Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Abstract

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6 × 10 7 time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5 × 10 5 coefficients and requiring a shorter computation time.

Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics

“…25. However, the introduction of a new representation for the potential energy operator will require changes to the practical equations of motion for ML-MCTDH.…”

“…If the Hamiltonian is suitably structured (more on that below), MCTDH can be used to treat realistic systems up to around 20D [11][12][13][14][15][16] , and even more if the system is weakly correlated or if low accuracy is sufficient 17,18 . The multi-layer generalization of the MCTDH scheme (ML-MCTDH), first formulated by Wang and Thoss 19 and a) E-mail: Frank.Otto@pci.uni-heidelberg.de later reformulated by Manthe 20 as a recursive algorithm for arbitrary layering schemes, has already been used to treat systems with hundreds of DOFs 19,[21][22][23][24][25][26] . ML-MCTDH uses a tensor decomposition which has then become known in the mathematical literature as hierarchical tensor or hierarchical Tucker (HT) format 27 , and developing techniques for operating on tensors in HTand related formats is an active field of research.…”

Multiconfigurational time-dependent Hartree method to describe particle loss due to absorbing boundary conditions

“…Today, the de facto standard approach in ab initio quantummechanical many-particle propagation is the multiconfigurational time-dependent Hartree method (MCTDH) and its variations [1][2][3][4][5][6][7]. Already for N = 2 electrons in three dimensions, the full six-dimensional time-dependent Schrödinger equation is very hard to solve and can only be handled on supercomputers.…”

“…Current implementations can handle N ≤ 8 electrons in cylindrical geometries reliably [8,9]. For bosons, the Pauli exclusion principle is absent, and MCTDH can treat hundreds [10] and even thousands of particles [11] in one-dimensional geometries, and recent multi-layer MCTDH techniques allow distinguishable dimensions in the thousands with relative ease [7], showing great promise of extending the domain of application of MCTDH methods.…”

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

“…The OQS dynamics has been treated by a multitude of computational methods such as the Feynman-Vernon path integral formalism [7] leading to the hierarchical equations of motion (HEOM) [8] or time non-local master equations with perturbative approximation [9] coming from the Nakajima-Zwanzig projection technique [10] or time local methods [6,11] from the Hashitsume expansion [12]. Alternative methods are the stochastic approach [13,14], density matrix renormalization group [15] or the simulation of the bath by a finite number of oscillators treated by multi configuration time dependent Hartree (MCTDH) [16,17] with the multi-layer implementation (ML-MCTDH) simulations [18] or the time-dependent variational matrix product states [19].…”