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

The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH) is a highly efficient scheme for studying the dynamics of high-dimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system possesses a particular structure through which the multi-dimensional matrix elements can be computed efficiently. In the field of quantum molecular dynamics, the effective interaction between the atoms is often described by potential energy surfaces (PES), and it is necessary to fit such PES into the desired structure. For high-dimensional systems, the current approaches for this fitting process either lead to fits that are too large to be practical, or their accuracy is difficult to predict and control. This article introduces multi-layer Potfit (MLPF), a novel fitting scheme that results in a PES representation in the hierarchical tensor (HT) format. The scheme is based on the hierarchical singular value decomposition, which can yield a near-optimal fit and give strict bounds for the obtained accuracy. Here, a recursive scheme for using the HT-format PES within ML-MCTDH is derived, and theoretical estimates as well as a computational example show that the use of MLPF can reduce the numerical effort for ML-MCTDH by orders of magnitude, compared to the traditionally used POTFIT representationmore » of the PES. Moreover, it is shown that MLPF is especially beneficial for high-accuracy PES representations, and it turns out that MLPF leads to computational savings already for comparatively small systems with just four modes.« less
Authors:
 [1]
  1. Theoretische Chemie, Universit├Ąt Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
22253662
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; DECOMPOSITION; FORMATES; HAMILTONIANS; INTERACTIONS; LAYERS; MATRIX ELEMENTS; MOLECULAR DYNAMICS METHOD; POTENTIAL ENERGY; TIME DEPENDENCE