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Title: Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes

Abstract

The existence of a generalized Hartree–Fock solution in C 60 has led to controversy on whether C 60 is polyradicaloid (or strongly correlated). We attempt to end the controversy with κ -OOMP2 which removes the illusion of this artificial symmetry breaking. We conclude that C 60 is not strongly correlated.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Department of Chemistry, University of California, Berkeley, USA, Chemical Sciences Division
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1494777
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Physical Chemistry Chemical Physics. PCCP (Print)
Additional Journal Information:
Journal Name: Physical Chemistry Chemical Physics. PCCP (Print) Journal Volume: 21 Journal Issue: 9; Journal ID: ISSN 1463-9076
Publisher:
Royal Society of Chemistry (RSC)
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Lee, Joonho, and Head-Gordon, Martin. Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes. United Kingdom: N. p., 2019. Web. https://doi.org/10.1039/C8CP07613H.
Lee, Joonho, & Head-Gordon, Martin. Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes. United Kingdom. https://doi.org/10.1039/C8CP07613H
Lee, Joonho, and Head-Gordon, Martin. Wed . "Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes". United Kingdom. https://doi.org/10.1039/C8CP07613H.
@article{osti_1494777,
title = {Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C 60 , C 36 , and C 20 fullerenes},
author = {Lee, Joonho and Head-Gordon, Martin},
abstractNote = {The existence of a generalized Hartree–Fock solution in C 60 has led to controversy on whether C 60 is polyradicaloid (or strongly correlated). We attempt to end the controversy with κ -OOMP2 which removes the illusion of this artificial symmetry breaking. We conclude that C 60 is not strongly correlated.},
doi = {10.1039/C8CP07613H},
journal = {Physical Chemistry Chemical Physics. PCCP (Print)},
number = 9,
volume = 21,
place = {United Kingdom},
year = {2019},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1039/C8CP07613H

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Cited by: 12 works
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Works referenced in this record:

Electronic and structural properties of the cage-like molecules C20 to C36
journal, January 2003

  • Paulus, Beate
  • Physical Chemistry Chemical Physics, Vol. 5, Issue 16
  • DOI: 10.1039/b304539k

Relative stabilities of fullerene, cumulene, and polyacetylene structures for C n  : n =18–60
journal, February 1992

  • Feyereisen, Martin; Gutowski, Maciej; Simons, Jack
  • The Journal of Chemical Physics, Vol. 96, Issue 4
  • DOI: 10.1063/1.461989

Phosphorescence of C60 in rare gas matrices
journal, October 1996


C36, a hexavalent building block for fullerene compounds and solids
journal, February 1999


C 36 :  The Best Fullerene for Covalent Bonding
journal, April 1999

  • Fowler, Patrick W.; Mitchell, Dean; Zerbetto, Francesco
  • Journal of the American Chemical Society, Vol. 121, Issue 13
  • DOI: 10.1021/ja983853o

C20 Carbon Clusters: Fullerene–Boat–Sheet Generation, Mass Selection, Photoelectron Characterization
journal, August 2006

  • Prinzbach, Horst; Wahl, Fabian; Weiler, Andreas
  • Chemistry - A European Journal, Vol. 12, Issue 24
  • DOI: 10.1002/chem.200501611

MP2, Tamm-Dancoff, and RPA methods based on the generalized HF solution
journal, January 2000


Electronic Structure of Small Fullerenes: Evidence for the High Stability of C 32
journal, December 1998


Approximate symmetry-breaking in the independent particle model of monocyclic completely conjugated polyenes
journal, September 2007


Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988


Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes
journal, January 2017

  • Lee, Joonho; Small, David W.; Epifanovsky, Evgeny
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 2
  • DOI: 10.1021/acs.jctc.6b01092

Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model
journal, April 2001


Closed-shell electronic requirements for small fullerene cage structures
journal, August 1995


Jahn-Teller distortions in solid C20 and other fullerene structures
journal, October 1993


Enthalpy–entropy interplay for C[sub 36] cages: B3LYP/6-31G[sup ∗] calculations
journal, January 2000

  • Slanina, Zdeněk; Uhlı́k, Filip; Zhao, Xiang
  • The Journal of Chemical Physics, Vol. 113, Issue 12
  • DOI: 10.1063/1.1288368

