Representations of Shavitt Graphs Within the Graphical Unitary Group Approach

Shepard, Ron; Brozell, Scott R.; Gidofalvi, Gergely

doi:10.1002/jcc.26080

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 (a_k, b_k, c_k). 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:

^[1]; Brozell, Scott R. ^[1]; Gidofalvi, Gergely ^[2]

Argonne National Lab. (ANL), Lemont, IL (United States)
Gonzaga Univ., Spokane, WA (United States)

Publication Date:: 2019-10-10

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.  doi:10.1002/jcc.26080.

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                    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

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                    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.

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@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}

}

Copy to clipboard

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https://doi.org/10.1002/jcc.26080

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Figures / Tables:

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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
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The multifacet graphically contracted function method. I. Formulation and implementation
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Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R.
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Paldus, Josef
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Spin–orbit interaction with nonlinear wave functions
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Brozell, Scott R.; Shepard, Ron; Zhang, Zhiyong
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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
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The accuracy of molecular bond lengths computed by multireference electronic structure methods
journal, June 2008

Shepard, Ron; Kedziora, Gary S.; Lischka, Hans
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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
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Nonlinear wave function expansions: A progress report
journal, January 2007

Shepard, Ron; Minkoff, Michael; Brozell, Scott R.
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The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights
journal, August 2018

Shepard, Ron; Brozell, Scott R.
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A General Nonlinear Expansion Form for Electronic Wave Functions ^†
journal, December 2005

Shepard, Ron
The Journal of Physical Chemistry A, Vol. 109, Issue 50
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journal, November 2009

Brozell, Scott R.; Shepard, Ron
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journal, June 2016

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text, January 2015

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arXiv
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Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

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

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

Optimization of nonlinear wave function parameters journal, January 2006

Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems journal, December 1974

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

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

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

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

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

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

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

Hilbert space renormalization for the many-electron problem text, January 2015

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

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

Optimization of nonlinear wave function parameters
journal, January 2006

Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems
journal, December 1974

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

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

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

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

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

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

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

Hilbert space renormalization for the many-electron problem
text, January 2015