The use of effective Hamiltonians for the treatment of avoided crossings. I. Adiabatic potential curves

Abstract

Most of the CI algorithms for excited states treat variationally a certain class of determinants and add a perturbative contribution for the remaining ones. In weakly avoided crossings between states of the same symmetry, if one starts from multiconfigurational wavefunctions resulting from truncated CI, artefacts (concerning both the energies and the wavefunctions) may appear in usual non-degenerate perturbative treatment of the remaining CI contributions. This difficulty, due to local quasi-degeneracy, is exemplified for analytical examples and numerical large-scale configuration interactions. Applying the quasi-degenerate perturbation theory in a subspace of rationally selected multiconfigurational adiabatic wavefunctions leads to the construction of an effective Hamiltonian, the solutions of which do not exhibit the previously mentioned defects. The method (an effective Hamiltonian version of the CIPSI algorithm) may be applied all along the potential curves without encountering the intruder-state problem.