The Importance of Orbital Analysis

It has long been known that there are multiple solutions to the self-consistent Hartree-Fock equations. This can be problematic if careful attention is not given to the orbital occupation and electronic state in the converged wave function. The issues with convergence have been demonstrated through the calculation of potential energy curves for O₂, F₂, Cl₂, Br₂, LiF, NaCl, CaO, MgO, ScO, FeO, TiO, YO, and ZrO. Hartree-Fock (HF) calculations were used to compute the points on the potential energy surface, with dynamic electron correlation included through the use of the completely renormalized coupled cluster, including singles, doubles, and perturbative triples [CR-CC(2,3)]. Even in regions with little to no multireference character, as determined by the T₁/D₁ diagnostics, HF does not always converge to the ground electronic state. As HF provides the reference wave function for CR-CC(2,3), and other post-Hartree-Fock ab initio methods, treatment of electron correlation does not necessarily result in a smooth potential energy curve, especially if HF is unable to produce a smooth curve. Even the convergence rate of multireference methods can be affected as the initial orbitals that form the basis for multireference calculations are frequently obtained from HF calculations.