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Hierarchical Tensor Decompositions: A Tool for Computing Energy Levels of Molecules with More than 6 Atoms

Banff International Research Station for Mathematical Innovation and Discovery

Whenever coupling is important, numerical methods must be used to compute ro-vibrational spectra and model the dynamics of molecules and reacting systems. However, they become expensive as the number of atoms increases due to the explosion of data needed to represent the wavefunction. This phenomenon, known as the "curse of dimensionality", makes it impossible to store wavefunctions computed in direct-product basis, for molecules having more than 4-5 atoms, effectively limiting quantum dynamics to small molecules. Tensor decomposition methods show promise for alleviating the curse, enabling quantum dynamics on larger molecules. We recently computed energy levels for some 6- and 7-atom molecules using a sum-of-products tensor format, known as canonical polyadic (CP), to store the wavefunction. By arranging the coordinates of the molecule into a tree and computing energy levels for a series of Hamiltonians involving subsets of the coordinates, it is possible to compute energy levels for even larger molecules.

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Queen's University

2016-07-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58589

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/