Фундаментальный анализ сингулярных и резонансных явлений в колебательных полиадах молекулы дифторсилилена

Abstract

The singular structure of the lower vibrational states of the difluorosilylene molecule (up to four quanta of total excitation) was studied by expanding the energies of each state in the series of high-order Rayleigh-Schrödinger perturbation theory and analyzing their implicit multivalued properties using the fourth degree Padé-Hermite approximants. The quartic potential energy surface in dimensionless normal coordinates was calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of the values of multivalued approximants reproduces the variational solution with high accuracy, while other values, starting from the fourth polyad, in many cases coincide with the energies of other states of the polyad. The Fermi and Darling-Dennison resonances are analyzed on the basis of the coincidence of the singular complex branch points of the approximants for interacting states inside or near a circle of unit radius on the complex plane. It was found that a pair of states can have several coinciding branch points of solutions, including those inside the unit circle. It is concluded that this approach is an effective method for determining the polyad structure of vibrational states. The calculation parameters are selected, which are necessary for the reproducibility of key results. The calculations were carried out using a software package in the Fortran language using a package of arithmetic calculations with a long mantissa of real numbers (200 digits).