A spin correction procedure for unrestricted Hartree-Fock and Møller-Plesset wavefunctions for singlet diradicals and polyradicals
journal, September 1988


Coupled cluster geometries and energies of C20 carbon cluster isomers – A new benchmark study
journal, June 2015


Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model
journal, February 2009

  • Small, David W.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 130, Issue 8
  • DOI: 10.1063/1.3069296

Characterizing the Dimerizations of Phenalenyl Radicals by ab Initio Calculations and Spectroscopy:  σ-Bond Formation versus Resonance π-Stabilization
journal, December 2005

  • Small, David; Rosokha, Sergiy V.; Kochi, Jay K.
  • The Journal of Physical Chemistry A, Vol. 109, Issue 49
  • DOI: 10.1021/jp054244n

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

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Size-consistent Brueckner theory limited to double substitutions
journal, December 1989


Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules
journal, April 2007

  • Lochan, Rohini C.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 126, Issue 16
  • DOI: 10.1063/1.2718952

Exploring the competition between localization and delocalization of the neutral soliton defect in polyenyl chains with the orbital optimized second order opposite spin method
journal, February 2012

  • Kurlancheek, Westin; Lochan, Rohini; Lawler, Keith
  • The Journal of Chemical Physics, Vol. 136, Issue 5
  • DOI: 10.1063/1.3679658

Diradicals
journal, July 2013


Why does unrestricted Mo/ller–Plesset perturbation theory converge so slowly for spin‐contaminated wave functions?
journal, December 1988

  • Gill, Peter M. W.; Pople, John A.; Radom, Leo
  • The Journal of Chemical Physics, Vol. 89, Issue 12
  • DOI: 10.1063/1.455312

Comparison of configuration interaction expansions based on different orbital transformations
journal, January 1976

  • Shavitt, Isaiah; Rosenberg, Bruce J.; Palalikit, Surat
  • International Journal of Quantum Chemistry, Vol. 10, Issue S10
  • DOI: 10.1002/qua.560100804

A nonorthogonal CI treatment of symmetry breaking in sigma formyloxyl radical
journal, May 1998

  • Ayala, Philippe Y.; Schlegel, H. Bernhard
  • The Journal of Chemical Physics, Vol. 108, Issue 18
  • DOI: 10.1063/1.476190

Some surprising failures of Brueckner coupled cluster theory
journal, May 2000

  • Crawford, T. Daniel; Stanton, John F.
  • The Journal of Chemical Physics, Vol. 112, Issue 18
  • DOI: 10.1063/1.481424

Coupled cluster valence bond theory for open-shell systems with application to very long range strong correlation in a polycarbene dimer
journal, July 2017

  • Small, David W.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 147, Issue 2
  • DOI: 10.1063/1.4991797

Nuclear Saturation and Two-Body Forces. II. Tensor Forces
journal, October 1954


On the structure and vibrational frequencies of C20
journal, January 1996

  • Martin, Jan M. L.; El-Yazal, Jamal; François, Jean-Pierre
  • Chemical Physics Letters, Vol. 248, Issue 5-6
  • DOI: 10.1016/0009-2614(95)01334-2

What Are the Ground State Structures of C 20 and C 24 ? An Explicitly Correlated Ab Initio Approach
journal, December 2015

  • Manna, Debashree; Martin, Jan M. L.
  • The Journal of Physical Chemistry A, Vol. 120, Issue 1
  • DOI: 10.1021/acs.jpca.5b10266

UHF natural orbitals for defining and starting MC‐SCF calculations
journal, April 1988

  • Pulay, Peter; Hamilton, Tracy P.
  • The Journal of Chemical Physics, Vol. 88, Issue 8
  • DOI: 10.1063/1.454704

A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock
journal, March 2015

  • Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 142, Issue 9
  • DOI: 10.1063/1.4913740

Polyradical Character and Spin Frustration in Fullerene Molecules: An Ab Initio Non-Collinear Hartree–Fock Study
journal, October 2014

  • Jiménez-Hoyos, Carlos A.; Rodríguez-Guzmán, R.; Scuseria, Gustavo E.
  • The Journal of Physical Chemistry A, Vol. 118, Issue 42
  • DOI: 10.1021/jp508383z

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014


Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory
journal, January 2015

  • Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 142, Issue 2
  • DOI: 10.1063/1.4905120

Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes
journal, April 2014

  • Small, David W.; Lawler, Keith V.; Head-Gordon, Martin
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 5
  • DOI: 10.1021/ct500112y

Stability of Buckminsterfullerene, C60
journal, November 2003


Spin contamination and noncollinearity in general complex Hartree–Fock wave functions
journal, October 2015


Structure and Bonding in Carbon Clusters C 14 to C 24 : Chains, Rings, Bowls, Plates, and Cages
journal, July 1997


Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model
journal, December 1998

  • Krylov, Anna I.; Sherrill, C. David; Byrd, Edward F. C.
  • The Journal of Chemical Physics, Vol. 109, Issue 24
  • DOI: 10.1063/1.477764

Use of approximate integrals in ab initio theory. An application in MP2 energy calculations
journal, June 1993

  • Feyereisen, Martin; Fitzgerald, George; Komornicki, Andrew
  • Chemical Physics Letters, Vol. 208, Issue 5-6
  • DOI: 10.1016/0009-2614(93)87156-W

Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
journal, February 2002

  • Weigend, Florian; Köhn, Andreas; Hättig, Christof
  • The Journal of Chemical Physics, Vol. 116, Issue 8
  • DOI: 10.1063/1.1445115

Discussion on The Hartree-Fock Approximation
journal, July 1963


A study of the isomers of C36 fullerene using single and multireference MP2 perturbation theory
journal, August 2002


Energetics of carbon clusters C20 from all-electron quantum Monte Carlo calculations
journal, June 2000


Unrestricted Hartree-Fock theory and its applications to molecules and chemical reactions
journal, November 1981

  • Fukutome, Hideo
  • International Journal of Quantum Chemistry, Vol. 20, Issue 5
  • DOI: 10.1002/qua.560200502

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


The influence of polarization functions on molecular orbital hydrogenation energies
journal, January 1973

  • Hariharan, P. C.; Pople, J. A.
  • Theoretica Chimica Acta, Vol. 28, Issue 3
  • DOI: 10.1007/BF00533485

Isomers of C20. Dramatic effect of gradient corrections in density functional theory
journal, November 1993


Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
journal, September 1969

  • Hehre, W. J.; Stewart, R. F.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 51, Issue 6
  • DOI: 10.1063/1.1672392

Symmetry breaking in molecular calculations and the reliable prediction of equilibrium geometries. The formyloxyl radical as an example
journal, October 1985

  • McLean, A. D.; Lengsfield, B. H.; Pacansky, J.
  • The Journal of Chemical Physics, Vol. 83, Issue 7
  • DOI: 10.1063/1.449162

On the performance of density functional theory for symmetry-breaking problems
journal, March 1999


Gas-phase production and photoelectron spectroscopy of the smallest fullerene, C20
journal, September 2000

  • Prinzbach, Horst; Weiler, Andreas; Landenberger, Peter
  • Nature, Vol. 407, Issue 6800
  • DOI: 10.1038/35024037

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20−
journal, May 2005

  • An, Wei; Gao, Yi; Bulusu, Satya
  • The Journal of Chemical Physics, Vol. 122, Issue 20
  • DOI: 10.1063/1.1903946

Spin contamination in single-determinant wavefunctions
journal, September 1991


Large-scale correlated electronic structure calculations: the RI-MP2 method on parallel computers
journal, March 1996


LDA Predictions of C 20 Isomerizations:  Neutral and Charged Species
journal, January 1996

  • Bylaska, Eric J.; Taylor, Peter R.; Kawai, Ryoichi
  • The Journal of Physical Chemistry, Vol. 100, Issue 17
  • DOI: 10.1021/jp9528323

Post-modern valence bond theory for strongly correlated electron spins
journal, January 2011

  • Small, David W.; Head-Gordon, Martin
  • Physical Chemistry Chemical Physics, Vol. 13, Issue 43
  • DOI: 10.1039/c1cp21832h

Computational studies on C36 and its dimer
journal, May 1999


Regularized orbital-optimized second-order perturbation theory
journal, December 2013

  • Stück, David; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 139, Issue 24
  • DOI: 10.1063/1.4851816

An examination of the Brueckner condition for the selection of molecular orbitals in correlated wavefunctions
journal, February 1977


On the nature of electron correlation in C 60
journal, November 2011

  • Stück, David; Baker, Thomas A.; Zimmerman, Paul
  • The Journal of Chemical Physics, Vol. 135, Issue 19
  • DOI: 10.1063/1.3661158

