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

Title: Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4884951· OSTI ID:22311378
 [1]
  1. Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (United States)
+ Show Author Affiliations

We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix form in an atomic orbital basis, where the Green's function and self-energy are built on the imaginary frequency and imaginary time domain, respectively, and fast Fourier transform is used to efficiently transform these quantities as needed. We apply this method to several archetypical examples of strong correlation, such as a H{sub 32} finite lattice that displays a highly multireference electronic ground state even at equilibrium lattice spacing. In all cases, GF2 gives a physically meaningful description of the metal to insulator transition in these systems, without resorting to spin-symmetry breaking. Our results show that self-consistent Green's function many-body theory offers a viable route to describing strong correlations while remaining within a computationally tractable single-particle formalism.

OSTI ID:
22311378
Journal Information:
Journal of Chemical Physics, Vol. 140, Issue 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
Country of Publication:
United States
Language:
English

References (84)

On green's functions and their applications journal March 1990
Electron propagator theory: an approach to prediction and interpretation in quantum chemistry: Electron propagator theory journal September 2012
The Dalton quantum chemistry program system: The Dalton program
  • Aidas, Kestutis; Angeli, Celestino; Bak, Keld L.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3 https://doi.org/10.1002/wcms.1172
journal September 2013
Green's function calculations of ground-state correlation energies journal July 1977
Problems in electron propagator calculations of the correlation energy journal July 1982
A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach journal May 1980
How much double excitation character do the lowest excited states of linear polyenes have? journal October 2006
The ALPS project release 1.3: Open-source software for strongly correlated systems journal March 2007
Combining long-range configuration interaction with short-range density functionals journal August 1997
Challenges for Density Functional Theory journal December 2011
Second-order perturbation theory with a CASSCF reference function journal July 1990
Strong Correlation in Acene Sheets from the Active-Space Variational Two-Electron Reduced Density Matrix Method: Effects of Symmetry and Size journal June 2011
Entanglement and Polyradical Character of Polycyclic Aromatic Hydrocarbons Predicted by Projected Hartree–Fock Theory journal May 2013
Predicting Singlet–Triplet Energy Splittings with Projected Hartree–Fock Methods journal July 2013
A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics journal January 2006
New electron correlation theories for transition metal chemistry journal January 2011
Optimization of density matrix functionals by the Hartree–Fock–Bogoliubov method journal December 2002
Many‐Body Green's Functions for Finite, Nonuniform Systems: Applications to Closed Shell Atoms journal August 1972
Describing static correlation in bond dissociation by Kohn–Sham density functional theory journal March 2005
Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation journal April 2005
Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group journal October 2006
On the universality of the long-/short-range separation in multiconfigurational density-functional theory journal February 2007
The restricted active space followed by second-order perturbation theory method: Theory and application to the study of CuO2 and Cu2O2 systems journal May 2008
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian journal October 2008
Levels of self-consistency in the GW approximation journal March 2009
Strong correlations via constrained-pairing mean-field theory journal September 2009
Constrained-pairing mean-field theory. II. Exact treatment of dissociations to nondegenerate orbitals journal October 2009
Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method journal July 2010
Dynamical mean-field theory from a quantum chemical perspective journal March 2011
The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule journal February 1981
Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces journal August 1988
A comparison between the Mo/ller–Plesset and Green’s function perturbative approaches to the calculation of the correlation energy in the many‐electron problem journal October 1990
Second‐order perturbation theory with a complete active space self‐consistent field reference function journal January 1992
One‐electron density matrices and energy gradients in second‐order electron propagator theory journal June 1992
Projected Hartree–Fock theory journal April 2012
A multiconfigurational hybrid density-functional theory journal July 2012
Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories journal April 2013
Valence one-electron and shake-up ionization bands of carbon clusters. I. The Cn (n=3,5,7,9) chains journal October 1999
Communication: Random phase approximation renormalized many-body perturbation theory journal November 2013
Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange journal January 2014
Coupled cluster channels in the homogeneous electron gas journal March 2014
Static correlation beyond the random phase approximation: Dissociating H 2 with the Bethe-Salpeter equation and time-dependent GW journal April 2014
Electron correlation and the self-interaction error of density functional theory journal June 2002
The connection between self-interaction and static correlation: a random phase approximation perspective journal August 2010
A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method journal January 1980
Correlation Energy of an Electron Gas at High Density journal April 1957
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
A Collective Description of Electron Interactions. I. Magnetic Interactions journal June 1951
A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions journal January 1952
A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas journal November 1953
Beyond the random-phase approximation: A new approximation scheme for the polarization propagator journal November 1982
New approach to the one-particle Green's function for finite Fermi systems journal September 1983
Particle-particle propagator in the algebraic diagrammatic construction scheme at third order journal February 1989
Simplified Green-function approximations: Further assessment of a polarization model for second-order calculation of outer-valence ionization potentials in molecules journal November 1991
Variational energy functionals of the Green function and of the density tested on molecules journal January 2006
Self-interaction in Green’s-function theory of the hydrogen atom journal March 2007
Self-interaction correction to density-functional approximations for many-electron systems journal May 1981
Molecular tests of the random phase approximation to the exchange-correlation energy functional journal October 2001
Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study journal December 2011
Self-consistent G W : All-electron implementation with localized basis functions journal August 2013
Ab initio self-consistent Gorkov-Green's function calculations of semimagic nuclei: Formalism at second order with a two-nucleon interaction journal December 2011
Ab initio Gorkov-Green's function calculations of open-shell nuclei journal January 2013
Ab initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei: Numerical implementation at second order with a two-nucleon interaction journal February 2014
Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory journal April 2013
Range-Separated Brueckner Coupled Cluster Doubles Theory journal April 2014
Total Energy Method from Many-Body Formulation journal April 2002
Comment on “Total Energy Method from Many-Body Formulation” journal May 2003
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal January 1996
The density-matrix renormalization group journal April 2005
VESTA : a three-dimensional visualization system for electronic and structural analysis journal May 2008
Fully self-consistent GW calculations for atoms and molecules journal October 2006
A Unified View of the Theoretical Description of Magnetic Coupling in Molecular Chemistry and Solid State Physics journal July 2006
Strong correlations via constrained-pairing mean-field theory text January 2009
Dynamical mean-field theory from a quantum chemical perspective text January 2010
Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction text January 2011
Strong electronic correlation in the Hydrogen chain: a variational Monte Carlo study text January 2011
Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory text January 2012
Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange text January 2013
Self-consistent GW: All-electron implementation with localized basis functions text January 2013
Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GW text January 2013
The density-matrix renormalization group text January 2004
Describing static correlation in bond dissociation by Kohn-Sham density functional theory text January 2004
Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group text January 2006
Self-interaction in Green's-function theory of the hydrogen atom preprint January 2007

