A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock
Abstract
We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO{sub 2}. For these dissociation processes, the GHF wave functions transform from lowspin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to highspin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.
 Authors:
 Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
 Publication Date:
 OSTI Identifier:
 22416208
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CARBON DIOXIDE; DISSOCIATION; ELECTRONIC STRUCTURE; HARTREEFOCK METHOD; MOLECULES; SPIN; SYMMETRY BREAKING; WAVE FUNCTIONS
Citation Formats
Small, David W., Sundstrom, Eric J., and HeadGordon, Martin. A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock. United States: N. p., 2015.
Web. doi:10.1063/1.4913740.
Small, David W., Sundstrom, Eric J., & HeadGordon, Martin. A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock. United States. doi:10.1063/1.4913740.
Small, David W., Sundstrom, Eric J., and HeadGordon, Martin. 2015.
"A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock". United States.
doi:10.1063/1.4913740.
@article{osti_22416208,
title = {A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock},
author = {Small, David W. and Sundstrom, Eric J. and HeadGordon, Martin},
abstractNote = {We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO{sub 2}. For these dissociation processes, the GHF wave functions transform from lowspin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to highspin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.},
doi = {10.1063/1.4913740},
journal = {Journal of Chemical Physics},
number = 9,
volume = 142,
place = {United States},
year = 2015,
month = 3
}
DOI: 10.1063/1.4913740
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