The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights

Shepard, Ron; Brozell, Scott R.

doi:10.1080/00268976.2019.1635275

Title: The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights

Abstract

The All Configuration Mean Energy (ACME) conditions are a special case of state averaging for Multiconfigurational Self-Consistent-Field (MCSCF) orbital optimisation. The method is formulated using the Graphical Unitary Group Approach (GUGA) in which the Configuration State Function (CSF) basis is represented as walks within a Shavitt graph. This graphical formulation leads to efficient recursive algorithms for the energy and reduced density matrices (RDM) that are independent of the CSF dimension and that scale only as O(n2) where n is the number of occupied orbitals. The Hamiltonian matrix diagonalization step is obviated and the CSF expansion coefficients are neither referenced nor required. This allows MCSCF orbital optimisation to be performed for essentially unlimited numbers of active orbitals and arbitrarily large CSF expansions. The discussion includes various types of CSF expansion spaces, the partitioning of the essential and redundant orbital optimisation parameters, the computation of the spin-density, and the formulation of state-specific analytic gradients and nonadiabatic coupling for high-level electronic structure methods that use the ACME MCSCF orbitals.

Authors:

Shepard, Ron ^[1]; Brozell, Scott R. ^[1]

Argonne National Lab. (ANL), Lemont, IL (United States)

Publication Date:: Fri Jun 28 00:00:00 EDT 2019

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division

OSTI Identifier:: 1543139

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Molecular Physics

Additional Journal Information:: Journal Volume: 117; Journal Issue: 17; Journal ID: ISSN 0026-8976

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; MCSCF; analytic gradient; electronic structure; nonadiabatic coupling; state averaging

Citation Formats


                    Shepard, Ron, and Brozell, Scott R. The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights.  United States: N. p., 2019. 
Web.  doi:10.1080/00268976.2019.1635275.

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                    Shepard, Ron, & Brozell, Scott R. The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights.  United States.  https://doi.org/10.1080/00268976.2019.1635275

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                    Shepard, Ron, and Brozell, Scott R. Fri .  
"The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights".  United States.  https://doi.org/10.1080/00268976.2019.1635275.  https://www.osti.gov/servlets/purl/1543139.

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@article{osti_1543139,

  title        = {The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights},

  author       = {Shepard, Ron and Brozell, Scott R.},

  abstractNote = {The All Configuration Mean Energy (ACME) conditions are a special case of state averaging for Multiconfigurational Self-Consistent-Field (MCSCF) orbital optimisation. The method is formulated using the Graphical Unitary Group Approach (GUGA) in which the Configuration State Function (CSF) basis is represented as walks within a Shavitt graph. This graphical formulation leads to efficient recursive algorithms for the energy and reduced density matrices (RDM) that are independent of the CSF dimension and that scale only as O(n2) where n is the number of occupied orbitals. The Hamiltonian matrix diagonalization step is obviated and the CSF expansion coefficients are neither referenced nor required. This allows MCSCF orbital optimisation to be performed for essentially unlimited numbers of active orbitals and arbitrarily large CSF expansions. The discussion includes various types of CSF expansion spaces, the partitioning of the essential and redundant orbital optimisation parameters, the computation of the spin-density, and the formulation of state-specific analytic gradients and nonadiabatic coupling for high-level electronic structure methods that use the ACME MCSCF orbitals.},

  doi          = {10.1080/00268976.2019.1635275},

  journal      = {Molecular Physics},

  number       = 17,

  volume       = 117,

  place        = {United States},

  year         = {Fri Jun 28 00:00:00 EDT 2019},

  month        = {Fri Jun 28 00:00:00 EDT 2019}

}

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Journal Article:

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https://doi.org/10.1080/00268976.2019.1635275

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Cited by: 7 works

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Figures / Tables:

Table 1: All segment values^† for $H_{kk}$ and ACME RDMs.

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Works referenced in this record:

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Works referencing / citing this record:

Representations of Shavitt Graphs Within the Graphical Unitary Group Approach
journal, October 2019

Shepard, Ron; Brozell, Scott R.; Gidofalvi, Gergely
Journal of Computational Chemistry, Vol. 41, Issue 2
DOI: 10.1002/jcc.26080

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Title: The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights

Abstract

Citation Formats

Figures / Tables:

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Multireference Nature of Chemistry: The Coupled-Cluster View journal, December 2011

Two-Electron Reduced Density Matrix as the Basic Variable in Many-Electron Quantum Chemistry and Physics journal, August 2011

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SCF theory for excited states: I. Optimal orbitals for the states of a configuration journal, November 1974

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Hamiltonian Matrix and Reduced Density Matrix Construction with Nonlinear Wave Functions journal, July 2006

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

Localized Atomic and Molecular Orbitals journal, July 1963

Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces journal, August 1988

Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. I. Method journal, November 2003

Analytic MRCI gradient for excited states: formalism and application to the n-π∗ valence- and n-(3s,3p) Rydberg states of formaldehyde journal, June 2002

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

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

Optimization of nonlinear wave function parameters journal, January 2006

Atomic self-consistent-field program by the basis set expansion method: Columbus version journal, August 2012

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Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications
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MCSCF optimization through combined use of natural orbitals and the brillouin-levy-berthier theorem
journal, November 1979

Multiconfiguration wavefunctions for excited states. Selection of optimal configurations: The b ¹ Σ ⁺ and d ¹ Σ ⁺ states of NH
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Optimization of orbitals for multiconfigurational reference states
journal, October 1978

A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method
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General second order MCSCF theory: A density matrix directed algorithm
journal, July 1980

The Construction and Interpretation of Mcscf Wavefunctions
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Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
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Many – Body Methods in Chemistry and Physics
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Systematic design of active spaces for multi-reference calculations of singlet–triplet gaps of organic diradicals, with benchmarks against doubly electron-attached coupled-cluster data
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Hamiltonian Matrix and Reduced Density Matrix Construction with Nonlinear Wave Functions
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On the evaluation of analytic energy derivatives for correlated wave functions
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