Sielk, J., von Horsten, H. F., Kruger, F., Schneider, Ralph and Hartke, Bernd (2009) Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation. Physical Chemistry Chemical Physics, 11 (3). pp. 463-475. DOI 10.1039/b814315c.

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Abstract

We present an extension of our earlier work on adaptive quantum wavepacket dynamics [B. Hartke, Phys. Chem. Chem. Phys., 2006, 8, 3627]. In this dynamically pruned basis representation the wavepacket is only stored at places where it has non-negligible contributions. Here we enhance the former 1D proof-of-principle implementation to higher dimensions and optimize it by a new basis set, interpolating Gaussians with collocation. As a further improvement the TNUM approach from Lauvergnat and Nauts [J. Chem. Phys., 2002, 116, 8560] was implemented, which in combination with our adaptive representation offers the possibility of calculating the whole Hamiltonian on-the-fly. For a two-dimensional artificial benchmark and a three-dimensional real-life test case, we show that a sparse matrix implementation of this approach saves memory compared to traditional basis representations and comes even close to the efficiency of the fast Fourier transform method. Thus we arrive at a quantum wavepacket dynamics implementation featuring several important black-box characteristics: it can treat arbitrary systems without code changes, it calculates the kinetic and potential part of the Hamiltonian on-the-fly, and it employs a basis that is automatically optimized for the ongoing wavepacket dynamics.

Document Type:	Article
Keywords:	dependent schrodinger-equationdiscrete variable representation wave-packet dynamics boundary truncation method reactive scattering molecular-dynamics fourier method operators grids approximations
Research affiliation:	Kiel University OceanRep > The Future Ocean - Cluster of Excellence
Refereed:	Yes
Open Access Journal?:	No
Publisher:	Nature Publishing Group
Projects:	Future Ocean
Date Deposited:	11 Feb 2011 12:15
Last Modified:	23 Sep 2019 23:25
URI:	https://oceanrep.geomar.de/id/eprint/9732

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