skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock

Authors:
 [1];  [1];  [1]
  1. Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1228121
Grant/Contract Number:
AC02-05CH11231
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 9; Related Information: CHORUS Timestamp: 2018-02-14 14:54:18; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Small, David W., Sundstrom, Eric J., and Head-Gordon, 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., & Head-Gordon, 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 Head-Gordon, Martin. Sat . "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_1228121,
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 Head-Gordon, Martin},
abstractNote = {},
doi = {10.1063/1.4913740},
journal = {Journal of Chemical Physics},
number = 9,
volume = 142,
place = {United States},
year = {Sat Mar 07 00:00:00 EST 2015},
month = {Sat Mar 07 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4913740

Citation Metrics:
Cited by: 3works
Citation information provided by
Web of Science

Save / Share:
  • 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 low-spin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to high-spin UHF type states, phenomena that are succinctly illustrated by the constituents ofmore » the collinearity test. This complements earlier GHF work on this molecule.« less
  • The method of alternant molecular orbitals has been applied to the calculation of the lowest singlet and triplet states of 4n-cyclopolyenes with incompletely filled degenerate one-electron levels. The solutions obtained have the symmetry of the nuclear skeleton.
  • Theoretical methods have been developed for the analytic determination of second energy derivatives (i.e., force constants) from restricted Hartree--Fock wave functions for certain types of open-shell systems. Specifically treated are systems for which all electrons outside closed shells have their spins parallel. Although the open-shell formalism is somewhat complicated, its application once implemented, is not greatly more arduous than the closed-shell theory presented in 1979 by Pople and co-workers. Like previous procedures for the evaluation of the second derivatives of electrons repulsion integrals, the present method exploits the Rys polynomial concept. Beyond this general framework, however, significant departures appear, andmore » these differences are described. Preliminary application of the new method has been to the two lowest triplet states of the formaldehyde molecule, for which both equilibrium geometry and harmonic vibrational frequencies have been evaluated.« less
  • The renormalization of a gapless {phi}-derivable Hartree-Fock approximation to the O(N)-symmetric {lambda}{phi}{sup 4} theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005).] in order to preserve all the desirable features of {phi}-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu-Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree-Fock approximation this approach allows for a scale-independent renormalization in the vacuum.more » However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree-Fock approximation at fixed renormalization scale {mu} is discussed.« less
  • Interrelations between the local and the global aspects of the stability, continuity, and symmetry properties of variational wave functions are discussed. The spherical limit of one-electron diatomic molecules and the Hartree-Fock approximation of the ground state of the two-electron atom are shown to exhibit the various concepts involved in an ab initio, yet sufficiently simple, manner.