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POTFIT and Multigrid POTFIT. Transforming general multi-potential energy surfaces to product form. Applications to H3O2-.

Banff International Research Station for Mathematical Innovation and Discovery

The Multi–Configuration Time–Dependent Hartree (MCTDH) approach [1–4] and its recent extension multi-layer MCTDH (ML–MCTDH) [5–7] are revisited. These methods were originally derived by expanding high–dimensional (wave–) functions into sums of products of low dimensional ones. Repre- senting functions on a grid, however, turns them into vectors or tensors. Then the MCTDH method can be viewed as a time–dependent Tucker expansion of a time–dependent tensor, which, in turn, represents the multi–dimensional wave function. ML–MCTDH can be viewed as a more complicated tensor decom- position, which is best described by a tree structure. [1] H.–D. Meyer, U. Manthe, and L. S. Cederbaum: The multi–configurational time–dependent Hartree approach. Chem. Phys. Lett. 165 (1990), 73. [2] U. Manthe, H.–D. Meyer, and L. S. Cederbaum: Wave–packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl. J. Chem. Phys. 97 (1992), 3199. [3] M. H. Beck, A. J ̈ackle, G. A. Worth, and H.–D. Meyer: The multiconfiguration time–dependent Hartree method: A highly efficient algorithm for propagating wavepackets. Phys. Rep. 324 (2000), 1. [4] H.–D. Meyer, F. Gatti, and G. A. Worth, editors: Multidimensional Quantum Dynamics: MCTDH Theory and Applications. Wiley–VCH, (2009), Weinheim, ISBN: 978-3-527-32018-9. [5] H. Wang and M. Thoss: Multilayer formulation of the multiconfiguration time–dependent Hartree theory. J. Chem. Phys. 119 (2003), 1289. [6] U. Manthe: A multilayer multiconfigurational time–dependent Hartree approach for quantum dynam- ics on general potential energy surfaces. J. Chem. Phys. 128 (2008), 164116. [7] O. Vendrell and H.–D. Meyer: Multilayer multiconfiguration time–dependent Hartree method: Imple- mentation and applications to a Henon–Heiles Hamiltonian and to pyrazine. J. Chem. Phys. 134 (2011), 044135.

Mathematics; Quantum theory; Partial differential equations; Mathematical physics

video/mp4

Author affiliation: University of Heidelberg

2014-08-06

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49345

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/