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

Title: Fractional charge and spin errors in self-consistent Green’s function theory

Abstract

We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Here, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.

Authors:
 [1];  [1];  [1]
  1. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Research Org.:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1843751
Alternate Identifier(s):
OSTI ID: 1228202
Grant/Contract Number:  
SC0010381; ER16391
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Hybrid density functional calculations; Self consistent field methods; Perturbation theory; Random phase approximation; Becke; Three-parameter; Lee-Yang-Parr; Dyson-Schwinger equation; Free electron model; Correlation energy; Density functional theory

Citation Formats

Phillips, Jordan J., Kananenka, Alexei A., and Zgid, Dominika. Fractional charge and spin errors in self-consistent Green’s function theory. United States: N. p., 2015. Web. doi:10.1063/1.4921259.
Phillips, Jordan J., Kananenka, Alexei A., & Zgid, Dominika. Fractional charge and spin errors in self-consistent Green’s function theory. United States. https://doi.org/10.1063/1.4921259
Phillips, Jordan J., Kananenka, Alexei A., and Zgid, Dominika. 2015. "Fractional charge and spin errors in self-consistent Green’s function theory". United States. https://doi.org/10.1063/1.4921259. https://www.osti.gov/servlets/purl/1843751.
@article{osti_1843751,
title = {Fractional charge and spin errors in self-consistent Green’s function theory},
author = {Phillips, Jordan J. and Kananenka, Alexei A. and Zgid, Dominika},
abstractNote = {We examine fractional charge and spin errors in self-consistent Green’s function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Here, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.},
doi = {10.1063/1.4921259},
url = {https://www.osti.gov/biblio/1843751}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 19,
volume = 142,
place = {United States},
year = {Tue May 19 00:00:00 EDT 2015},
month = {Tue May 19 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 33 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Communication: A density functional with accurate fractional-charge and fractional-spin behaviour for s -electrons
journal, August 2011


Generalized Gradient Approximation Made Simple
journal, October 1996


Wave function methods for fractional electrons
journal, August 2013


Perturbation Theory for an Infinite Medium of Fermions. II
journal, February 1961


Exchange and correlation in open systems of fluctuating electron number
journal, October 2007


Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation
journal, April 2005


Fractional charge perspective on the band gap in density-functional theory
journal, March 2008


The connection between self-interaction and static correlation: a random phase approximation perspective
journal, August 2010


Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals
journal, June 2014


Communication: Random phase approximation renormalized many-body perturbation theory
journal, November 2013


Correlation Energy of an Electron Gas at High Density
journal, April 1957


Failure of the random-phase-approximation correlation energy
journal, April 2012


Delocalization errors in density functionals and implications for main-group thermochemistry
journal, November 2008


Systematically improvable multi-scale solver for correlated electron systems
text, January 2014


Local Hamiltonians for quantitative Green's function embedding methods
journal, November 2014


The Dalton quantum chemistry program system: The Dalton program
journal, September 2013

  • Aidas, Kestutis; Angeli, Celestino; Bak, Keld L.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3
  • https://doi.org/10.1002/wcms.1172

Systematically improvable multiscale solver for correlated electron systems
journal, March 2015


Fractional spins and static correlation error in density functional theory
journal, September 2008


Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
journal, August 2009


Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+
journal, March 2007


Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation
journal, September 2013


Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms
journal, January 2009


Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993


Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
text, January 1988


Extension of many-body theory and approximate density functionals to fractional charges and fractional spins
journal, September 2013


Toward the construction of parameter-free doubly hybrid density functionals
journal, December 2014


Fractional charge perspective on the band-gap in density-functional theory
text, January 2007


Tests of functionals for systems with fractional electron number
journal, April 2007


Static correlation and electron localization in molecular dimers from the self-consistent RPA and G W approximation
journal, April 2015


The ALPS project release 1.3: Open-source software for strongly correlated systems
journal, March 2007


Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
journal, April 2008


Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems
journal, February 2009


Many-electron self-interaction error in approximate density functionals
journal, November 2006


Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999


Second-Order Perturbation Theory with Fractional Charges and Fractional Spins
journal, March 2009


Levels of self-consistency in the GW approximation
journal, March 2009


Many-electron self-interaction and spin polarization errors in local hybrid density functionals
journal, October 2010


Fractional spins and static correlation error in density functional theory
text, January 2008


Inhomogeneous Electron Gas
journal, March 1973


Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory
journal, June 2014


Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation
journal, May 2014


Metal−Ligand Delocalization in Magnetic Orbitals of Binuclear Complexes
journal, September 2002


Generalized gradient approximation to the angle- and system-averaged exchange hole
journal, September 1998


Electron correlation and the self-interaction error of density functional theory
journal, June 2002


Self-Consistent Approximations in Many-Body Systems
journal, August 1962


Note on an Approximation Treatment for Many-Electron Systems
journal, October 1934


Works referencing / citing this record:

Testing self-energy embedding theory in combination with GW
journal, October 2017


Effect of propagator renormalization on the band gap of insulating solids
text, January 2018


Communication: Towards ab initio self-energy embedding theory in quantum chemistry
journal, December 2015


Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT
journal, April 2019


Self-consistent second-order Green’s function perturbation theory for periodic systems
journal, February 2016


Fractional-charge and fractional-spin errors in range-separated density-functional theory
journal, August 2016


Chebyshev polynomial representation of imaginary-time response functions
journal, August 2018


Finite temperature quantum embedding theories for correlated systems
journal, February 2017


Effect of propagator renormalization on the band gap of insulating solids
journal, August 2019


Efficient computation of the second-Born self-energy using tensor-contraction operations
journal, November 2019


Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules
journal, January 2020


Describing strong correlation with fractional-spin correction in density functional theory
journal, September 2018


Comparison of Green’s functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD)
journal, June 2018


Sparse sampling approach to efficient ab initio calculations at finite temperature
journal, January 2020


Sparse sampling approach to efficient ab initio calculations at finite temperature
journal, January 2020