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Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: the MCTDH[n] hierarchy

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Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method : the MCTDH[n] hierarchy. / Madsen, Niels Kristian; Hansen, Mads Bøttger; Worth, Graham A.; Christiansen, Ove.

I: Journal of Chemical Physics, Bind 152, Nr. 8, 084101, 02.2020.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Madsen, Niels Kristian ; Hansen, Mads Bøttger ; Worth, Graham A. ; Christiansen, Ove. / Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method : the MCTDH[n] hierarchy. I: Journal of Chemical Physics. 2020 ; Bind 152, Nr. 8.

Bibtex

@article{acaa486359444c84961b608031b08961,
title = "Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: the MCTDH[n] hierarchy",
abstract = "The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schr{\"o}dinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schr{\"o}dinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon-Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.",
author = "Madsen, {Niels Kristian} and Hansen, {Mads B{\o}ttger} and Worth, {Graham A.} and Ove Christiansen",
year = "2020",
month = feb,
doi = "10.1063/1.5142459",
language = "English",
volume = "152",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "AMER INST PHYSICS",
number = "8",

}

RIS

TY - JOUR

T1 - Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method

T2 - the MCTDH[n] hierarchy

AU - Madsen, Niels Kristian

AU - Hansen, Mads Bøttger

AU - Worth, Graham A.

AU - Christiansen, Ove

PY - 2020/2

Y1 - 2020/2

N2 - The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon-Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.

AB - The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon-Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.

U2 - 10.1063/1.5142459

DO - 10.1063/1.5142459

M3 - Journal article

C2 - 32113340

AN - SCOPUS:85080101211

VL - 152

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084101

ER -