University of Illinois Urbana-Champaign

New variational methods for computing vibrational spectra of molecules with up to 11 atoms

Carrington, Tucker

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2689.pdf
986863.pdf

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https://hdl.handle.net/2142/97043

Description

Title
New variational methods for computing vibrational spectra of molecules with up to 11 atoms
Author(s)
Carrington, Tucker
Contributor(s)
  • Thomas, Phillip
  • Brown, James
Issue Date
2017-06-19
Keyword(s)
Comparing theory and experiment
Date of Ingest
  • 2017-07-27T20:15:36Z
  • 2018-01-29T23:06:31Z
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).
Publisher
International Symposium on Molecular Spectroscopy
Type of Resource
text
Genre of Resource
Conference Paper / Presentation
Language
eng
Permalink
http://hdl.handle.net/2142/97043
DOI
https://doi.org/10.15278/isms.2017.MI06
Copyright and License Information
Copyright 2017 Tucker Carrington

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Abstracts & Presentations - 2017 International Symposium on Molecular Spectroscopy PRIMARY