Madsen, NK;
Hansen, MB;
Worth, GA;
Christiansen, O;
(2020)
Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy.
The Journal of Chemical Physics
, 152
(8)
, Article 084101. 10.1063/1.5142459.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1063/1.5142459 |
| Publisher version: | http://dx.doi.org/10.1063/1.5142459 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Chemistry |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10092233 |
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