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Van Haeften A, Ash C, Worth G. Propagating multi-dimensional density operators using the multi-layer-ρ multi-configurational time-dependent Hartree method. J Chem Phys 2023; 159:194114. [PMID: 37982483 DOI: 10.1063/5.0172956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 10/19/2023] [Indexed: 11/21/2023] Open
Abstract
Solving the Liouville-von-Neumann equation using a density operator provides a more complete picture of dynamical quantum phenomena than by using a wavepacket and solving the Schrödinger equation. As density operators are not restricted to the description of pure states, they can treat both thermalized and open systems. In practice, however, they are rarely used to study molecular systems as the computational resources required are even more prohibitive than those needed for wavepacket dynamics. In this paper, we demonstrate the potential utility of a scheme based on the powerful multi-layer multi-configurational time-dependent Hartree algorithm for propagating multi-dimensional density operators. Studies of two systems using this method are presented at a range of temperatures and including up to 13 degrees of freedom. The first case is single proton transfer in salicylaldimine, while the second is double proton transfer in porphycene. A comparison is also made with the approach of using stochastic wavepackets.
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Affiliation(s)
- Alice Van Haeften
- Department of Chemistry, University College London, London WC1H 0AJ, UK
| | - Ceridwen Ash
- Department of Chemistry, University College London, London WC1H 0AJ, UK
| | - Graham Worth
- Department of Chemistry, University College London, London WC1H 0AJ, UK
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Fischer EW, Saalfrank P. A thermofield-based multilayer multiconfigurational time-dependent Hartree approach to non-adiabatic quantum dynamics at finite temperature. J Chem Phys 2021; 155:134109. [PMID: 34624972 DOI: 10.1063/5.0064013] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a thermofield-based formulation of the multilayer multiconfigurational time-dependent Hartree (MCTDH) method to study finite temperature effects on non-adiabatic quantum dynamics from a non-stochastic, wave function perspective. Our approach is based on the formal equivalence of bosonic many-body theory at zero temperature with a doubled number of degrees of freedom and the thermal quasi-particle representation of bosonic thermofield dynamics (TFD). This equivalence allows for a transfer of bosonic many-body MCTDH as introduced by Wang and Thoss to the finite temperature framework of thermal quasi-particle TFD. As an application, we study temperature effects on the ultrafast internal conversion dynamics in pyrazine. We show that finite temperature effects can be efficiently accounted for in the construction of multilayer expansions of thermofield states in the framework presented herein. Furthermore, we find our results to agree well with existing studies on the pyrazine model based on the ρMCTDH method.
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Affiliation(s)
- Eric W Fischer
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
| | - Peter Saalfrank
- Theoretische Chemie, Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany
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Mainali S, Gatti F, Iouchtchenko D, Roy PN, Meyer HD. Comparison of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) for ground state properties of linear rotor chains. J Chem Phys 2021; 154:174106. [PMID: 34241072 DOI: 10.1063/5.0047090] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for larger system sizes contain nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.
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Affiliation(s)
- Samrit Mainali
- Université Paris-Saclay, Institut des Sciences Moléculaires d'Orsay ISMO, UMR CNRS 8214, F-91405 Orsay, France
| | - Fabien Gatti
- Université Paris-Saclay, Institut des Sciences Moléculaires d'Orsay ISMO, UMR CNRS 8214, F-91405 Orsay, France
| | - Dmitri Iouchtchenko
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
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Mendive-Tapia D, Meyer HD. Regularizing the MCTDH equations of motion through an optimal choice on-the-fly (i.e., spawning) of unoccupied single-particle functions. J Chem Phys 2020; 153:234114. [DOI: 10.1063/5.0035581] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Mendive-Tapia
- Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Hans-Dieter Meyer
- Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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Martinazzo R, Burghardt I. Local-in-Time Error in Variational Quantum Dynamics. PHYSICAL REVIEW LETTERS 2020; 124:150601. [PMID: 32357037 DOI: 10.1103/physrevlett.124.150601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 03/26/2020] [Indexed: 06/11/2023]
Abstract
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrödinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. Based on these findings, we demonstrate the rigorous formulation of an adaptive scheme that resizes on the fly the underlying variational manifold and, hence, optimizes the overall computational cost of a quantum dynamical simulation. Such adaptive schemes are a crucial requirement for devising and applying direct quantum dynamical methods to molecular and condensed-phase problems.
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Affiliation(s)
- Rocco Martinazzo
- Department of Chemistry, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
- Istituto di Scienze e Tecnologie Molecolari, CNR, via Golgi 19, 20133 Milano, Italy
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Strasse 7, D-60438 Frankfurt/Main, Germany
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Larsson HR. Computing vibrational eigenstates with tree tensor network states (TTNS). J Chem Phys 2019; 151:204102. [DOI: 10.1063/1.5130390] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Henrik R. Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Mendive-Tapia D, Mangaud E, Firmino T, de la Lande A, Desouter-Lecomte M, Meyer HD, Gatti F. Multidimensional Quantum Mechanical Modeling of Electron Transfer and Electronic Coherence in Plant Cryptochromes: The Role of Initial Bath Conditions. J Phys Chem B 2017; 122:126-136. [DOI: 10.1021/acs.jpcb.7b10412] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- David Mendive-Tapia
- Institut
Charles Gerhardt Montpellier, UMR 5253, CNRS-UM-ENSCM, CTMM, Université Montpellier, CC 15001, Place Eugène Bataillon, 34095 Montpellier, France
- Theoretische
Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, INF 229, D-69120 Heidelberg, Germany
| | - Etienne Mangaud
- Laboratoire
Collisions Agrégats Réactivité, UMR 5589, IRSAMC, Université Toulouse III Paul Sabatier, F-31062 Toulouse, France
| | - Thiago Firmino
- Laboratoire
de Chimie Physique, CNRS, Université Paris-Sud, Université Paris Saclay, Orsay F-91405, France
| | - Aurélien de la Lande
- Laboratoire
de Chimie Physique, CNRS, Université Paris-Sud, Université Paris Saclay, Orsay F-91405, France
| | - Michèle Desouter-Lecomte
- Laboratoire
de Chimie Physique, CNRS, Université Paris-Sud, Université Paris Saclay, Orsay F-91405, France
| | - Hans-Dieter Meyer
- Theoretische
Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, INF 229, D-69120 Heidelberg, Germany
| | - Fabien Gatti
- Institut
des Sciences Moléculaires d’Orsay, UMR-CNRS 8214, Université Paris-Sud, Université Paris Saclay, Orsay F-91405, France
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Larsson HR, Tannor DJ. Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics. J Chem Phys 2017; 147:044103. [DOI: 10.1063/1.4993219] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- H. R. Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - D. J. Tannor
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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