A second-order multi-reference perturbation method for molecular vibrations

We present a general multi-reference framework for treating strong correlation in vibrational structure theory, which we denote the vibrational active space self-consistent field (VASSCF) approach. Active configurations can be selected according to excitation level or the degrees of freedom involved, or both. We introduce a novel state-specific second-order multi-configurational perturbation correction that accounts for the remaining weak correlation between the vibrational modes. The resulting VASPT2 method is capable of accurately and efficiently treating strong correlation in the form of large anharmonic couplings, at the same time as correctly resolving resonances between states. These methods have been implemented in our new dynamics package DYNAMOL, which can currently treat up to four-body Hamiltonian coupling terms. We present a pilot application of the VASPT2 method to the trans isomer of formic acid. We have constructed a new analytic potential that reproduces frozen core CCSD(T)(F12*)/cc-pVDZ-F12 energies to within 0.25% RMSD over the energy range 0-15 000 cm^-1. The computed VASPT2 fundamental transition energies are accurate to within 9 cm^-1 RMSD from experimental values, which is close to the accuracy one can expect from a CCSD(T) potential energy surface.