Abstract A theoretical description of IR spectroscopy data for a hydrogen bond (HB) is constructed on the base of trigonometric double-well potential for which an exact analytic solution of the one-dimensional Schrodinger equation (SE) is available. The wave functions (full orthogonal basis) are expressed via the spheroidal function while its spectrum of eigenvalues yields the corresponding energy levels (both special functions are implemented in Mathematica). Then an approximate solution of two-dimensional SE taking into account the excitation state of heavy atoms stretching mode in HB is obtained. It is constructed by decomposing over the above mentioned basis within the framework of standard adiabatic separating the proton motion from that of the heavy atoms. We exemplify the general theory by calculating the IR relative absorption intensities for HB in the Zundel ion H 5 O 2 + (oxonium hydrate).

中文翻译：

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从精确可解的薛定谔方程计算氢键的红外吸收强度

摘要 基于三角双阱势，对氢键（HB）的红外光谱数据进行了理论描述，其中一维薛定谔方程（SE）的精确解析解是可用的。波函数（完全正交基）通过椭球函数表示，而其特征值谱产生相应的能级（这两个特殊函数都在 Mathematica 中实现）。然后得到了考虑重原子激发态在HB中拉伸模式的二维SE的近似解。它是通过在标准绝热分离质子运动与重原子运动的框架内分解上述基础​​而构建的。