Subject: Summary: B3LYP proper reference

From: Mikael Johansson <[email-masked]>
Date: Wed, 22 May 2002 17:15:23 +0300 (EET DST)

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@[...]>
To: [email-masked]
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@[...].

  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@[...]>
To: [email-masked]
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
B3PW91.

===========================================
Date: Wed, 15 May 2002 13:58:55 -0400 (EDT)
From: Dmitry Khoroshun <dima@[...]>
To: Mikael Johansson <[email-masked]>
Subject: Re: CCL:Proper B3LYP reference?

Hello!

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 <[email-masked]>
To: [email-masked]
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@[...]>
To: Mikael Johansson <[email-masked]>
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@[...]>
To: Mikael Johansson <[email-masked]>
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 <gaussian.com!fox@[...]>
To: Mikael Johansson
    <uunet!pcu.helsinki.fi!mpjohans%[...]@uunet.uu.net>
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@[...]>
To: Mikael Johansson <[email-masked]>
Subject: B3LYP

[...]

B3LYP historien är faktiskt lite svårt att följa med. Men om jag har
förstått det rätt. så började det hela med utvecklingen av hybridmethoder
så som HH (Becke 92) vilka använder 'adiabatic connection' (Becke 88). HH
methoden var inte så värst framgångsrik och Becke kom sen med ett föreslag
som baserade på CGA (och inte på LDA som Beckes HH method) den blev känd
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 LYP
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 <[email-masked]>
To: <[email-masked]>
Subject: Proper B3LYP reference?

Hello All!

What's the "proper" B3LYP reference to use? Usually Becke's paper [1] is
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
    [email-masked]
    http://www.helsinki.fi/~mpjohans/
    Phone: +358-9-191 50185
    FAX  : +358-9-191 50169