Summary: B3LYP proper reference

 Hello All!
 Many thanks to all who replied! Special thanks to Prof Philip Stephens and
 Dr Mike Frisch who had a very interesting tale to tell about the history
 of B3LYP.
 My original post asked for suggestions for a proper reference to the B3LYP
 functional, given that no paper was an obvious choice. Now I am wiser in
 the ways of DFT, and I think my future B3LYP citings will include B3 [1],
 LYP [2], VWN [3], and the assembly [4]. A brief citation could be [1,4]
 as suggested by Dr Frisch. Feel free to make your own choice.
 All replies are summarised below, trimmed down to the relevant parts (as
 defined by my newly gained wisdom :-) I also truncated the e-mail
 addresses. Read and enjoy!
 Have a nice day,
     Mikael J.
 [1] A.D. Becke, J.Chem.Phys. 98 (1993) 5648-5652
 [2] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785-789
 [3] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200-1211
 [4] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch,
     J.Phys.Chem. 98 (1994) 11623-11627
 Date: Mon, 20 May 2002 18:00:58 +0000
 From: philip stephens <stephens_philip -x- at -x- [...]>
 To: mikael.johansson -x- at -x-
 Subject: B3LYP
      Thank you for your email. I can answer you as follows:  in the early
 1990s we (at USC) were interested in using DFT harmonic force fields in
 predicting VCD spectra ( since we already knew that HF force fields were of
 insufficient accuracy  and that MP2 force fields gave much better results,
 but were computationally too expensive). After some unsuccessful initial
 attempts with numerical DFT force fields, we began a collaboration with Mike
 Frisch at Gaussian at the time that analytical second derivatives had just
 been implemented. Mike was interested in using the comparison of predicted
 vibrational spectra to experiment as a way of evaluating the relative
 accuracies of different functionals.  We therefore studied a number of
 molecules using a range of functionals. The hybrid functionals of Becke had
 just been introduced and were of particular interest. For reasons that are
 unknown to me Mike decided to create a new hybrid functional - the now
 famous B3LYP - and this was included as well as the Becke functional -
 B3PW91. It turned out to be a good idea!
   So, the short answer to your question is: the B3LYP functional used in our
 work and used in the Gaussian program was invented by Mike Frisch. If you
 want more of the history of this situation you should contact Mike directly:
   frisch -x- at -x- [...].
   By the way, there is another paper with the definition of B3LYP spelled
 out and some further discussion of its composition:  Stephens, Devlin,
 Ashvar, Chabalowski and Frisch, Disc. Faraday Soc. vol 99, pp103-119, 1994.
 Date: Tue, 21 May 2002 13:39:55 -0400 (EDT)
 From: Mike Frisch <frisch -x- at -x- [...]>
 To: uunet!!mikael.johansson -x- at -x-
 Subject: Re: Origins of B3LYP
 When I first decided to make use of Becke's parametrization based on
 adiabatic connection, we had not yet coded the PW91 correlation functional
 in Gaussian.  We had coded the earlier Perdew correlation functional (P86)
 but found that LYP seemed to work better for molecules.  I felt that if the
 parameters Becke had optimized represented real physical content in the
 model and not just curve fitting, then the same values should be useful with
 other functionals of the same general type (i.e., GGAs).  So I tested the
 same parameters with BLYP instead of BPW91, and found that indeed they gave a
 similar improvement in predicted energetics.  Just as importantly, the
 parameters, which Becke fit to dissociation energies of neutral molecules at
 fixed geometries, also improved predicted structures and vibrational
 frequencies as compared to pure DFT, and also worked well for ionization
 potentials and electron affinities.  So both the transferability of the
 parameters to different functionals and the fact that parameters fit to one
 property improve virtually all other properties confirmed that Becke's scheme
 improves the physical content of the model and is not just fitting a
 particular type of property.
 The reason for including VWN was that, unlike most correlation functionals,
 LYP does not have distinct local and gradient-corrected terms.  So to adjust
 the amount of non-local correlation from LYP as required by Becke's
 parameters, I needed to use a separate local correlation functional.
 That is, instead of Becke's:
   1.0 x (local correlation) + 0.81 XC(gradient-correction for correlation)
 I did
   0.81 (LYP local+gradient-correction) + 0.19 (VWN3 local)
 Unfortunetly, I wasn't as precise as I should have been in the paper and
 didn't specify which version of VWN (VWN3) I used for the local
 correlation.  This has led to a bit of confusion, with some people using
 VWN5 in their implementations for the local part.  The difference between
 the two versions is a small variation in total energy, but the predictions
 are basically the same regardless of which local functional is used to
 provide the small non-gradient-corrected part.
 We have since coded PW91 and found that B3PW91 is not quite as good as
 B3LYP.  I think this reflects the fact that PW91 isn't as good as LYP for
 molecules, not any difference in optimal values for the 3 parameters.  PW91
 is exact for the uniform electron gas, which physicist like, while LYP is
 wrong in this limit.  However, LYP was designed to make He come out right.
 Since He is a better example of the highly non-uniform electron density
 in molecules than the uniform electron gas, it is not surprising that BLYP
 and B3LYP are (slightly) better approximations for molecules than BPW91 and
 Date: Wed, 15 May 2002 13:58:55 -0400 (EDT)
 From: Dmitry Khoroshun <dima -x- at -x- [...]>
 To: Mikael Johansson <mpjohans -x- at -x->
 Subject: Re: CCL:Proper B3LYP reference?
