多层多组态含时Hartree方法的实现及其对Henon-Heiles哈密顿量和吡嗪的应用
Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
摘要：
讨论了多层多配置时间相关Hartree（ML-MCTDH）方法，并且给出了基于Manthe [J. Chem. Phys. { \bf 128}，164116（2008）]给出的递归ML-MCTDH算法的用于任意层数的完全通用的实现。该方法首先适用于广义Henon-Heiles（HH）哈密尔顿。对于6D HH，ML-MCTDH的开销使得该方法比MCTDH慢，但是对于18 D HH，ML-MCTDH开始具有竞争力。我们报告，以及1458 D模拟HH哈密顿使用七层计划。用Raab { \em et. al.} [J. Chem. Phys. { \bf 110}，936（1999）]为该方法提供了现实的分子测试情况。快速和小型ML-MCTDH计算需要参考MCTDH计算的一小部分时间和资源，已经提供了具有所有正确特征的光谱。接受稍大的偏差，计算可以加快到只需7分钟。当推动收敛的方法，类似的质量比最好的可用的MCTDH基准，这是基于波包与$4.6\times 10^7$时间相关的系数，得到了一个更紧凑的波函数组成的只有$4.5\times 10^5$系数，需要更短的计算时间。
英文摘要：
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. {\bf 128}, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab {\em et. al.} [J. Chem. Phys. {\bf 110}, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 minutes. When pushing the method towards convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with $4.6\times 10^7$ time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only $4.5\times 10^5$ coefficients and requiring a shorter computation time.
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