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Author Manthe, Uwe
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ♦ MATHEMATICAL METHODS AND COMPUTING ♦ DENSITY MATRIX ♦ EQUATIONS OF MOTION ♦ PARTICLES ♦ SIMULATION ♦ TIME DEPENDENCE ♦ VARIATIONAL METHODS ♦ WAVE FUNCTIONS
Abstract 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.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2015-06-28
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 142
Issue Number 24


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