Comparative study of multireference perturbative theories for ground and excited states

Three recently developed multireference perturbation theories (PTs)-generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH2 system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied. Both Moller-Plesset (MP) and Epstein-Nesbet partition are used for MCPT and SS-MRPT, while GVVPT uses MP partitioning. An important thrust in our comparative study is to ascertain the degree of interplay of dynamical and nondynamical correlation for both ground and excited states. The same basis set and the same set of orbitals are used in all calculations to keep artifactual differences away when comparing the results. Nonparallelity error is used as a measure of the performance of the respective theories. Significant differences among the three methods appear when an intruder state is present. Additionally, difficulties arise (a) in MCPT when the choice of a pivot determinant becomes problematic, and (b) in SS-MRPT when there are small coefficients of the model function and there is implicit division by these coefficients, which generates a potential instability of the solutions. Ways to alleviate these latter shortcomings are suggested.