A general nuclear motion Hamiltonian and non-internal curvilinear coordinates.
A general nuclear motion Hamiltonian and non-internal curvilinear coordinates.
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一般核运动哈密顿量和非内曲线坐标。
DOI：
10.1063/1.4793627
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Scheurer
中科院分区：
文献类型：
--
作者：
D. Strobusch;C. Scheurer
本文导出了一般曲线坐标系下核运动的精确哈密顿量。它演示了如何将这个哈密尔顿变换成公认的表达式，如威尔逊霍华德哈密尔顿或迈耶Günthard哈密尔顿，如果一般的坐标被限制为直线或内部。此外，一个紧凑的表达式表示在非内部曲线坐标的哈密顿量，这使得这个坐标类可用于应用程序中以一种简单的方式，因为只有相对于旋转框架坐标的雅可比矩阵必须计算。一个例子，采用水模型的潜力，说明如何不同的坐标系从所有三个坐标类（直线，内部和非内部）导致振动光谱，这是非常一致的。从而证明了广义哈密顿量的适用性和正确性。
An exact Hamiltonian for nuclear motions in general curvilinear coordinates is derived. It is demonstrated how this Hamiltonian transforms into well-established expressions, such as the Wilson Howard Hamiltonian or the Meyer Günthard Hamiltonian, if the general coordinates are restricted to be rectilinear or internal. Furthermore, a compact expression for the Hamiltonian expressed in non-internal curvilinear coordinates is provided, which makes this coordinate class available for applications in a simple way, since only the Jacobian matrix with respect to the rotating frame coordinates must be calculated. An example, employing a water model potential, exemplifies how different coordinate systems from all three coordinate classes (rectilinear, internal, and non-internal) lead to vibrational spectra, which are in excellent agreement. Thereby, the applicability of the general Hamiltonian is demonstrated and also its correctness is confirmed.