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Title: Representations of Shavitt Graphs Within the Graphical Unitary Group Approach

Abstract

The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach. The DRT is a compact representation of the entire configuration state function expansion space within a molecular electronic structure calculation. Each node of the graph is associated with an integer triple (ak, bk, ck). These integers may be mapped to other quantum numbers, including the number of orbitals, number of electrons, and spin quantum number, and used to display Shavitt graphs in various ways that emphasize different aspects of the expansion space or that reveal different aspects of computed wave functions. In conclusion, the features of several graph density plots are discussed, including electron-hole symmetries and the bonding-antibonding wave function character.

Authors:
ORCiD logo [1];  [1];  [2]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Gonzaga Univ., Spokane, WA (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
OSTI Identifier:
1606234
Alternate Identifier(s):
OSTI ID: 1570045
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Chemistry
Additional Journal Information:
Journal Volume: 41; Journal Issue: 2; Journal ID: ISSN 0192-8651
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; GUGA; Shavitt graph; UGA; graphical unitary group approach; unitary group approach

Citation Formats

Shepard, Ron, Brozell, Scott R., and Gidofalvi, Gergely. Representations of Shavitt Graphs Within the Graphical Unitary Group Approach. United States: N. p., 2019. Web. https://doi.org/10.1002/jcc.26080.
Shepard, Ron, Brozell, Scott R., & Gidofalvi, Gergely. Representations of Shavitt Graphs Within the Graphical Unitary Group Approach. United States. https://doi.org/10.1002/jcc.26080
Shepard, Ron, Brozell, Scott R., and Gidofalvi, Gergely. Thu . "Representations of Shavitt Graphs Within the Graphical Unitary Group Approach". United States. https://doi.org/10.1002/jcc.26080. https://www.osti.gov/servlets/purl/1606234.
@article{osti_1606234,
title = {Representations of Shavitt Graphs Within the Graphical Unitary Group Approach},
author = {Shepard, Ron and Brozell, Scott R. and Gidofalvi, Gergely},
abstractNote = {The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach. The DRT is a compact representation of the entire configuration state function expansion space within a molecular electronic structure calculation. Each node of the graph is associated with an integer triple (ak, bk, ck). These integers may be mapped to other quantum numbers, including the number of orbitals, number of electrons, and spin quantum number, and used to display Shavitt graphs in various ways that emphasize different aspects of the expansion space or that reveal different aspects of computed wave functions. In conclusion, the features of several graph density plots are discussed, including electron-hole symmetries and the bonding-antibonding wave function character.},
doi = {10.1002/jcc.26080},
journal = {Journal of Computational Chemistry},
number = 2,
volume = 41,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
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Table 1 Table 1: Step Description.

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Works referenced in this record:

Hilbert space renormalization for the many-electron problem
journal, February 2016

  • Li, Zhendong; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 144, Issue 8
  • DOI: 10.1063/1.4942174

The multifacet graphically contracted function method. I. Formulation and implementation
journal, August 2014

  • Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R.
  • The Journal of Chemical Physics, Vol. 141, Issue 6
  • DOI: 10.1063/1.4890734

Optimization of nonlinear wave function parameters
journal, January 2006

  • Shepard, Ron; Minkoff, Michael
  • International Journal of Quantum Chemistry, Vol. 106, Issue 15
  • DOI: 10.1002/qua.21140

Spin–orbit interaction with nonlinear wave functions
journal, January 2007

  • Brozell, Scott R.; Shepard, Ron; Zhang, Zhiyong
  • International Journal of Quantum Chemistry, Vol. 107, Issue 15
  • DOI: 10.1002/qua.21496

Spin−Orbit Configuration Interaction Using the Graphical Unitary Group Approach and Relativistic Core Potential and Spin−Orbit Operators
journal, July 1999

  • Yabushita, Satoshi; Zhang, Zhiyong; Pitzer, Russell M.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 29
  • DOI: 10.1021/jp9901242

The accuracy of molecular bond lengths computed by multireference electronic structure methods
journal, June 2008


Wave function analysis with Shavitt graph density in the graphically contracted function method
journal, July 2014

  • Gidofalvi, Gergely; Brozell, Scott R.; Shepard, Ron
  • Theoretical Chemistry Accounts, Vol. 133, Issue 9
  • DOI: 10.1007/s00214-014-1512-7

Nonlinear wave function expansions: A progress report
journal, January 2007

  • Shepard, Ron; Minkoff, Michael; Brozell, Scott R.
  • International Journal of Quantum Chemistry, Vol. 107, Issue 15
  • DOI: 10.1002/qua.21503

The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights
journal, August 2018


A General Nonlinear Expansion Form for Electronic Wave Functions
journal, December 2005

  • Shepard, Ron
  • The Journal of Physical Chemistry A, Vol. 109, Issue 50
  • DOI: 10.1021/jp0543431

Evaluation of the Spin−Orbit Interaction within the Graphically Contracted Function Method
journal, November 2009

  • Brozell, Scott R.; Shepard, Ron
  • The Journal of Physical Chemistry A, Vol. 113, Issue 45
  • DOI: 10.1021/jp9059032

Variations in the Nature of Triple Bonds: The N 2 , HCN, and HC 2 H Series
journal, June 2016


The unitary group approach in Configuration Interaction (CI) methods
journal, May 1984


State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve
journal, October 2004

  • Chan, Garnet Kin-Lic; Kállay, Mihály; Gauss, Jürgen
  • The Journal of Chemical Physics, Vol. 121, Issue 13
  • DOI: 10.1063/1.1783212