# PBE vs. PBEPBE functional

I've found good explanation what the PBE functional is. However, sometimes I see PBEPBE and I cannot find any good information about what this means and how it's different from PBE.

The Gaussian manual explains PBE and also provides the reference but at other points they talk about PBEPBE without any reference.

Can someone explain the difference? Does the second PBE just describe some kind of modification?

• Is it PBEPBE or PBE1PBE? The PBE1PBE functional, aka PBE0, would be a hybrid functional based on the PBE GGA functional. – Philipp Jul 19 '17 at 21:36
• @Philipp PBEPBE. But Feodoran already cleared up the confusion. – DSVA Jul 19 '17 at 21:39

The designation PBEPBE is an actual terrible artefact from researchers using Gaussian. The actual publication[1, 2] only refers to it as PBE, and most other program packages (I know) implement it as such. Often they make the correlation and exchange parts separately available via PBEC and PBEX, or similar. Unfortunately this designation also made it into the literature.
The confusion further continues since Gaussian uses the PBE1PBE designation for the (standalone) hybrid functional, which is in most other packages known as PBE0.

But it doesn't stop there, for TPSS you may find similar naming/ reference schemes. The BP86 functional keyword requests the VWN(III) version, while many other programs use VWN(V) for this. The latter is available via BVP86, but misses any implementation of dispersion. We could go on with this...

In the end what is important is the correct referencing of the methodology so that the results are reproducible, i.e. look at the literature cited. Gaussian actually does a good job referencing those sources. And when you publish, you'd do us all a favour and not use the keyword designations of Gaussian.

[1] John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865. DOI: 10.1103/PhysRevLett.77.3865. Mirrored at Burke's page: dft.uci.edu/publications.php

[2] (Erratum) John P. Perdew, Kieron Burke, Matthias Ernzerhof, Phys. Rev. Lett. 1997, 78, 1396. DOI: 10.1103/PhysRevLett.78.1396

• My old group has combined the Becke 88 exchange functional with PBE correlation before and designated this B-PBE, IIRC, for experiments on new GGA functionals. I thus believe that there is some merit to the Gaussian notation, although many of their choices are not good. The point about correct referencing cannot be stressed enough. – TAR86 Jul 20 '17 at 9:18
• @TAR86 Yes, true, there should always be a possibility to arrange functionals differently, and a keyword simply is not the name of the method; unfortunately that does not mean it's not used as such. (I still think they could have made it clearer which one you actually are requesting.) – Martin - マーチン Jul 20 '17 at 9:26

If you want to use a LDA or GGA functional in Gaussian you always need specify the desired Exchange and Correlation functional. In case of PBE you need to specify it twice, only using PBE will result in an error.

This is also explained in the online manual: http://gaussian.com/dft/ (Tab "Keyword: Pure Functionals")

• Oh I seemed to have missed that sentence. So if people speak about PBE they always mean Exchange and Correlation functional being PBE? – DSVA Jul 19 '17 at 21:38
• I am not sure how PBE is defined, but I think it includes both, exchange and correlation functional. Therefore the term PBE refers to both of them as a pair. The doubling of the name is just a quirk of Gaussians input notation. – Feodoran Jul 19 '17 at 21:48
• +1. Have you considered committing to Materials Modeling Stack Exchange? area51.stackexchange.com/proposals/122958/… – user1271772 Mar 21 at 22:07

I came across this question by chance, and even if you already solved the problem, I wanted to add my contribution because of the many reads it keeps receiving. Actually, that notation (which is common mostly in Gaussian) implies that you are specifying both the exchange and the correlation part of the functional. It assumes that you write the functional as exchangecorrelation altogether, i.e. PBEPBE uses PBE exchange and PBE correlation. Following the same schemes, PBE1PBE (popular because of Gaussian, but it actually makes sense too) stands for "1 parameter hybrid" using PBE exchange and PBE correlation (it is the same as PBE0, as originally defined by Adamo and Barone). B3PW91, the first 3-parameter hybrid proposed by Becke stands for "3-parameter hybrid" using B88 exchange and PW91 correlation. Many other functionals are defined using this scheme. I hope this helps following readers!