Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems

Abstract

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1869496͔The last decade has witnessed significant progress in quantum mechanical studies of dynamical chemical processes at the molecular level. The development of the timedependent wave packet ͑TDWP͒ method has made it possible to perform exact quantum mechanical calculations for four-atom systems. [1][2][3][4] The recent report on the state-to-state integral cross sections for the H + H 2 O reaction suggests that we are close to solving four-atom reactive scattering problems completely. 2 The grand challenge in the field of quantum dynamics now is to develop practical yet accurate methods to study polyatomic dynamical problems involving many atoms. However, due to the fact that computational effort grows exponentially with dimensionality, it is impractical at present to study polyatomic dynamical processes exactly in full dimensions although there has been some progress in this direction. 5 Naturally, one has to resort to the reduced dimensionality approach to cut down the number of degrees of freedom included in dynamical studies, or some computational approximate methods to overcome the scaling of effort with dimensionality.A promising approach is the time-dependent selfconsistent field ͑TDSCF͒ method. [6][7][8][9][10][11][12][13][14][15] In the simplest version, i.e., the single configuration time-dependent self-consistent field ͑SC-TDSCF͒ approach, the wave function of the system is written as a direct product of the wave functions for subsystems. [7][8][9][10]12 A principal drawback of SC-TDSCF is that it replaces exact interaction between subsystems by meanfield coupling, resulting in the lack of correlations between subsystems. One way to account for the important correlations neglected in SC-TDSCF is to add wave functions with different configurations to give more flexibility to the wave function of the system, resulting in the so-called multiconfiguration time-dependent self-consistent field ͑MC-TDSCF͒ method. 6,13-15 Wave functions with different configurations are usually constructed by imposing orthogonal condition explicitly, making it hard to use more than a few configurations in numerical implementation. Furthermore, the resulting equations for MC-TDSCF are very complicated compared to those in SC-TDSCF method. For these reasons, MC-TDSCF has only been applied to some model problems. The closely related multiconfiguration time-dependent Hartree method ͑MCTDH͒ generalizes MC-TDSCF in a systematic way, thus eliminating the need for choices of the TDSCF states. 16,17 It ha...

Unitary Approaches to Dissipative Quantum Dynamics

“…Several variants are possible (e.g., replacing the DVR states with energy eigenstates or fully flexible system states) and can be found in the original literature [35,36]. Also, the closely related CC-TDSCF method [49] in which the CSs are replaced by fully flexible functions has been shown to provide essentially the same results as LCSA [36], thereby showing the soundness of the CS approximation for the (local) bath dynamics.…”

“…These are highly localized objects in configuration space which underlie the use of any "grid". See Refs [49,50]. for a formal introduction 17.…”

Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics

“…Among these is the Gaussian-based MCTDH (G-MCTDH) method, − which partially replaces the fully flexible single-particle functions with Gaussian functions, allowing considerable savings of both CPU time and random access memory by focusing attention on the most important degrees of freedom. Variants specifically designed for system-bath problems are the local coherent-state approximation (LCSA) method and its generalization, which extend the previous continuous-configuration time-dependent self-consistent field method (see also ref ) by introducing a simplified description of the bath dynamics while preserving as much as possible the important system-bath correlations.…”

Reduced and Exact Quantum Dynamics of the Vibrational Relaxation of a Molecular System Interacting with a Finite-Dimensional Bath

“…However, tremendous progress has been recently made in this direction, especially in the development of time-dependent multiconfiguration methods such as the MCTDH (multiconfiguration time-dependent Hartree) approach . This method has been successfully applied to many quantum dynamical processes in polyatomic molecules, and also to adsorbate–surface problems with a large number of bath degrees of freedom. , Other variants of the method designed for true dissipative systems have also been derived, such as G-MCTDH (Gaussian MCTDH , ), ML-MCTDH (multilayer MCTDH , ), CC-TDSCF (continuous-configuration time-dependent self-consistent field , ), and LCSA (local coherent state approximation , ).…”