On the variational computation of a large number of vibrational energy levels and wave functions for medium-sized molecules.
On the variational computation of a large number of vibrational energy levels and wave functions for medium-sized molecules.
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关于中等尺寸分子的大量振动能级和波函数的变分计算。
DOI：
10.1063/1.3187528
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
A. Császár
中科院分区：
文献类型：
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作者：
E. Mátyus;J. Šimunek;A. Császár
在最近的出版物[J. Chem. Phys. 127，084102（2007）]中，几乎可变的DEWE方法（DEWE表示沃森哈密顿量的离散变量表示，使用Eckart框架和任意选择的坐标中表示的势能面的精确包含）被开发用于计算介质的大量（ro）振动本征对。具有单个明确定义的最小值的尺寸半刚性分子。在本出版物中，DEWE以及任何DEWE类型方法的内存、CPU和硬盘使用要求都得到了仔细考虑、分析和优化。特别注意稀疏矩阵向量乘法，最昂贵的部分的计算，并在迭代Lanczos eigensolver的速率确定步骤，包括频谱变换，reorthogonalization，并重新开始的迭代。在相当详细地讨论了动力学的改进。给出了甲烷分子（12）CH（4）和（12）CH（2）D（2）同位素振动带起源的数值计算结果。在这些计算期间，在个人计算机上处理的最大矩阵的大小为（4x10（8））x（4x10（8））。确定振动本征对的最佳策略在很大程度上取决于所需计算的实际细节。然而，对于一个通常的情况下，需要大量的最低本征对的哈密顿矩阵的组合的厚重启Lanczos方法，移位折叠过滤，和定期reorthogonalization似乎导致在计算上最可行的方法。
In a recent publication [J. Chem. Phys. 127, 084102 (2007)], the nearly variational DEWE approach (DEWE denotes Discrete variable representation of the Watson Hamiltonian using the Eckart frame and an Exact inclusion of a potential energy surface expressed in arbitrarily chosen coordinates) was developed to compute a large number of (ro)vibrational eigenpairs for medium-sized semirigid molecules having a single well-defined minimum. In this publication, memory, CPU, and hard disk usage requirements of DEWE, and thus of any DEWE-type approach, are carefully considered, analyzed, and optimized. Particular attention is paid to the sparse matrix-vector multiplication, the most expensive part of the computation, and to rate-determining steps in the iterative Lanczos eigensolver, including spectral transformation, reorthogonalization, and restart of the iteration. Algorithmic improvements are discussed in considerable detail. Numerical results are presented for the vibrational band origins of the (12)CH(4) and (12)CH(2)D(2) isotopologues of the methane molecule. The largest matrix handled on a personal computer during these computations is of the size of (4x10(8))x(4x10(8)). The best strategy for determining vibrational eigenpairs depends largely on the actual details of the required computation. Nevertheless, for a usual scenario requiring a large number of the lowest eigenpairs of the Hamiltonian matrix the combination of the thick-restart Lanczos method, shift-fold filtering, and periodic reorthogonalization appears to result in the computationally most feasible approach.