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Title:NEW VARIATIONAL METHODS FOR COMPUTING VIBRATIONAL SPECTRA OF MOLECULES WITH_x000d_ UP TO 11 ATOMS
Author(s):Carrington, Tucker
Contributor(s):Thomas, Phillip; Brown, James
Subject(s):Comparing theory and experiment
Abstract:_x000d_ I shall present two new variational methods for computing vibrational spectra. Both rely on the Hamiltonian being a sum of products (SOP). To use a_x000d_ variational method one represents wavefunctions_x000d_ in a basis and uses methods of numerical linear algebra to_x000d_ determine the basis function coefficients. A direct product_x000d_ basis has the advantage that it enables one to efficiently_x000d_ calculate the eigenvalues and eigenvectors of the Hamiltonian _x000d_ matrix using an iterative eigensolver. A direct product_x000d_ basis has the crucial disadvantage that the memory cost of a calculation scales exponentially with the number of atoms in the molecule. _x000d_ One of the new methods uses an expanding basis of products of 1D functions and an iterative eigensolver._x000d_ For ethylene oxide (7 atoms), converged results are obtained with a basis that is many orders of magnitude smaller than the direct product basis with which similar results would be obtained. _x000d_ The second new method uses sum-of-product basis functions_x000d_ stored in canonical polyadic (CP) tensor format and generated by evaluating matrix-vector products._x000d_ The memory cost scales linearly with the number of atoms in the molecule. Recent improvements make it possible to compute the spectrum of cyclopentadiene_x000d_ (11 atoms).
Issue Date:6/19/2017
Publisher:International Symposium on Molecular Spectroscopy
Citation Info:APS
Genre:CONFERENCE PAPER/PRESENTATION
Type:Text
Language:English
URI:http://hdl.handle.net/2142/97043
DOI:10.15278/isms.2017.MI06
Date Available in IDEALS:2017-07-27


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