Fundamental analysis of singular and resonance phenomena in vibrational polyads of the difluorosilylene molecule

The singular structure of lower vibrational states of the difluorosilylene molecule (up to four total excitation quanta) is studied by expansion of energies of each state into series of the high-order Rayleigh–Schrödinger perturbation theory and analysis of their implicit properties of multiple-valuedness using Padé–Hermite fourth-order approximants. The quartic surface of potential energy in dimensionless normal coordinates is calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of values of multiple-valued approximants reproduces the variational solution with a high accuracy, while other values (beginning with the fourth polyad) in many cases coincide with energies of other states of the same polyad. The Fermi and Darling–Dennison resonances are analyzed based on facts of coincidence of singular complex branch points of the approximants for mutually interacting states inside a unit circle or near it on the complex plane. It is found that a pair of states can have several coinciding branch points of the solutions (in particular, inside the unit circle). A conclusion is made that this approach is an effective method for the determination of the polyad structure of vibrational states. Calculation parameters necessary for the reproducibility of key results are selected. The calculations are carried out by means of a Fortran-based software package using an arithmetic calculation package with a long mantissa of real numbers (200 digits).