Symmetry breaking in polyatomic molecules: real and artifactual
journal, November 1983

  • Davidson, Ernest R.; Borden, Weston Thatcher
  • The Journal of Physical Chemistry, Vol. 87, Issue 24
  • DOI: 10.1021/j150642a005

Structural Isomers of C20 Revisited: The Cage and Bowl Are Almost Isoenergetic
journal, February 2002


C36, a new carbon solid
journal, June 1998

  • Piskoti, C.; Yarger, J.; Zettl, A.
  • Nature, Vol. 393, Issue 6687
  • DOI: 10.1038/31668

Generalized Hartree–Fock Description of Molecular Dissociation
journal, July 2011

  • Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 9
  • DOI: 10.1021/ct200345a

Characterizing unpaired electrons from the one-particle density matrix
journal, April 2003


A fusion of the closed-shell coupled cluster singles and doubles method and valence-bond theory for bond breaking
journal, September 2012

  • Small, David W.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 137, Issue 11
  • DOI: 10.1063/1.4751485

Do small fullerenes exist only on the computer? Experimental results on C=/−20 and C+/−24
journal, March 1993


Theory of self‐consistent electron pairs. An iterative method for correlated many‐electron wavefunctions
journal, April 1976

  • Meyer, Wilfried
  • The Journal of Chemical Physics, Vol. 64, Issue 7
  • DOI: 10.1063/1.432551

The two lowest energy 2 A ′ states of NO 2
journal, April 1976

  • Jackels, Charles F.; Davidson, Ernest R.
  • The Journal of Chemical Physics, Vol. 64, Issue 7
  • DOI: 10.1063/1.432552

Artifacts in the Electron Paramagnetic Resonance Spectra of C 60 Fullerene Ions:  Inevitable C 120 O Impurity
journal, April 2002

  • Paul, Parimal; Kim, Kee-Chan; Sun, Dayong
  • Journal of the American Chemical Society, Vol. 124, Issue 16
  • DOI: 10.1021/ja011832f

XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule
journal, April 1949

  • Coulson, C. A.; Fischer, I.
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 303
  • DOI: 10.1080/14786444908521726

Addressing first derivative discontinuities in orbital-optimised opposite-spin scaled second-order perturbation theory with regularisation
journal, December 2016


Matplotlib: A 2D Graphics Environment
journal, January 2007


Brueckner's Theory and the Method of Superposition of Configurations
journal, March 1958


Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics
journal, October 2009

  • Neese, Frank; Schwabe, Tobias; Kossmann, Simone
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 11
  • DOI: 10.1021/ct9003299

A First-Principles Study on the Structural and Electronic Properties of C 36 Molecules
journal, July 2000

  • Yuan, Lan-Feng; Yang, Jinlong; Deng, Ke
  • The Journal of Physical Chemistry A, Vol. 104, Issue 28
  • DOI: 10.1021/jp0009913

Correlated ab Initio Spin Densities for Larger Molecules: Orbital-Optimized Spin-Component-Scaled MP2 Method
journal, November 2010

  • Kossmann, Simone; Neese, Frank
  • The Journal of Physical Chemistry A, Vol. 114, Issue 43
  • DOI: 10.1021/jp105647c

Do C36 and C36H6 molecules have [36-D6h]fullerene structure?
journal, September 2000


Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method
journal, November 2004

  • Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D.
  • The Journal of Chemical Physics, Vol. 121, Issue 20
  • DOI: 10.1063/1.1809602

Structural predictions for open-shell systems: a comparative assessment of ab initio procedures
journal, January 1983

  • Farnell, Leslie; Pople, John A.; Radom, Leo
  • The Journal of Physical Chemistry, Vol. 87, Issue 1
  • DOI: 10.1021/j100224a019

C20: the smallest fullerene?
journal, September 1991


Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+
journal, September 1998

  • Sherrill, C. David; Krylov, Anna I.; Byrd, Edward F. C.
  • The Journal of Chemical Physics, Vol. 109, Issue 11
  • DOI: 10.1063/1.477023

Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules
journal, March 1972

  • Hehre, W. J.; Ditchfield, R.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 56, Issue 5, p. 2257-2261
  • DOI: 10.1063/1.1677527