A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry

Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming; Chan, Garnet K. -L.

doi:10.1021/acs.jctc.6b00316

Title: A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry

Abstract

Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. Furthermore, we explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S_N2 reaction.

Authors:

Wouters, Sebastian ^[1]; Jiménez-Hoyos, Carlos A. ^[1]; Sun, Qiming ^[1]; Chan, Garnet K. -L. ^[1]

Department of Chemistry, Frick Chemistry Laboratory, Princeton University, Princeton, New Jersey 08544, United States

Publication Date:: Thu May 26 00:00:00 EDT 2016

Research Org.:: Princeton Univ., NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1254515

Alternate Identifier(s):: OSTI ID: 1257267; OSTI ID: 1258032

Grant/Contract Number:: SC0010530

Resource Type:: Published Article

Journal Name:: Journal of Chemical Theory and Computation

Additional Journal Information:: Journal Name: Journal of Chemical Theory and Computation Journal Volume: 12 Journal Issue: 6; Journal ID: ISSN 1549-9618

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Wouters, Sebastian, Jiménez-Hoyos, Carlos A., Sun, Qiming, and Chan, Garnet K. -L. A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.  United States: N. p., 2016. 
Web.  doi:10.1021/acs.jctc.6b00316.

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                    Wouters, Sebastian, Jiménez-Hoyos, Carlos A., Sun, Qiming, & Chan, Garnet K. -L. A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.  United States.  https://doi.org/10.1021/acs.jctc.6b00316

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                    Wouters, Sebastian, Jiménez-Hoyos, Carlos A., Sun, Qiming, and Chan, Garnet K. -L. Thu .  
"A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry".  United States.  https://doi.org/10.1021/acs.jctc.6b00316.

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@article{osti_1254515,

  title        = {A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry},

  author       = {Wouters, Sebastian and Jiménez-Hoyos, Carlos A. and Sun, Qiming and Chan, Garnet K. -L.},

  abstractNote = {Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. Furthermore, we explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction.},

  doi          = {10.1021/acs.jctc.6b00316},

  journal      = {Journal of Chemical Theory and Computation},

  number       = 6,

  volume       = 12,

  place        = {United States},

  year         = {Thu May 26 00:00:00 EDT 2016},

  month        = {Thu May 26 00:00:00 EDT 2016}

}

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Title: A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry

Abstract

Citation Formats

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory journal, February 2013

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory journal, January 2016

Molecular Electronic-Structure Theory book, August 2000

Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts journal, October 2013

New approach to large-scale nuclear structure calculations journal, May 2001

Density functionals for coulomb systems journal, September 1983

Successive Approximations by the Rayleigh-Ritz Variation Method journal, May 1933

Many – Body Methods in Chemistry and Physics book, January 2009

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory journal, November 2012

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Coupled‐cluster calculations of nuclear magnetic resonance chemical shifts journal, September 1995

The Coupled-Cluster Approximation: A Simple Approach to Spin-Lattice and Hubbard Models journal, February 1990

Cluster density matrix embedding theory for quantum spin systems journal, May 2015

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal, January 1989

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model journal, April 2014

Ab initio quantum chemistry using the density matrix renormalization group journal, March 1999

Correlated Lattice Fermions in d = ∞ Dimensions journal, January 1989

Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal, May 1992

Electron correlation in solids via density embedding theory journal, August 2014

Density matrix formulation for quantum renormalization groups journal, November 1992

The density matrix renormalization group for ab initio quantum chemistry journal, September 2014

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal, January 1996

Geminal embedding scheme for optimal atomic basis set construction in correlated calculations journal, December 2015

Dynamical Mean-Field Theory for Quantum Chemistry journal, March 2011

A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities journal, January 2003

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group journal, October 2006

On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods journal, December 1966

Numerical solution of the d =∞ Hubbard model: Evidence for a Mott transition journal, August 1992

Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries journal, August 2014

Short-range correlations in nuclear wave functions journal, June 1960

Density matrix embedding from broken symmetry lattice mean fields journal, January 2014

Investigation of metal–insulator-like transition through the ab initio density matrix renormalization group approach journal, December 2014

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms journal, December 2015

Dynamical mean-field theory from a quantum chemical perspective journal, March 2011

Thouless theorem for matrix product states and subsequent post density matrix renormalization group methods journal, August 2013

Spectral functions of strongly correlated extended systems via an exact quantum embedding journal, April 2015

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory
journal, February 2013

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
journal, January 2016

Molecular Electronic-Structure Theory
book, August 2000

Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts
journal, October 2013

New approach to large-scale nuclear structure calculations
journal, May 2001

Density functionals for coulomb systems
journal, September 1983

Successive Approximations by the Rayleigh-Ritz Variation Method
journal, May 1933

Many – Body Methods in Chemistry and Physics
book, January 2009

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
journal, November 2012

CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry
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Density matrix embedding in an antisymmetrized geminal power bath
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Coupled‐cluster calculations of nuclear magnetic resonance chemical shifts
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The Coupled-Cluster Approximation: A Simple Approach to Spin-Lattice and Hubbard Models
journal, February 1990

Cluster density matrix embedding theory for quantum spin systems
journal, May 2015

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
journal, April 2014

Ab initio quantum chemistry using the density matrix renormalization group
journal, March 1999

Correlated Lattice Fermions in $d = \infty$ Dimensions
journal, January 1989

Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions
journal, May 1992

Electron correlation in solids via density embedding theory
journal, August 2014

Density matrix formulation for quantum renormalization groups
journal, November 1992

The density matrix renormalization group for ab initio quantum chemistry
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Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

Geminal embedding scheme for optimal atomic basis set construction in correlated calculations
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A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities
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Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group
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Numerical solution of the d =∞ Hubbard model: Evidence for a Mott transition
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Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
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