相关离散变量表示法再探讨
The correlation discrete variable representation revisited
AI总结：
本文重新审视了非分层CDVR，提出了一种避免显式投影到单孔空间的新方法，提高了计算效率和准确性，展示了在NOCl光解离、甲基振动态和吡嗪非绝热量子动力学中的应用效果。
摘要：
相关离散变量表示法（CDVR）通过多层多配置时间依赖哈特里-福克（MCTDH）方法在一般势能面上实现了高效的量子动力学计算。它利用时间依赖的四阶计算势能矩阵元素，从而消除了将势能重新拟合为乘积形式的需要。非分层CDVR保留了树状波函数表示的内在对称性，并大幅减少了网格点数量，相比原始分层CDVR。然而，它需要在树的每个节点上投影到单孔函数（SHFs）的空间，这可能引入非物理耦合，特别是在未收敛的基组中。在本文中，非分层CDVR被重新审视，提出了一种避免显式投影到单孔空间的新方法。修订后的方案的计算成本与单粒子函数（SPFs）数量呈有利比例：对于每个节点有三条边的树，以及每个边有n个SPFs，实现n^4的标度。此外，还提出了一种使用人工SPFs系统地提高CDVR四阶精度的方案。研究NOCl光解离、甲基振动态和光激发吡嗪的非绝热量子动力学展示了修订后的非分层CDVR的准确性和效率。值得注意的是，对于24维的吡嗪系统，使用CDVR并不增加所需的CPU时间，与使用振动-电子耦合模型的乘积形式计算相比。
英文摘要：
The correlation discrete variable representation (CDVR) enables efficient quantum dynamics calculation with the multi-layer multi-configurational time-dependent Hartree (MCTDH) approach on general potential energy surfaces. It employs a time-dependent quadrature to compute potential energy matrix elements, thereby eliminating the need to refit the potential to a sum of products form. The non-hierarchical CDVR conserves the inherent symmetry properties of tree-shaped wavefunction representations and drastically reduces the number of grid points compared to the original hierarchical CDVR. However, it requires projection on the space spanned by the single-hole functions (SHFs) at each node of the tree, which can introduce unphysical couplings for unconverged basis sets. In this work, the non-hierarchical CDVR is revisited and a revised approach that avoids explicit projection on the single-hole space is introduced. The computational costs of the revised approach scale favorably with the number of single-particle functions (SPFs): for a tree with three edges at each node and $n$ SPFs at each edge, a n^4 scaling is achieved. Furthermore, a revised scheme that uses artificial SPFs to systematically increase the accuracy of the CDVR quadrature is presented. Computations studying the photodissociation of NOCl, the vibrational states of methyl, and the non-adiabatic quantum dynamics of photoexcited pyrazine demonstrate the accuracy and efficiency of the revised non-hierarchical CDVR. Notably, for the 24-dimensional pyrazine system the use of the CDVR does not increase the required CPU time compared to calculations utilizing the sum of products form of the vibronic coupling model.
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