Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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.
Copy to clipboard
Wang, Haobin, & Meyer, Hans -Dieter. On regularizing the ML-MCTDH equations of motion. United States. https://doi.org/10.1063/1.5042776
Copy to clipboard
Wang, Haobin, and Meyer, Hans -Dieter. Fri . "On regularizing the ML-MCTDH equations of motion". United States. https://doi.org/10.1063/1.5042776. https://www.osti.gov/servlets/purl/1543876.
Copy to clipboard
@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}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5042776
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

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

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

Ultrafast Nonadiabatic Dynamics of Singlet Fission: Quantum Dynamics with the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) Method
journal, January 2016

  • Zheng, Jie; Xie, Yu; Jiang, Shengshi
  • The Journal of Physical Chemistry C, Vol. 120, Issue 3
  • DOI: 10.1021/acs.jpcc.5b09921

Theoretical Study of Ultrafast Heterogeneous Electron Transfer Reactions at Dye−Semiconductor Interfaces:  Coumarin 343 at Titanium Oxide †
journal, February 2006

  • Kondov, Ivan; Thoss, Michael; Wang, Haobin
  • The Journal of Physical Chemistry A, Vol. 110, Issue 4
  • DOI: 10.1021/jp054162z

Simulation of a complex spectrum: Interplay of five electronic states and 21 vibrational degrees of freedom in C5H4+
journal, November 2005

  • Markmann, Andreas; Worth, Graham A.; Mahapatra, Susanta
  • The Journal of Chemical Physics, Vol. 123, Issue 20
  • DOI: 10.1063/1.2104531

Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach
journal, October 2007

  • Craig, Ian R.; Thoss, Michael; Wang, Haobin
  • The Journal of Chemical Physics, Vol. 127, Issue 14
  • DOI: 10.1063/1.2772265

Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring
journal, December 2014

On regularizing the MCTDH equations of motion
journal, March 2018

  • Meyer, Hans-Dieter; Wang, Haobin
  • The Journal of Chemical Physics, Vol. 148, Issue 12
  • DOI: 10.1063/1.5024859

Multilayer Multiconfiguration Time-Dependent Hartree Theory
journal, June 2015

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions
journal, December 2011

  • Wang, Haobin; Pshenichnyuk, Ivan; Härtle, Rainer
  • The Journal of Chemical Physics, Vol. 135, Issue 24
  • DOI: 10.1063/1.3660206

Bistability signatures in nonequilibrium charge transport through molecular quantum dots
journal, August 2012

  • Albrecht, Klaus Ferdinand; Wang, Haobin; Mühlbacher, Lothar
  • Physical Review B, Vol. 86, Issue 8
  • DOI: 10.1103/physrevb.86.081412

Explicit Correlated Exciton-Vibrational Dynamics of the FMO Complex
journal, May 2015

Quantum Dynamics of Photoinduced Electron-Transfer Reactions in Dye−Semiconductor Systems:  First-Principles Description and Application to Coumarin 343−TiO 2
journal, July 2007

  • Kondov, Ivan; Čížek, Martin; Benesch, Claudia
  • The Journal of Physical Chemistry C, Vol. 111, Issue 32
  • DOI: 10.1021/jp072217m

Numerically exact, time-dependent study of correlated electron transport in model molecular junctions
journal, April 2013

  • Wang, Haobin; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 138, Issue 13
  • DOI: 10.1063/1.4798404

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

Theoretical study of ultrafast heterogeneous electron transfer reactions at dye–semiconductor interfaces
journal, September 2004

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

Correlated electron-nuclear dynamics in ultrafast photoinduced electron-transfer reactions at dye-semiconductor interfaces
journal, October 2007

Full-dimensional multilayer multiconfigurational time-dependent Hartree study of electron transfer dynamics in the anthracene/C60 complex
journal, February 2015

  • Xie, Yu; Zheng, Jie; Lan, Zhenggang
  • The Journal of Chemical Physics, Vol. 142, Issue 8
  • DOI: 10.1063/1.4909521

All mode dynamics at the conical intersection of an octa-atomic molecule: Multi-configuration time-dependent Hartree (MCTDH) investigation on the butatriene cation
journal, August 2001

  • Cattarius, Chr.; Worth, G. A.; Meyer, H. -D.
  • The Journal of Chemical Physics, Vol. 115, Issue 5
  • DOI: 10.1063/1.1384872

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

Multilayer Multiconfiguration Time-Dependent Hartree Study of Vibrationally Coupled Electron Transport Using the Scattering-State Representation
journal, April 2013

  • Wang, Haobin; Thoss, Michael
  • The Journal of Physical Chemistry A, Vol. 117, Issue 32
  • DOI: 10.1021/jp401464b

Quantum Dynamical Simulation of Electron-Transfer Reactions in an Anharmonic Environment †
journal, October 2007

  • Wang, Haobin; Thoss, Michael
  • The Journal of Physical Chemistry A, Vol. 111, Issue 41
  • DOI: 10.1021/jp072367x

