreciably from those of the ground state.