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Title: On regularizing the ML-MCTDH equations of motion

Abstract

In a recent paper [H.-D. Meyer and H. Wang, J. Chem. Phys. 148, 124105 (2018)], we have examined the regularization of the equations of motion (EOMs) of the multiconfiguration time-dependent Hartree (MCTDH) approach. We could show that the standard regularization scheme used by almost all researchers in the field is not optimal. The improved regularization allows for larger values of the regularization parameter ϵ, is less sensitive to the actual choice of ϵ, and performs the rotation of initially unoccupied single-particle functions into the “correct” direction in Hilbert space much faster than the old scheme. Here, the latter point increases both the accuracy and efficiency of time propagation for challenging problems. For simple problems, the new scheme requires some additional numerical work as compared with the old scheme, ranging from negligible to almost doubling the total numerical labor. For demanding problems, on the other hand, the additional numerical work of the new scheme is often overcompensated by less steps taken by the integrator. In the present paper, we generalize the new regularization scheme to the multi-layer (ML) extension of MCTDH. Although the principle idea of the new regularization scheme remains unaltered, it was not obvious how the new scheme shouldmore » be implemented into ML-MCTDH. The ML-MCTDH EOMs are much more complicated than the MCTDH ones, and for optimal numerical performance it was necessary to derive a recursive algorithm for implementing the new regularization scheme.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Univ. of Colorado Denver, Denver, CO (United States); Beijing Computational Science Research Center, Beijing (China)
  2. Univ. Heidelberg, Heidelberg (Germany)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1543876
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Physics

Citation Formats

Wang, Haobin, and Meyer, Hans -Dieter. On regularizing the ML-MCTDH equations of motion. United States: N. p., 2018. Web. doi:10.1063/1.5042776.
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Wang, Haobin, & Meyer, Hans -Dieter. On regularizing the ML-MCTDH equations of motion. United States. doi:https://doi.org/10.1063/1.5042776
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Wang, Haobin, and Meyer, Hans -Dieter. Fri . "On regularizing the ML-MCTDH equations of motion". United States. doi:https://doi.org/10.1063/1.5042776. https://www.osti.gov/servlets/purl/1543876.
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@article{osti_1543876,
title = {On regularizing the ML-MCTDH equations of motion},
author = {Wang, Haobin and Meyer, Hans -Dieter},
abstractNote = {In a recent paper [H.-D. Meyer and H. Wang, J. Chem. Phys. 148, 124105 (2018)], we have examined the regularization of the equations of motion (EOMs) of the multiconfiguration time-dependent Hartree (MCTDH) approach. We could show that the standard regularization scheme used by almost all researchers in the field is not optimal. The improved regularization allows for larger values of the regularization parameter ϵ, is less sensitive to the actual choice of ϵ, and performs the rotation of initially unoccupied single-particle functions into the “correct” direction in Hilbert space much faster than the old scheme. Here, the latter point increases both the accuracy and efficiency of time propagation for challenging problems. For simple problems, the new scheme requires some additional numerical work as compared with the old scheme, ranging from negligible to almost doubling the total numerical labor. For demanding problems, on the other hand, the additional numerical work of the new scheme is often overcompensated by less steps taken by the integrator. In the present paper, we generalize the new regularization scheme to the multi-layer (ML) extension of MCTDH. Although the principle idea of the new regularization scheme remains unaltered, it was not obvious how the new scheme should be implemented into ML-MCTDH. The ML-MCTDH EOMs are much more complicated than the MCTDH ones, and for optimal numerical performance it was necessary to derive a recursive algorithm for implementing the new regularization scheme.},
doi = {10.1063/1.5042776},
journal = {Journal of Chemical Physics},
number = 4,
volume = 149,
place = {United States},
year = {2018},
month = {7}
}
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DOI:  https://doi.org/10.1063/1.5042776
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