School of Chemistry, University of Leeds, Leeds LS2 9JT, UK.
J Phys Chem A. 2013 Aug 15;117(32):6948-59. doi: 10.1021/jp310976d. Epub 2013 May 23.
In this paper, a new numerical implementation and a test of the modified variational multiconfigurational Gaussian (vMCG) equations are presented. In vMCG, the wave function is represented as a superposition of trajectory guided Gaussian coherent states, and the time derivatives of the wave function parameters are found from a system of linear equations, which in turn follows from the variational principle applied simultaneously to all wave function parameters. In the original formulation of vMCG, the corresponding matrix was not well-behaved and needed regularization, which required matrix inversion. The new implementation of the modified vMCG equations seems to have improved the method, which now enables straightforward solution of the linear system without matrix inversion, thus achieving greater efficiency, stability and robustness. Here the new version of the vMCG approach is tested against a number of benchmarks, which previously have been studied by split-operator, multiconfigurational time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH) techniques. The accuracy and efficiency of the new implementation of vMCG is directly compared with the method of coupled coherent states (CCS), another technique that uses trajectory guided grids. More generally we demonstrate that trajectory guided Gaussian based methods are capable of simulating quantum systems with tens or even hundreds of degrees of freedom previously accessible only for MCTDH and ML-MCTDH.
本文提出了一种新的数值实现方法，并对修正变分多组态高斯（vMCG）方程进行了测试。在 vMCG 中，波函数表示为轨迹引导高斯相干态的叠加，波函数参数的时间导数是从一组线性方程组中得到的，而这组线性方程组又遵循同时应用于所有波函数参数的变分原理。在 vMCG 的原始公式中，相应的矩阵表现不佳，需要正则化，这需要矩阵求逆。修正 vMCG 方程的新实现似乎改进了该方法，现在可以直接求解线性系统，而无需矩阵求逆，从而实现更高的效率、稳定性和鲁棒性。在此，我们用 vMCG 方法对一些基准进行了测试，这些基准以前曾被分裂算符、多组态含时哈特里（MCTDH）和多层 MCTDH（ML-MCTDH）技术研究过。vMCG 的新实现的准确性和效率与耦合相干态（CCS）方法直接进行了比较，后者是另一种使用轨迹引导网格的技术。更一般地，我们证明了基于轨迹引导高斯的方法能够模拟以前只有 MCTDH 和 ML-MCTDH 才能模拟的具有数十甚至数百个自由度的量子系统。
