Madsen Niels Kristian, Hansen Mads Bøttger, Worth Graham A, Christiansen Ove
Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
Department of Chemistry, University College London, 20, Gordon St., WC1H 0AJ London, United Kingdom.
J Chem Theory Comput. 2020 Jul 14;16(7):4087-4097. doi: 10.1021/acs.jctc.0c00379. Epub 2020 Jul 2.
Solving the time-dependent Schrödinger equation (TDSE) for large molecular systems is a complicated task due to the inherent exponential scaling of the problem. One of the most successful and versatile methods for obtaining numerically converged solutions for small to medium-sized systems is multiconfiguration time-dependent Hartree (MCTDH). In a recent publication [ , , 084101] we introduced a hierarchy of approximations to the MCTDH method which mitigate the exponential scaling by truncating the configuration space based on a maximum excitation level w.r.t. a selected reference configuration. The MCTDH[] methods are able to treat large systems, but the single-reference Ansatz is not optimal in cases where one (or a few) degrees of freedom are special. Examples could be double-well systems, intramolecular vibrational-energy redistribution (IVR) calculations, or nonadiabatic dynamics. In this work we introduce a multireference (MR) extension to the MCTDH[] methods where selected higher-order excitations for the special degrees of freedom can be introduced in a simple but flexible way. The resulting MR-MCTDH[] methods allow for, for example, treating nonadiabatic dynamics within the single-set formalism with the wave packets on each electronic surface described using the same level of approximation. Example calculations are performed on formyl fluoride (IVR), salicylaldimine (double well), and pyrazine (nonadiabatic dynamics). The results show that fast convergence is achieved by extending the configuration space in the special modes that govern the quantum dynamics.
对于大分子系统求解含时薛定谔方程（TDSE）是一项复杂的任务，因为该问题存在固有的指数级增长。对于中小规模系统获得数值收敛解的最成功且通用的方法之一是多组态含时哈特里（MCTDH）方法。在最近的一篇出版物[,, 084101]中，我们引入了MCTDH方法的一系列近似，通过基于相对于选定参考组态的最大激发水平截断组态空间来减轻指数级增长。MCTDH[]方法能够处理大型系统，但在一个（或几个）自由度特殊的情况下，单参考假设并非最优。例如双阱系统、分子内振动能量重新分布（IVR）计算或非绝热动力学。在这项工作中，我们引入了MCTDH[]方法的多参考（MR）扩展，其中可以以简单但灵活的方式引入特殊自由度的选定高阶激发。由此产生的MR - MCTDH[]方法允许，例如，在单组形式内处理非绝热动力学，每个电子表面上的波包使用相同的近似水平来描述。对甲酰氟（IVR）、水杨醛亚胺（双阱）和吡嗪（非绝热动力学）进行了示例计算。结果表明，通过在控制量子动力学的特殊模式中扩展组态空间可实现快速收敛。
