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

Madsen, N.; Hansen, Mads Bøttger; Worth, Graham A.; Christiansen, Ove

doi:10.1063/1.5142459

Cited by 16 publications

(45 citation statements)

References 58 publications

(118 reference statements)

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“…Inserting Eq. (1) into the Dirac-Frenkel TDVP results in EOMs for the configurationspace coefficients and the time-dependent modals 18 ,…”

Section: Mctdh[n] Theory and Extension To Non-adiabatic Dynamics 21 Summary Of Mctdh Theory In Second Quantizationmentioning

confidence: 99%

“…The MCTDH[n] wave function is based on a single-reference Ansatz 18 , order to obtain a fully variational wave function 18 ). This is used in section 3 for introducing the MR extension to the MCTDH[n] approximation.…”

Section: The Mctdh[n] Approximationmentioning

confidence: 99%

“…This choice of constraint is computationally much cheaper than the fully variational solution and, thus, the MCTDH[n,D] methods can be applied to quite large systems 18 . The downside is that Eq.…”

Section: The Mctdh[n] Approximationmentioning

confidence: 99%

“…As in Ref. 18 the initial wave packet is generated by performing a VSCF calculation targeting the [0,0,0,0,0,2] state (the C-H stretch) on a PES with all the coupling terms removed, i.e. a set of uncoupled anharmonic oscillators.…”

Section: Intramolecular Vibrational-energy Redistributionmentioning

confidence: 99%

“…The MCTDH[n] method presented in Ref. 18 reduces the computational scaling of MCTDH by truncating the number of configurations based on excitation level w.r.t. a reference configuration in line with the vibrational configuration interaction (VCI) 19,20 and vibrational coupled cluster (VCC) [21][22][23] methods for solving the time-independent Schrödinger equation (TISE), and also very recently timedependent vibrational coupled cluster (TDVCC) theory.…”

Section: Introductionmentioning

confidence: 99%

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MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework

Madsen

Hansen

Worth

2020

J. Chem. Theory Comput.

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Solving the time-dependent Schrödinger equation (TDSE) for large molecular systems is a complicated task due to the inherent exponential scaling of the problem. One of the most successful and versatile methods for obtaining numerically converged solutions for small to medium-sized systems is multiconfiguration time-dependent Hartree (MCTDH). In a recent publication [J. Chem. Phys. 152, 084101 (2020)] we introduced a hierarchy of approximations to the MCTDH method which mitigate the exponential scaling by truncating the configuration space based on a maximum excitation level w.r.t. a selected reference configuration. The MCTDH[n] methods are able to treat large systems, but the single-reference Ansatz is not optimal in cases where one (or a few) degrees of freedom are special. Examples could be double-well systems, intramolecular vibrational-energy redistribution (IVR) calculations, or non-adiabatic dy-1 namics. In this work we introduce a multi-reference (MR) extension to the MCTDH [n] methods where selected higher-order excitations for the special degrees of freedom can be introduced in a simple but flexible way. The resulting MR-MCTDH[n] methods allow for e.g. treating non-adiabatic dynamics within the single-set formalism with the wave packets on each electronic surface described using the same level of approximation. Example calculations are performed on formyl fluoride (IVR), salicylaldimine (double well), and pyrazine (non-adiabatic dynamics). The results show that fast convergence is achieved by extending the configuration space in the special modes that govern the quantum dynamics.

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“…Inserting Eq. (1) into the Dirac-Frenkel TDVP results in EOMs for the configurationspace coefficients and the time-dependent modals 18 ,…”

Section: Mctdh[n] Theory and Extension To Non-adiabatic Dynamics 21 Summary Of Mctdh Theory In Second Quantizationmentioning

confidence: 99%

Section: The Mctdh[n] Approximationmentioning

confidence: 99%

Section: The Mctdh[n] Approximationmentioning

confidence: 99%

Section: Intramolecular Vibrational-energy Redistributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework

Madsen

Hansen

Worth

2020

J. Chem. Theory Comput.

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Using collocation and solutions for a sum-of-product potential to compute vibrational energy levels for general potentials

Simmons

Carrington

2021

Chemical Physics Letters

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Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction

Høyer,

Christiansen

2024

J. Chem. Theory Comput.

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We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the timedependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single-and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

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

Abstract: The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation

Cited by 16 publications

References 58 publications

MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework

MR-MCTDH[n]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[n] Framework

Using collocation and solutions for a sum-of-product potential to compute vibrational energy levels for general potentials

Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction

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