We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide and cyclopentadiene , with 7 and 11 atoms, respectively.
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28 May 2017
Research Article|
May 31 2017
An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms Available to Purchase
Phillip S. Thomas;
Phillip S. Thomas
a)
Chemistry Department,
Queen’s University
, Kingston, Ontario K7L 3N6, Canada
Search for other works by this author on:
Tucker Carrington, Jr.
Tucker Carrington, Jr.
b)
Chemistry Department,
Queen’s University
, Kingston, Ontario K7L 3N6, Canada
Search for other works by this author on:
Phillip S. Thomas
a)
Chemistry Department,
Queen’s University
, Kingston, Ontario K7L 3N6, Canada
Tucker Carrington, Jr.
b)
Chemistry Department,
Queen’s University
, Kingston, Ontario K7L 3N6, Canada
a)
E-mail: [email protected]
b)
E-mail: [email protected]. Fax: 613-533-6669.
J. Chem. Phys. 146, 204110 (2017)
Article history
Received:
February 14 2017
Accepted:
May 05 2017
Citation
Phillip S. Thomas, Tucker Carrington; An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms. J. Chem. Phys. 28 May 2017; 146 (20): 204110. https://doi.org/10.1063/1.4983695
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