ИСТИНА

A presence of vibrational cubic Fermi and quartic Darling-Dennison resonances in a molecule requires the inclusion of the corresponding resonance terms in the form of the effective Hamiltonians describing a certain spectral range. There are several ways of detecting such resonances, both by ab initio theoretical methods and experimentally, using various techniques. The vast majority of all these approaches have a significant portion of uncertainty in dealing with weaker resonances. In other words, while theoretical methods rely on somewhat empirical criteria,1-2 experimental methods also depend on certain human choices. In a wider context, a reliable knowledge of all resonances defines the form of a polyad quantum number. A fundamental method of studying vibrational resonances can be established by combining the Rayleigh-Schrödinger perturbation theory (RSPT) with a subsequent procedure of representing typically divergent large order vibrational energy series by multivalued Padé-Hermite approximants (PHA). So far, a number of such studies were accomplished on non-linear molecules.3-4 In this work we extend this method to a few isotopologues of a three-atomic linear molecule OCS. The ab initio vibrational Watson Hamiltonian with Sayvetz condition is used to formulate purely vibrational problem. Large order (~200) RSPT series are calculated for vibrational states up to 12-th polyad. Obtained series are treated by quartic PHA and their critical points were found as discriminant roots. According to Katz theorem, a pair of matrix eigenvalues may be connected by Hermitian conjugate complex critical points. The definitive condition of a resonance case can be formulated as a location of critical points within a unit circle on the complex plane. Moreover, non-principal branches of quartic approximants often coincide with other nearby resonant states. In conclusion, the OCS literature resonances (0,40,–1) and (1,–20,0) are acknowledged,5 in accord with the polyad form (2,4,1).6 Moreover, the presence of a weaker interpolyad resonance (5,00,–2) is theoretically found as well, approving the experimental observations in vibration-rotation spectra.7 References [1] J.M.L. Martin, T.J. Lee, P.R. Taylor, J.-P. François, J. Chem. Phys. 103, 2589, 1995 [2] V. Barone, J. Chem. Phys., 122, 014108, 2005 [3] A.N. Duchko, A.D. Bykov, J. Chem. Phys. 143, 154102, 2015 [4] X. Chang, E.O. Dobrolyubov, S.V. Krasnoshchekov, Phys. Chem. Chem. Phys., 24, 6655, 2022 [5] Y. Morino, T. Nakagawa, J. Mol. Spectrosc. 26, 496, 1968 [6] José Zúñiga, A. Bastida, M. Alacid, A. Requena, J. Chem. Phys. 113, 5695, 2000 [7] E. Rbaihi, A. Belafhal, J. Vander Auwera, S. Naïm, A. Fayt, J. Mol. Spectrosc. 191, 32, 1998