Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA.
Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany.
J Chem Phys. 2023 Jun 28;158(24). doi: 10.1063/5.0157810.
The correlation discrete variable representation (CDVR) enables (multilayer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. The CDVR employs a set of grids corresponding to single-particle functions to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. In standard CDVR approaches, the number of grid points employed is tied to the number of corresponding single-particle functions. This limits the accuracy of the quadrature, which can be achieved for a given single-particle function basis. In this work, an extended CDVR approach that facilitates a numerically exact quadrature of all potential matrix elements is introduced. The number of grid points employed can be increased independent of the number of corresponding single-particle function to achieve any desired quadrature accuracy. The properties of the new scheme are illustrated by numerical calculations studying the photodissociation of NOCl and the vibrational states of CH3. Fast convergence with respect to the number of additional quadrature points is observed: Employing a single additional point in each physical or logical coordinate already ensures negligible quadrature errors.
关联离散变量表示（CDVR）使具有一般势能的（多层）多组态含时哈特ree（MCTDH）计算成为可能。CDVR 使用一组与单粒子函数相对应的网格，以有效地评估出现在 MCTDH 运动方程中的所有势能矩阵元。在标准的 CDVR 方法中，所采用的网格点数与相应的单粒子函数的数量相关。这限制了可以为给定的单粒子函数基实现的求积的精度。在这项工作中，引入了一种扩展的 CDVR 方法，该方法便于对所有势能矩阵元进行数值精确的求积。所采用的网格点数可以独立于相应的单粒子函数的数量而增加，以实现任何所需的求积精度。通过数值计算研究 NOCl 的光解和 CH3 的振动状态，说明了新方案的性质。观察到与附加求积点数的快速收敛：在每个物理或逻辑坐标中仅使用一个附加点，就可以确保可以忽略不计的求积误差。
