skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On regularizing the MCTDH equations of motion

Abstract

The Multiconfiguration Time-Dependent Hartree (MCTDH) approach leads to equations of motion (EOM) which become singular when there are unoccupied so-called single-particle functions (SPFs). Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their “correct direction” in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Lastly, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.

Authors:
ORCiD logo [1];  [2]
  1. Univ. Heidelberg, Heidelberg (Germany). Physikalisch-Chemisches Institut
  2. Univ. of Colorado Denver, Denver, CO (United States) Department of Chemistry; Beijing Computational Science Research Center, Beijing (China)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1498101
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 12; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Meyer, Hans -Dieter, and Wang, Haobin. On regularizing the MCTDH equations of motion. United States: N. p., 2018. Web. doi:10.1063/1.5024859.
Meyer, Hans -Dieter, & Wang, Haobin. On regularizing the MCTDH equations of motion. United States. doi:10.1063/1.5024859.
Meyer, Hans -Dieter, and Wang, Haobin. Fri . "On regularizing the MCTDH equations of motion". United States. doi:10.1063/1.5024859. https://www.osti.gov/servlets/purl/1498101.
@article{osti_1498101,
title = {On regularizing the MCTDH equations of motion},
author = {Meyer, Hans -Dieter and Wang, Haobin},
abstractNote = {The Multiconfiguration Time-Dependent Hartree (MCTDH) approach leads to equations of motion (EOM) which become singular when there are unoccupied so-called single-particle functions (SPFs). Starting from a Hartree product, all SPFs, except the first one, are unoccupied initially. To solve the MCTDH-EOMs numerically, one therefore has to remove the singularity by a regularization procedure. Usually the inverse of a density matrix is regularized. Here we argue and show that regularizing the coefficient tensor, which in turn regularizes the density matrix as well, leads to an improved performance of the EOMs. The initially unoccupied SPFs are rotated faster into their “correct direction” in Hilbert space and the final results are less sensitive to the choice of the value of the regularization parameter. For a particular example (a spin-boson system studied with a transformed Hamiltonian), we could even show that only with the new regularization scheme could one obtain correct results. Lastly, in Appendix A, a new integration scheme for the MCTDH-EOMs developed by Lubich and co-workers is discussed. It is argued that this scheme does not solve the problem of the unoccupied natural orbitals because this scheme ignores the latter and does not propagate them at all.},
doi = {10.1063/1.5024859},
journal = {Journal of Chemical Physics},
number = 12,
volume = 148,
place = {United States},
year = {2018},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 8 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Full-dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. I. Hamiltonian setup and analysis of the ground vibrational state
journal, November 2007

  • Vendrell, Oriol; Gatti, Fabien; Lauvergnat, David
  • The Journal of Chemical Physics, Vol. 127, Issue 18
  • DOI: 10.1063/1.2787588

Loss of Memory in H + CH 4 → H 2 + CH 3 State-to-State Reactive Scattering
journal, January 2015

  • Welsch, Ralph; Manthe, Uwe
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 3
  • DOI: 10.1021/jz502525p

Electronic decoherence following photoionization: Full quantum-dynamical treatment of the influence of nuclear motion
journal, March 2017


Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl
journal, September 1992

  • Manthe, U.; Meyer, H. ‐D.; Cederbaum, L. S.
  • The Journal of Chemical Physics, Vol. 97, Issue 5
  • DOI: 10.1063/1.463007

Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian
journal, January 1999

  • Raab, A.; Worth, G. A.; Meyer, H. -D.
  • The Journal of Chemical Physics, Vol. 110, Issue 2
  • DOI: 10.1063/1.478061

The role of the transition state in polyatomic reactions: Initial state-selected reaction probabilities of the H + CH 4 → H 2 + CH 3 reaction
journal, November 2014

  • Welsch, Ralph; Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 141, Issue 17
  • DOI: 10.1063/1.4900735

Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology
journal, August 2001

  • Wang, Haobin; Thoss, Michael; Miller, William H.
  • The Journal of Chemical Physics, Vol. 115, Issue 7
  • DOI: 10.1063/1.1385561

The multi-configurational time-dependent Hartree approach revisited
journal, June 2015

  • Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 142, Issue 24
  • DOI: 10.1063/1.4922889

Quantum dynamics of the H+CH4→H2+CH3 reaction in curvilinear coordinates: Full-dimensional and reduced dimensional calculations of reaction rates
journal, February 2010

  • Schiffel, Gerd; Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 132, Issue 8
  • DOI: 10.1063/1.3304920

Quantum dynamical simulation of ultrafast photoinduced electron transfer processes in a mixed-valence compound
journal, May 2002


Studying molecular quantum dynamics with the multiconfiguration time-dependent Hartree method: Multiconfiguration time-dependent Hartree
journal, September 2011

  • Meyer, Hans-Dieter
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • DOI: 10.1002/wcms.87

Intramolecular proton transfer in malonaldehyde: Accurate multilayer multi-configurational time-dependent Hartree calculations
journal, June 2011

  • Hammer, Thorsten; Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 134, Issue 22
  • DOI: 10.1063/1.3598110

Theoretical Study of Ultrafast Photoinduced Electron Transfer Processes in Mixed-Valence Systems
journal, April 2003

  • Wang, Haobin; Thoss, Michael
  • The Journal of Physical Chemistry A, Vol. 107, Issue 13
  • DOI: 10.1021/jp0272668

CH 5 + : Symmetry and the Entangled Rovibrational Quantum States of a Fluxional Molecule
journal, October 2015


Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics
journal, January 2015

  • Lubich, Christian
  • Applied Mathematics Research eXpress, Vol. 2015, Issue 2
  • DOI: 10.1093/amrx/abv006

Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach
journal, May 2017

  • Kloss, Benedikt; Burghardt, Irene; Lubich, Christian
  • The Journal of Chemical Physics, Vol. 146, Issue 17
  • DOI: 10.1063/1.4982065

Time-dependent multiconfiguration theory for electronic dynamics of molecules in an intense laser field
journal, July 2004


Multilayer Multiconfiguration Time-Dependent Hartree Theory
journal, June 2015


An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method
journal, November 1997

  • Beck, M. H.; Meyer, H. -D.
  • Zeitschrift f�r Physik D Atoms, Molecules and Clusters, Vol. 42, Issue 2
  • DOI: 10.1007/s004600050342

Calculation of the vibrational excited states of malonaldehyde and their tunneling splittings with the multi-configuration time-dependent Hartree method
journal, July 2014

  • Schröder, Markus; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 141, Issue 3
  • DOI: 10.1063/1.4890116

Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics
journal, November 2007

  • Vendrell, Oriol; Gatti, Fabien; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 127, Issue 18
  • DOI: 10.1063/1.2787596

Rotational effects on the dissociation dynamics of CHD 3 on Pt(111)
journal, January 2016

  • Füchsel, Gernot; Thomas, Phillip S.; den Uyl, Jurriaan
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 11
  • DOI: 10.1039/c5cp07898a

Multilayer formulation of the multiconfiguration time-dependent Hartree theory
journal, July 2003

  • Wang, Haobin; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 119, Issue 3
  • DOI: 10.1063/1.1580111

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
journal, March 2008


The multiconfiguration time-dependent Hartree–Fock method for quantum chemical calculations
journal, March 2005

  • Nest, M.; Klamroth, T.; Saalfrank, P.
  • The Journal of Chemical Physics, Vol. 122, Issue 12
  • DOI: 10.1063/1.1862243

Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method
journal, June 2003


Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine
journal, January 2011

  • Vendrell, Oriol; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 134, Issue 4
  • DOI: 10.1063/1.3535541

Communication: Reactivity borrowing in the mode selective chemistry of H + CHD 3 → H 2 + CD 3
journal, December 2017

  • Ellerbrock, Roman; Manthe, Uwe
  • The Journal of Chemical Physics, Vol. 147, Issue 24
  • DOI: 10.1063/1.5018254

Theoretical studies of the tunneling splitting of malonaldehyde using the multiconfiguration time-dependent Hartree approach
journal, June 2011

  • Schröder, Markus; Gatti, Fabien; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 134, Issue 23
  • DOI: 10.1063/1.3600343