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 (${\lambda }^n,0\le n\le 203$) divergent RSPT series, using multivalued quartic 40-th degree Padé-Hermite diagonal approximants up to terms $O\left({\lambda }^{n+1}\right)$ 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 $\left|\lambda \right|=\mathfrak{Re}{\left(\lambda \right)}^2+\mathfrak{Im}{\left(\lambda \right)}^2\le 1,$ 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.

使用Rayleigh-Schrödinger微扰理论（RSPT）发散级数的恢复技术，对HOF（次花酸）分子在其较低的100个较低振动能级下的振动共振现象进行了定量研究。通过矩阵组态相互作用（VCI）方法，二阶Van Vleck算子摄动理论（CVPT2）和高阶RSPT级数来计算HOF的非谐振动态。CVPT2预测弱的费米共振（0,1，–2）和中等的二阶共振（1，–2，–1）。恢复高阶（${\lambda }^{ñ}，0\le ñ\le 203$）发散的RSPT系列，使用多值四次方四十度Padé-Hermite对角线逼近项 $Ø（{\lambda }^{ñ+\mathrm{1个}}）$对于低洼状态的子集，恢复其正确的能量。考虑中$\lambda$作为一个复杂参数，解决方案分支点被发现为判别多项式的根。根据Katz定理和条件的状态对的优势分支点的重合$\left|\lambda \right|=\mathfrak{关于}{（\lambda ）}^{\mathrm{2个}}+\mathfrak{我是}{（\lambda ）}^{\mathrm{2个}}\le \mathrm{1个}，$揭示共振耦合。重构了研究态的块对角多元结构，并得到了多元量子数$P=（8，3，\mathrm{2个}）$ 被确定为对所有研究状态均有利的形态，长达近14,000厘米${}^{-\mathrm{1个}}$。演示了用于共振和多元信号现象的定量表征的先进技术的优势。