Hartree–Fock orbital instability envelopes in highly correlated single-reference wave functions

The effects of Hartree–Fock orbital instabilities on force constant predictions at both Hartree–Fock and correlated levels of theory are investigated. Due to the quadratic dependence of the second derivative of correlated energies on the orbital rotation parameters, anomalous force constant singularities enveloped by “instability volcanoes” are given by the single-reference correlation methods examined here. Infinite-order coupled-cluster methods are indeed affected by the reference instability, but over a rather small region of the potential surface, whereas perturbative triples corrections tend to widen the coupled-cluster volcano. Finite-order many-body perturbation theory yields very wide volcanoes, and corresponding predictions of vibrational spectra may be seriously compromised if the geometry of interest lies at all in the vicinity of an instability in the reference determinant.