Ellerbrock Roman, Manthe Uwe
Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA.
Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany.
J Chem Phys. 2022 Apr 7;156(13):134107. doi: 10.1063/5.0088509.
The correlation discrete variable representation (CDVR) facilitates (multi-layer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. It employs a layered grid representation to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. The original CDVR approach and its multi-layer extension show a hierarchical structure: the size of the grids employed at the different layers increases when moving from an upper layer to a lower one. In this work, a non-hierarchical CDVR approach, which uses identically structured quadratures at all layers of the MCTDH wavefunction representation, is introduced. The non-hierarchical CDVR approach crucially reduces the number of grid points required, compared to the hierarchical CDVR, shows superior scaling properties, and yields identical results for all three representations showing the same topology. Numerical tests studying the photodissociation of NOCl and the vibrational states of CH demonstrate the accuracy of the non-hierarchical CDVR approach.
相关离散变量表示（CDVR）有助于使用一般势进行（多层）多组态含时 Hartree（MCTDH）计算。它采用分层网格表示来有效评估出现在 MCTDH 运动方程中的所有势矩阵元。原始的 CDVR 方法及其多层扩展呈现出一种层次结构：当从上层向下层移动时，不同层所采用网格的大小会增加。在这项工作中，引入了一种非层次 CDVR 方法，该方法在 MCTDH 波函数表示的所有层都使用结构相同的求积法。与层次 CDVR 相比，非层次 CDVR 方法显著减少了所需的网格点数，显示出优越的缩放特性，并且对于具有相同拓扑结构的所有三种表示都产生相同的结果。研究 NOCl 光解离和 CH 振动态的数值测试证明了非层次 CDVR 方法的准确性。