 You might want to cite the following paper:
 Hertwig, R. H.; Koch, W. Chem. Phys. Lett. 1997, 268, 345
 "On the parametrization of the local correlation functional.
 What is Becke-3-LYP?"
 Date: Wed, 15 May 2002 14:12:46 -0400
 From: James Kubicki <kubicki -x- at -x->
 To: mpjohans -x- at -x-
 Subject: Re: CCL:Proper B3LYP reference?
 You might try -
 Becke A. D., Density-functional exchange-energy approximation with
 correct asymptotic-behavior. Phys. Rev. A, 38(6), 3098, 1988.
 Date: Wed, 15 May 2002 14:57:10 -0400
 From: elewars <elewars -x- at -x- [...]>
 To: Mikael Johansson <mpjohans -x- at -x->
 Subject: Re: CCL:Proper B3LYP reference?
 Re the question below about citing B3LYP
 The B3LYP functional is based on an exchange-correlation functional
 developed by Becke in 1993 and modified by stevens in 1994 by introduction
 of the Lee-Yang-Parr 1988 correlation functional. I would cite B3LYP as:
 P. J. Stephens, F. J. Devlin, C. F. Chablowski, and M. Frisch, J. Phys.
 Chem. 1994, 98, 11623, and refs therein.
 E. Lewars
 Date: Thu, 16 May 2002 09:11:25 +0200
 From: Patrik Johansson <patrikj -x- at -x- [...]>
 To: Mikael Johansson <mpjohans -x- at -x->
 Subject: Re: CCL:Proper B3LYP reference?
 Hej Mikael
 Jag har alltid anvant [1] tillsammans med orginal "LYP":
 Lee, Yang, Parr: Phys Rev B, 1988, 37, 785.
 Och om jag inte missminner mig tror jag mig ha last att detta ar de som
 ska anvandas som referenser (minimum alltsa). Detta aven om inte den
 "LYP" ar exakt den som anvands i B3LYP.
 Date: Thu, 16 May 2002 09:23:02 -0400 (EDT)
 From: Doug Fox <!fox -x- at -x- [...]>
 To: Mikael Johansson
     <uunet!!mpjohans%[...] -x- at -x->
 Subject: Re: CCL:Proper B3LYP reference?
    The combination of [2] and [1] is the recommended reference.  The
 combination was developed by Gaussian and then reported in applications
 papers.  Becke's paper documents the theory behind the coefficients
 of this hybrid method.
 Date: Thu, 16 May 2002 10:55:43 +0300 (EEST)
 From: Michael Patzschke <michaelp -x- at -x- [...]>
 To: Mikael Johansson <mpjohans -x- at -x->
 Subject: B3LYP
 B3LYP historien är faktiskt lite svårt att följa med. Men om jag
 förstått det rätt. så började det hela med utvecklingen
 av hybridmethoder
 så som HH (Becke 92) vilka använder 'adiabatic connection' (Becke 88).
 methoden var inte så värst framgångsrik och Becke kom sen med ett
 som baserade på CGA (och inte på LDA som Beckes HH method) den blev
 som B3 (Becke 93). Allt detta beträffa dock bara 'exchange' delen. I Becke
 93 användes B3 tillsammans med PW91 'correlation' funktionalen (Perdew
 92). Först senare (Stephens 94) kom föreslaget att använda B3 och
 funktionalen (Lee 88). Och fortfarande finns det oklarheter vilken av
 Beckes B3-formler borde användas (se t.ex.  Hertwig 97). Ännu
 värre, så
 finns det många olika sett att skriva LYP-funktionalen (se Miehlich 89
 och Lee 93).
 Becke 88 J.Chem.Phys.,1988,88,1053
 Lee 88 Phys.Rev.,1988,B37,785
 Miehlich 89 Chem.Phys.Lett.,1989,157,200
 Becke 92 J.Chem.Phys.,1992,98,1372
 Perdew 92 Phys.Rev.,1992,B46,6671
 Becke 93 J.Chem.Phys.,1993,98,5648
 Lee 93 Phys.Rev.B,1993,37,785
 Stephens 94 J.Phys.Chem.,1994,98,11623
 Hertwig 97 Chem.Phys.Lett.,1997,268,345
 Date: Wed, 15 May 2002 20:08:30 +0300 (EET DST)
 From: Mikael Johansson <mpjohans -x- at -x->
 To: <chemistry -x- at -x->
 Subject: Proper B3LYP reference?
 Hello All!
 What's the "proper" B3LYP reference to use? Usually Becke's paper [1]
 cited, and sometimes additionally the paper by Stephens et al. [2].
 Paper [1] does not contain the B3LYP-functional, altough it defines the 3
 parameters for the different types of contribution. Paper [2] explicitly
 explains the alterations to Becke's original formulation, but I find
 at least one earlier paper [3] mentioning/using B3LYP.
 > From the articles, I assume B3LYP was something introduced by the Gaussian
 program package, am I right? Furthermore, does anyone know of an even
 earlier B3LYP reference than [3]?
 [1] A.D. Becke, J.Chem.Phys. 98 (1993) 5648-5652
 [2] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J Frisch,
     J.Phys.Chem. 98 (1994) 11623-11627
 [3] K. Kim, K.D. Jordan, J.Phys.Chem. 98 (1994) 10089-10094
 Have a nice day,
     Mikael Johansson
     University of Helsinki
     Department of Chemistry
     mikael.johansson -x- at -x-
     Phone: +358-9-191 50185
     FAX  : +358-9-191 50169