一种用于在一般势能面上进行计算的具有与时间无关点的矩形配置多组态含时 Hartree（MCTDH）方法。

A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces.

作者信息

Wodraszka Robert, Carrington Tucker

机构信息

Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.

出版信息

J Chem Phys. 2021 Mar 21;154(11):114107. doi: 10.1063/5.0046425.

DOI:10.1063/5.0046425

PMID:33752363

Abstract

We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products. RC-MCTDH has the important advantage that it makes it simple to use time-independent collocation points. When using time-independent points, it is necessary to evaluate the potential energy function only once and not repeatedly during an MCTDH calculation. It is inexpensive and straightforward to use RC-MCTDH with combined modes. Using more collocation points than basis functions enables one to reduce errors in energy levels without increasing the size of the single-particle function basis. On the contrary, whenever a discrete variable representation is used, the only way to reduce the quadrature error is to increase the basis size, which then also reduces the basis-set error. We demonstrate that with RC-MCTDH and time-independent points, it is possible to calculate accurate eigenenergies of CH and CH.

摘要

我们介绍了一种基于配置的多组态含时 Hartree（MCTDH）方法，该方法使用的配置点比基函数更多。我们将其称为矩形配置 MCTDH（RC-MCTDH）方法。它不要求势能是乘积之和。RC-MCTDH 具有重要优势，即使用与时间无关的配置点变得简单。使用与时间无关的点时，在 MCTDH 计算期间仅需评估一次势能函数，而无需重复评估。将 RC-MCTDH 与组合模式一起使用既经济又直接。使用比基函数更多的配置点能够在不增加单粒子函数基大小的情况下降低能级误差。相反，每当使用离散变量表示时，减少求积误差的唯一方法是增加基的大小，这也会减少基组误差。我们证明，使用 RC-MCTDH 和与时间无关的点，可以计算出 CH 和 CH 的精确本征能量。