A quantitative study of the vibrational resonance phenomena of the HOF (hypoflorous acid) molecule for over 100 of its lower vibrational energy levels was carried out using resummation techniques of the Rayleigh-Schrodinger perturbation theory (RSPT) divergent series. Anharmonic vibrational states of HOF were calculated by the matrix configuration interaction (VCI) method, the second-order Van Vleck operator perturbation theory (CVPT2), and the high-order RSPT series. CVPT2 predicts a weak Fermi resonance (0,1,-2) and a medium second-order resonance (1,-2,-1). Resummation of the high-order (lambda(n), 0 <= n <= 203) divergent RSPT series, using multivalued quartic 40-th degree Pade-Hermite diagonal approximants up to terms O(lambda(n+1)) for a subset of low-lying states, restored their correct energies. Considering lambda as a complex parameter, solution branch points were found as roots of discriminant polynomials. The coincidence of dominant branch points for pairs of states according to the Katz theorem and the condition vertical bar lambda vertical bar = Re(lambda)(2) + Im(lambda)(2) <= 1, revealed resonance couplings. The block-diagonal polyad structure of studied states was reconstructed and the polyad quantum number P = ( 8, 3, 2) form determined as being good for all studied states, up to nearly 14,000 cm(-1). Advantages of the developed technique for quantitative characterization of resonance and polyad phenomena is demonstrated. (C) 2021 Elsevier Ltd. All rights reserved.