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

Multidimensional Quantum Mechanical Modeling of Electron Transfer and Electronic Coherence in Plant Cryptochromes: The Role of Initial Bath Conditions
journal, December 2017

  • Mendive-Tapia, David; Mangaud, Etienne; Firmino, Thiago
  • The Journal of Physical Chemistry B, Vol. 122, Issue 1
  • DOI: 10.1021/acs.jpcb.7b10412

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

Dynamics of the dissipative two-state system
journal, January 1987

  • Leggett, A. J.; Chakravarty, S.; Dorsey, A. T.
  • Reviews of Modern Physics, Vol. 59, Issue 1
  • DOI: 10.1103/revmodphys.59.1

Heat transport through model molecular junctions: A multilayer multiconfiguration time-dependent Hartree approach
journal, July 2008

Bistability in a nonequilibrium quantum system with electron-phonon interactions
journal, July 2013

The à 2 E/B̃ 2 B 2 Photoelectron Bands of Allene beyond the Linear Coupling Scheme:  An ab Initio Dynamical Study Including All Fifteen Vibrational Modes †
journal, June 2001

  • Mahapatra, S.; Worth, G. A.; Meyer, H. -D.
  • The Journal of Physical Chemistry A, Vol. 105, Issue 23
  • DOI: 10.1021/jp003727i

Lattice effects of surface cell: Multilayer multiconfiguration time-dependent Hartree study on surface scattering of CO/Cu(100)
journal, May 2017

  • Meng, Qingyong; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 146, Issue 18
  • DOI: 10.1063/1.4982962

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

The multi-configurational time-dependent Hartree approach
journal, January 1990

Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex
journal, May 2016

  • Schulze, Jan; Shibl, Mohamed F.; Al-Marri, Mohammed J.
  • The Journal of Chemical Physics, Vol. 144, Issue 18
  • DOI: 10.1063/1.4948563

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

From coherent motion to localization: dynamics of the spin-boson model at zero temperature
journal, November 2008

Multilayer-MCTDH approach to the energy transfer dynamics in the LH2 antenna complex
journal, August 2017

  • Shibl, Mohamed F.; Schulze, Jan; Al-Marri, Mohammed J.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 50, Issue 18
  • DOI: 10.1088/1361-6455/aa8374

Effects of intense femtosecond pumping on ultrafast electronic-vibrational dynamics in molecular systems with relaxation
journal, December 2008

  • Egorova, Dassia; Gelin, Maxim F.; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 129, Issue 21
  • DOI: 10.1063/1.3026509

Photodissociation of methyl iodide embedded in a host-guest complex: A full dimensional (189D) quantum dynamics study of CH 3 I@resorc[4]arene
journal, November 2011

  • Westermann, Till; Brodbeck, Ralf; Rozhenko, Alexander B.
  • The Journal of Chemical Physics, Vol. 135, Issue 18
  • DOI: 10.1063/1.3658040

A multilayer MCTDH study on the full dimensional vibronic dynamics of naphthalene and anthracene cations
journal, January 2013

  • Meng, Qingyong; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 138, Issue 1
  • DOI: 10.1063/1.4772779

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

Dynamics of electron transfer in complex glassy environment modeled by the Cole–Davidson spectral density
journal, May 2012

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

Quantum Dissipative Systems
book, March 2012

Explicit Correlated Exciton-Vibrational Dynamics of the FMO Complex
text, January 2015

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Excited‐state intramolecular proton transfer driven by conical intersection in hydroxychromones
    journal, January 2020

    • Anand, Neethu; Isukapalli, Sai Vamsi Krishna; Vennapusa, Sivaranjana Reddy
    • Journal of Computational Chemistry, Vol. 41, Issue 11
    • DOI: 10.1002/jcc.26152

    Matrix product state formulation of the multiconfiguration time-dependent Hartree theory
    journal, November 2018

    • Kurashige, Yuki
    • The Journal of Chemical Physics, Vol. 149, Issue 19
    • DOI: 10.1063/1.5051498

    Neural-network potential energy surface with small database and high precision: A benchmark of the H + H 2 system
    journal, September 2019

    • Song, Qingfei; Zhang, Qiuyu; Meng, Qingyong
    • The Journal of Chemical Physics, Vol. 151, Issue 11
    • DOI: 10.1063/1.5118692

    Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion
    journal, December 2019

    • Mangaud, Etienne; Lasorne, Benjamin; Atabek, Osman
    • The Journal of Chemical Physics, Vol. 151, Issue 24
    • DOI: 10.1063/1.5128852

    Computing vibrational eigenstates with tree tensor network states (TTNS)
    journal, November 2019

    • Larsson, Henrik R.
    • The Journal of Chemical Physics, Vol. 151, Issue 20
    • DOI: 10.1063/1.5130390

    Numerical assessment for accuracy and GPU acceleration of TD-DMRG time evolution schemes
    journal, January 2020

    • Li, Weitang; Ren, Jiajun; Shuai, Zhigang
    • The Journal of Chemical Physics, Vol. 152, Issue 2
    • DOI: 10.1063/1.5135363
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: