The kinetic energy operator for triatomic molecules with coordinate or distance-dependent nuclear masses has been derived. By combination of the chain rule method and the analysis of infinitesimal variations of molecular coordinates, a simple and general technique for the construction of the kinetic energy operator has been proposed. The asymptotic properties of the Hamiltonian have been investigated with respect to the ratio of the electron and proton mass. We have demonstrated that an ad hoc introduction of distance (and direction) dependent nuclear masses in Cartesian coordinates preserves the total rotational invariance of the problem. With the help of Wigner rotation functions, an effective Hamiltonian for nuclear motion can be derived. In the derivation, we have focused on the effective trinuclear Hamiltonian. All necessary matrix elements are given in closed analytical form. Preliminary results for the influence of non-adiabaticity on vibrational band origins are presented for ${\text{H}}_3^{+}$.

中文翻译：

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距离相关有效核质量的动能算子：三原子分子的推导

推导了具有与坐标或距离相关的核质量的三原子分子的动能算子。通过链规则法和分子坐标无穷小变化的分析相结合，提出了一种简单而通用的动能算子构造方法。关于电子和质子质量的比例，研究了哈密顿量的渐近性质。我们已经证明，一个临时在直角坐标系中引入与距离（和方向）相关的核质量，可以保留问题的总旋转不变性。借助维格纳旋转函数，可以得出有效的核运动哈密顿量。在推导中，我们集中在有效的三核哈密顿量上。所有必要的矩阵元素均以封闭的分析形式给出。给出了非绝热对振动带起源的影响的初步结果。${\text{H}}_3^{+}$。