ИСТИНА

Energy levels of a vibrating molecule can be conveniently evaluated using the vibrational self-consistent field method (VSCF).[1] Since accounting of anharmonicity within VSCF is only partial, the results can be refined using high order Møller-Plesset perturbation theory (VSCF/MPn). In a typical case of a resonance disturbance of vibrational levels the MPn series diverge. However, even divergent cases yield useful data that can be properly treated for revealing quantitative characteristics of vibrational resonances. The technique of resummation of such divergent series using Pad ́e-Hermite approximants reveals critical branch points and poles of the perturbation parameter λ considered as a complex number.[2] The location of branch points within the unit circle on the complex plane can serve as the definitive criterion of the resonance case. Alternatively, the operator version of the canonical Van Vleck perturbation theory (CVPT) yields resonance operators that correspond to another type of the dimensionless resonance criterion, expressed analytically in terms of Hamiltonian parameters hj and harmonic frequencies ωl:[3] (1) where mjl,njl are powers of the creation/annihilation operators for a normal mode Ql and summation is performed over M normal modes. Comparison of the aforementioned two conceptually different resonance criteria using a number of cases for H2O, HDO, H2S and H2C=O molecules makes it possible to rigorously adjust the latter criterion (1). We have discovered that cases with Ξj ≥ 0.09 should be considered as resonant. It was also found that this criterion shows a good level of correlation with the selection of resonances originating from the theory of vibrational polyads.[4] [1] doi:10.1002/9780470141199.ch4, R. B. Gerber and M. A. Ratner, Int. Rev. Phys. Chem., 70, 97–132 (1988). [2] doi:10.1002/wcms.92, D. Z. Goodson, WIREs Comput. Mol. Sci., 2, 743–761 (2012). [3] doi:10.1063/1.4903927, S. V. Krasnoshchekov, E. V. Isayeva and N. F. Stepanov, J. Chem. Phys., 141, 234114 (2014). [4] doi:10.1063/1.4829143, S. V. Krasnoshchekov and N. F. Stepanov, J. Chem. Phys., 139, 184101 (2013).