Vibrational resonance phenomena of the OCS isotopologues studied by resummation of high-order Rayleigh–Schrödinger perturbation theory

The high-order Rayleigh–Schrödinger perturbation theory (RSPT) can be applied for studying anharmonic vibrational problem formulated with the isomorphic Hougen Hamiltonian, but the resulting series usually possess slowly convergent or even divergent behavior. This flaw can be overcome by the resummation of such series with the multi-valued Hermite–Padé approximant (HPA) that accurately reproduces variational matrix eigenvalues provided the basis set is the same. Besides, the state-to-state juxtaposition of HPA branch points can provide an accurate quantitative description of resonance phenomena. Such resummation was earlier proven to be efficient for three- and four-atomic asymmetric top molecules, as well as for linear molecules CO2 and C2H2. In the present work, this technique was systematically applied for studying vibrational resonances of practically important isotopologues of the linear carbonyl sulfide molecule (16O12C32S, 16O12C34S, 16O13C32S, 18O12C32S, 16O12C33S, 16O13C34S). The isomorphic Hamiltonians were constructed using the ab initio equilibrium geometry and quartic PES calculated at the CCSD(T)/cc-pV(Q+d)Z level. The analysis of HPA common branch points of 125 vibrational states for each isotopologue predicted comprehensive resonance pictures. These resonances reproduced most of experimentally observed couplings and indicated a possible break down of the known polyad formula P=2v1+v2+4v3. The demonstrated efficiency of this purely ab initio approach opens a perspective of further studies of resonances phenomena of new and hardly accessible molecules.