skip to main content

SciTech ConnectSciTech Connect

Title: The multi-configurational time-dependent Hartree approach revisited

The multi-configurational time-dependent Hartree (MCTDH) approach facilitates accurate high-dimensional quantum dynamics simulations. In the approach, the wavefunction is expanded in a direct product of self-adapting time-dependent single-particle functions (SPFs). The equations of motion for the expansion coefficients and the SPFs are obtained via the Dirac-Frenkel variational principle. While this derivation yields well-defined differential equations for the motion of occupied SPFs, singularities in the working equations resulting from unoccupied SPFs have to be removed by a regularization procedure. Here, an alternative derivation of the MCTDH equations of motion is presented. It employs an analysis of the time-dependence of the single-particle density matrices up to second order. While the analysis of the first order terms yields the known equations of motion for the occupied SPFs, the analysis of the second order terms provides new equations which allow one to identify optimal choices for the unoccupied SPFs. The effect of the optimal choice of the unoccupied SPFs on the structure of the MCTDH equations of motion and their regularization is discussed. Generalized equations applicable in the multi-layer MCTDH framework are presented. Finally, the effects resulting from the initial choice of the unoccupied SPFs are illustrated by a simple numerical example.
Authors:
 [1]
  1. Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld (Germany)
Publication Date:
OSTI Identifier:
22490828
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 24; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; DENSITY MATRIX; EQUATIONS OF MOTION; PARTICLES; SIMULATION; TIME DEPENDENCE; VARIATIONAL METHODS; WAVE FUNCTIONS