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Title:A MULTILAYER SUM-OF-PRODUCTS METHOD FOR COMPUTING VIBRATIONAL SPECTRA WITHOUT STORING FULL-DIMENSIONAL VECTORS OR MATRCIES
Author(s):Carrington, Tucker
Contributor(s):Thomas, Phillip
Subject(s):Vibrational structure/frequencies
Abstract:By optimizing sum-of-products (SOP) basis functions, it is possible to compute vibrational spectra, using a direct product basis, without storing vectors with as many components as there are product basis functions. These ideas are presented in a recent paper: Leclerc and Carrington, J. Chem. Phys 140 174111 (2014). In that paper, the SOP basis functions are products of factors that depend on a single coordinate. When using factors that depend on one coordinate the number of terms (rank) in the SOP basis functions increases with the size of the molecule and the coupling strength. Using multi-dimensional factors makes it possible to incorporate some of the coupling into the factors and to calculate spectra of molecules with more than a dozen atoms. We use multi-dimensional factors that are eigenfunctions of reduced-dimension Hamiltonians. These can be constructed, in different ways, by organizing the factors into a multiple layer tree. Each node in a layer of a tree represents eigenfunctions of a reduced-dimension Hamiltonian for a group of coordinates. We have done calculations with tensor-train and binary tree structures. Efficiency is significantly enhanced by representing the potential with the same tree structure. The ideas are tested by computing energy levels of a 64-D model coupled oscillator Hamiltonian and of CH3CN (12 dimensions) with a realistic potential.
Issue Date:25-Jun-15
Publisher:International Symposium on Molecular Spectroscopy
Citation Info:ACS
Genre:CONFERENCE PAPER/PRESENTATION
Type:Text
Language:English
URI:http://hdl.handle.net/2142/79129
Date Available in IDEALS:2016-01-05


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