Summary: Becke 1988 exchange potential



 Here is a summary of the answers I have received to my query about
 the Becke 1988 nonlocal exchange potential.  Thanks to everyone who
 responded.
 I posted the following query on September 12, 1996.
 > I am seeking the formulas for the Becke 1988 nonlocal exchange
 > potential for the nonlocal exchange energy functional proposed in
 > the paper
 >
 > Becke, A. D., "Density-Functional Exchange-Energy Approximation
 > with Correct Asymptotic Behavior," Phys. Rev. A, 38(6), 3098-3100
 > (1988).
 To summarize the answer, this potential has been published in
 Fan, Liangyou and Ziegler, Tom, "The Influence of Self-Consistency
 on Nonlocal Density Functional Calculations," J. Chem. Phys., 94(9),
 6057--6063 (1991).
 An asymptotic form of the potential is given in
 Engel, E., Chevary, J. A., Macdonald, L. D., and Vosko, S. H.,
 "Asymptotic Properties of the Exchange Energy Density and the
 Exchange Potential of Finite Systems: Relevance for Generalized
 Gradient Approximations," Z. Phys. D, 23, 7-14 (1992).
 A form for spherically symmetric systems is given in
 Gritsenko, O. V., Cordero, N. A., Rubio, A., Balbas, L. C., and
 Alonso, J. A., "Weighted-Density Exchange and Local-Density Coulomb
 Correlation Energy Functionals for Finite Systems: Application to
 Atoms," Phys. Rev. A, 48(6), 4197-4212 (1993).
 A summary of the responses I received follows.
 *****************************************************************
 From Liang Lou at liang()at()wavefun.com:
              12-SEP-1996 18:20:59.72
 From:   IN%"liang()at()wavefun.com"
 To:     IN%"MAR()at()ecs.umass.edu"  "Perry Mar"
 CC:
 Subj:   RE: CCL:Becke 1988 nonlocal exchange potential
 One paper in a series published by Ziegler's group at Calgary
 L. Fan and T. Ziegler, JCP 6057 (1991)
 contains specifically the expansion you are seeking for.
 Regards,
 Liang Lou
 ***********************
 From Richard Hall at R.Hall()at()mcc.ac.uk:
              13-SEP-1996 03:56:18.07
 From:   IN%"mbdtsrh()at()afs.mcc.ac.uk"  "mbdtsrh"
 To:     IN%"mar()at()ecs.umass.edu"
 CC:
 Subj:   becke functional
 I'm not  *exactly*  sure if this is the  functional  you  require, but a
 paper by  Johnson  Gill and  Pople  gives the  formula  for a number  of
 functionals and their first derivatives.  The reference is
 B.G.Johnson, P.M.W.Gill and J.A.Pople, J.Chem.Phys. 98 p.5612 (1993)
 hope this helps.
 regards,
 Richard
 --
 ------------------------------------------------------------------------
    Richard Hall
 1) Computational Chemistry Support      email:  R.Hall()at()mcc.ac.uk
    Manchester Computing                   tel:  (0161) 275 7179
    University of Manchester
    Manchester, UK,  M13 9PL
 2) Department of Chemistry              email:  Richard.Hall()at()man.ac.uk
    University of Manchester               tel:  (0161) 275 4686
    Manchester, UK,  M13 9PL
 ------------------------------------------------------------------------
 ***********************
 From Reinaldo at pis_diez()at()nahuel.biol.unlp.edu.ar:
              13-SEP-1996 11:16:20.75
 From:   IN%"pis_diez()at()nahuel.biol.unlp.edu.ar"
 To:     IN%"MAR()at()ecs.umass.edu"  "Perry Mar"
 CC:
 Subj:   RE: CCL:Becke 1988 nonlocal exchange potential
                 Try E Engel, JA Chevary, LD MacDonald and SH Vosko, Z Phys D
 23 (1992) 7  and OV Gritsenko, NA Cordero, A Rubio, LC Balbas and JA Alonso,
 PRA 48 (1993) 4197.
                 REgards,
                     Reinaldo
 *****************************************************************
 Sincerely,
 Perry Mar
 Department of Chemical Engineering      E-mail:  mar()at()ecs.umass.edu
 University of Massachusetts             Phone:  (413) 545-0770
 Amherst, MA  01003-3110, USA            Fax:    (413) 545-1647