Vibrational coupled cluster theory with full two-mode and approximate three-mode couplings: the VCC[2pt3] model.

Vibrational coupled cluster (VCC) calculations of molecular vibrational energy levels can be characterized by the number of modes coupled in the Hamiltonian operator and the number of modes simultaneously excited in the parameter space. We propose a VCC model which includes all two-mode couplings in the Hamiltonian and excitation space but only an approximate treatment of three-mode couplings. The approximation is based on a perturbational analysis and the introduced concepts can also be used for even more accurate treatments. The method is iterative and allows the use of VCC response theory to obtain excitation energies. Furthermore, the method is shown to scale with the number of vibrational modes to the third power which is no higher than the corresponding VCC model with only two-mode couplings. Encouraging benchmark calculations are given for a test set of three- and four-atomic molecules. The fundamentals of the larger ethylene oxide molecule have been calculated as well using a grid-based potential energy surface obtained from electronic coupled cluster theory with singles, doubles, and perturbative triples (CCSD(T)).