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

Carrington, Tucker

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

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

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

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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