Cited By (31)

Local Hamiltonians for quantitative Green's function embedding methods journal November 2014
Fractional charge and spin errors in self-consistent Green’s function theory journal May 2015
Communication: Towards ab initio self-energy embedding theory in quantum chemistry journal December 2015
Self-consistent second-order Green’s function perturbation theory for periodic systems journal February 2016
Coupled cluster Green function: Model involving single and double excitations journal April 2016
Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function journal November 2016
One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms journal July 2017
Communication: Explicitly correlated formalism for second-order single-particle Green’s function journal September 2017
Comparison of Green’s functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD) journal June 2018
Even-handed subsystem selection in projection-based embedding journal October 2018
Low-scaling analytical gradients for the direct random phase approximation using an atomic orbital formalism journal December 2018
Explicitly correlated renormalized second-order Green’s function for accurate ionization potentials of closed-shell molecules journal June 2019
Stochastic resolution of identity second-order Matsubara Green’s function theory journal July 2019
Efficient computation of the second-Born self-energy using tensor-contraction operations journal November 2019
Local density approximation in site-occupation embedding theory journal May 2016
Properties of advanced coupled-cluster Green's function journal July 2017
Finite temperature quantum embedding theories for correlated systems journal February 2017
Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function journal December 2016
Effect of propagator renormalization on the band gap of insulating solids journal August 2019
Sparse sampling approach to efficient ab initio calculations at finite temperature journal January 2020
Systematically improvable multiscale solver for correlated electron systems journal March 2015
Testing self-energy embedding theory in combination with GW journal October 2017
Chebyshev polynomial representation of imaginary-time response functions journal August 2018
Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods journal September 2017
Systematically improvable multi-scale solver for correlated electron systems text January 2014
Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function text January 2016
Finite temperature quantum embedding theories for correlated systems text January 2016
Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods text January 2017
Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD) text January 2018
Even-handed subsystem selection in projection-based embedding text January 2018
Effect of propagator renormalization on the band gap of insulating solids text January 2018

Similar Records

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory
Journal Article · Wed Jun 25 00:00:00 EDT 2014 · Journal of Chemical Physics · OSTI ID:22311378
Fractional charge and spin errors in self-consistent Green’s function theory
Journal Article · Thu May 21 00:00:00 EDT 2015 · Journal of Chemical Physics · OSTI ID:22311378
Fractional charge and spin errors in self-consistent Green’s function theory
Journal Article · Tue May 19 00:00:00 EDT 2015 · Journal of Chemical Physics · OSTI ID:22311378

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
APPROXIMATIONS
FOURIER TRANSFORMATION
GREEN FUNCTION
GROUND STATES
MANY-BODY PROBLEM
PERTURBATION THEORY
SPIN