Projected Hartree-Fock theory

The Journal of Chemical Physics
Carlos A Jiménez-HoyosGustavo E Scuseria

Abstract

Projected Hartree-Fock (PHF) theory has a long history in quantum chemistry. PHF is here understood as the variational determination of an N-electron broken symmetry Slater determinant that minimizes the energy of a projected state with the correct quantum numbers. The method was actively pursued for several decades but seems to have been abandoned. We here derive and implement a "variation after projection" PHF theory using techniques different from those previously employed in quantum chemistry. Our PHF methodology has modest mean-field computational cost, yields relatively simple expressions, can be applied to both collinear and non-collinear spin cases, and can be used in conjunction with deliberate symmetry breaking and restoration of other molecular symmetries like complex conjugation and point group. We present several benchmark applications to dissociation curves and singlet-triplet energy splittings, showing that the resulting PHF wavefunctions are of high quality multireference character. We also provide numerical evidence that in the thermodynamic limit, the energy in PHF is not lower than that of broken-symmetry HF, a simple consequence of the lack of size consistency and extensivity of PHF.

References

Sep 1, 1988·Physical Review. D·J P Blaizot, G Ripka
Oct 19, 2010·The Journal of Chemical Physics·Takashi Tsuchimochi, Gustavo E Scuseria
Feb 17, 2011·The Journal of Chemical Physics·Takashi Tsuchimochi, Gustavo E Scuseria
Oct 7, 2011·The Journal of Chemical Physics·Gustavo E ScuseriaJason K Ellis
Sep 13, 2011·Journal of Chemical Theory and Computation·Carlos A Jiménez-HoyosGustavo E Scuseria

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Citations

Jul 20, 2013·The Journal of Physical Chemistry. a·Pablo RiveroGustavo E Scuseria
Mar 25, 2014·The Journal of Chemical Physics·Eric J Sundstrom, Martin Head-Gordon
Dec 24, 2013·The Journal of Chemical Physics·Thomas M Henderson, Gustavo E Scuseria
Dec 3, 2013·The Journal of Chemical Physics·Carlos A Jiménez-HoyosGustavo E Scuseria
Dec 18, 2013·The Journal of Chemical Physics·Carlos A Jiménez-HoyosGustavo E Scuseria
May 17, 2014·The Journal of Chemical Physics·Helen van AggelenWeitao Yang
Apr 12, 2013·The Journal of Chemical Physics·Alejandro J GarzaGustavo E Scuseria
Jun 2, 2014·The Journal of Chemical Physics·Roman SchutskiGustavo E Scuseria
Jun 9, 2014·The Journal of Chemical Physics·Tamar SteinGustavo E Scuseria
Nov 5, 2014·The Journal of Chemical Physics·Takashi Tsuchimochi, Troy Van Voorhis
Jan 10, 2016·The Journal of Chemical Physics·Takashi Tsuchimochi, Seiichiro Ten-No
Feb 2, 2015·The Journal of Chemical Physics·Alejandro J GarzaGustavo E Scuseria
Apr 24, 2015·The Journal of Chemical Physics·Joshua J GoingsXiaosong Li
Jan 17, 2015·The Journal of Chemical Physics·David W SmallMartin Head-Gordon
Nov 18, 2015·Journal of Chemical Theory and Computation·Katharina Boguslawski, Paul W Ayers
Oct 17, 2015·The Journal of Chemical Physics·Joshua J GoingsXiaosong Li
Mar 8, 2016·Journal of Chemical Theory and Computation·Takashi Tsuchimochi, Seiichiro Ten-no
Sep 8, 2015·The Journal of Chemical Physics·Laimutis BytautasKlaus Ruedenberg
Jul 3, 2015·The Journal of Chemical Physics·Sebastian KellerPeter Pulay
Apr 4, 2015·The Journal of Chemical Physics·Takashi Tsuchimochi, Troy Van Voorhis
Jul 28, 2016·Journal of Chemical Theory and Computation·Tianyuan Zhang, Francesco A Evangelista
Nov 3, 2016·The Journal of Chemical Physics·Zsuzsanna Tóth, Peter Pulay
Feb 28, 2017·Journal of Chemical Theory and Computation·Takashi Tsuchimochi, Seiichiro Ten-No
Mar 17, 2017·The Journal of Chemical Physics·Motoyuki Uejima, Seiichiro Ten-No
May 4, 2017·Journal of Chemical Theory and Computation·Zhendong Li, Garnet Kin-Lic Chan
May 23, 2017·The Journal of Physical Chemistry. a·Paul M Zimmerman
Aug 16, 2016·Physical Chemistry Chemical Physics : PCCP·Eloy Ramos-CordobaEduard Matito
Aug 8, 2015·Physical Chemistry Chemical Physics : PCCP·Alejandro J GarzaGustavo E Scuseria
Jul 19, 2013·Physical Review Letters·J Bonnard, O Juillet
Jan 15, 2018·The Journal of Chemical Physics·Lena C JakeGustavo E Scuseria
Feb 24, 2019·The Journal of Chemical Physics·Edgar Josué Landinez BordaMiguel A Morales
Feb 24, 2017·The Journal of Chemical Physics·Takashi Tsuchimochi, Seiichiro Ten-No
Jan 17, 2020·The Journal of Chemical Physics·Iliya SabzevariSandeep Sharma
Aug 6, 2020·The Journal of Chemical Physics·Nadia Ben AmorJean-Paul Malrieu

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Software Mentioned

CUHF
SGHF
PQT
SUHF
GAUSSIAN

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