Hypoflorous acid (HOF): A molecule with a rare (1,-2,-1) vibrational resonance and (8,3,2) polyad structure revealed by Padé-Hermite resummation of divergent Rayleigh-Schrödinger perturbation theory series

• Fermi resonances are characterized by common branch points of coupled states. • Vibrational polyad structure of HOF was found using Pade-Hermite approximants. • The dynamic (0,2,-3) resonance is a key for the organization of HOF excited states. 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-Schrödinger 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 ( λ n , 0 ≤ n ≤ 203 ) divergent RSPT series, using multivalued quartic 40-th degree Padé-Hermite diagonal approximants up to terms O ( λ n + 1 ) for a subset of low-lying states, restored their correct energies. Considering λ 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 | λ | = Re ( λ ) 2 + Im ( λ ) 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.