Transformation of rotational Hamiltonian coefficients between reductions and axis representations
Transformation of rotational Hamiltonian coefficients between reductions and axis representations
复制标题
旋转哈密顿系数在约简和轴表示之间的变换
DOI：
10.1016/0022-2852(81)90050-3
复制
发表时间：
1981
影响因子：
1.4
通讯作者：
W. Murphy
中科院分区：
文献类型：
--
作者：
W. Murphy
众所周知，使用最适合于所考虑的分子（3，4）的简化哈密顿量（I）和轴系统（2）来确定非对称顶部转动哈密顿量的系数是有利的。两个比较流行的约化被指定为（1）A约化和S约化，后者对近对称顶的情形是有用的。出于各种原因，可能感兴趣的是将使用一个归约和轴系统计算的系数变换到另一个。例如，在这个实验室中，已经编写了一个程序来计算非对称陀螺分子的拉曼（和红外）谱带轮廓（5）。本程序是用A约化哈密顿量和I '轴系统计算转动能级和波函数的。将文献系数转换到这种情况下以用于生成所需数据似乎更容易，而不是在每种不同情况下使用单独版本的程序。对于四次离心畸变系数，已经给出了用不同的轴系统和/或约化的哈密顿量获得的系数之间的变换（6）。在目前的工作中，这种方法已被扩展到包括六次系数和推广产生一个计算机程序，可用于任意组的系数之间的转换。该方法包括将可用系数Y（i）变换为由沃森（I）给出的可确定系数Xi：B，，，B，，，B，，，，这里，系数Xi不同于Ref. (1)因为为了方便在数值变换（3）中它们被二次系数的和归一化。如果需要坐标系变换，则适当地置换可确定的系数。然后，执行从可确定系数到期望系数的逆变换以获得期望结果。因此，变换可以以矩阵形式表示为：
It is well known that it is advantageous to determine the coefficients of the asymmetric-top rotational Hamiltonian using a reduced Hamiltonian (I) and axis system (2) which is best suited for the molecule being considered (3, 4). Two ofthe more popular reductions have been designated (1) as the A and the S reductions, the latter being useful for near-symmetric-top cases. For various reasons it may be of interest to transform coefficients calculated using one reduction and axis system to another. For example, in this laboratory a program has been written to calculate Raman (and infrared) band contours for asymmetric-top molecules (5). This program has been set up for rotational energy levels and wavefunctions calculated using an A-reduced Hamiltonian and a I’axis system. It appeared to be easier to convert literature coefficients to this case for use in generating the required data as opposed to having a separate version of the program for use in each of the different cases. The transformation between coefficients obtained with different axis systems and/or reduced Hamiltonians has been presented for quartic centrifugal distortion coefficients (6). In the present work this method has been extended to include sextic coefficients and generalized to produce a computer program which may be used to transform between arbitrary sets of coefficients. The method consists of transforming the available coefficients Y (to the determinable coefficients Xi as given by Watson (I): B,, B,, B,, T,,, T,,, T,,, T,, i;,@,,,, Q,,, Q’,,,, Q,, $,, &, and &. Here, the coefficients Xi differ from those in Ref.(1) in that they are normalized by the sum of the quadratic coefficients for convenience in the numerical transformation (3). If an axis system transformation is desired, the determinable coefficients are suitably permuted. Then, the reverse transformation from the determinable coefficients to the desired coefficients is carried out to obtain the desired result. Thus, the transformation may be expressed in matrix form as