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Two of the most popular (exchange and correlation) functionals for density functional theory are B3LYP and PBE. Out of the people I've worked with / learned from, mostly the computational chemists were using B3LYP, and the physicists were using PBE.

Now, different functionals have different strengths and weaknesses, but these two functionals seem to have a lot of overlap in their applicability. Right now I'm interested in ground-state properties of molecules with extended pi-frameworks in the gas-phase. For example, I'd like to compute the geometries, ground-state electron densities, and molecular polarizabilities of the acenes.

Does anyone have concrete information or references on the performance of B3LYP or PBE in this situation, or in general?

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    $\begingroup$ chemistry stackexchange? $\endgroup$
    – user26143
    Commented Nov 6, 2013 at 16:35
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    $\begingroup$ @user26143 There isn't much about DFT on either site, and I'm a physicist, and so is Kohn, although he got the Nobel Prize in Chemistry. Maybe if there is no answer on here after a couple days I'll try on CSE. $\endgroup$ Commented Nov 6, 2013 at 16:43
  • $\begingroup$ Both really are lacking in DFT experts, which is a real shame. P actually used to work in my department, and we've add our last two seminar speakers mention that in the context of their use of PBE. This isn't my area, but those talks might give me some leads that might be useful. $\endgroup$ Commented Nov 6, 2013 at 16:50
  • $\begingroup$ I guess one solution is to look for benchmark paper or run a few calculations oneself. It seems the highly conjugated acenes become multi-reference/strongly correlated, most approximated functionals are not reliable (although the geometry may not be sensitive to this multi-reference/strong correlation character)... As a may not be concrete example, some developers of DMRG tested these systems, arXiv:0707.3120v1 (and the papers which quote this one). Nevertheless from the singlet/triplet gap in Fig 2, B3LYP looks reasonable .. $\endgroup$
    – user26143
    Commented Nov 6, 2013 at 17:19
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    $\begingroup$ I think it is the right decision to keep DFT questions on Phys.SE rather than Chem.SE. Also cross-posting will likely not yield more answers. $\endgroup$
    – Qmechanic
    Commented Nov 7, 2013 at 18:42

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I would recommend to use a different functional, preferentially one having dispersion corrections and range separation. An experimentalist once asked me for polarizability data for organic molecular chains; I used $\omega$B97XD and got results with an errors of 1% or less with respect to experiment. I didn't bothered to do B3LYP and PBE but I doubt they can give better results. B3LYP and PBE are so popular because they were probably the best options in most applications when they came out, but there are better functionals out there these days.

If you want to stick to B3LYP and PBE, then you could use their range-separated versions CAM-B3LYP and LC-$\omega$PBE. If you do not know what a range separated hybrid then see, e.g., Iikura H et al. (2001) J Chem Phys 115:3540 and reference therein. If you can add dispersion corrections (like Grimme's D3 correction, Goerigk L, Grimme S (2011) Phys Chem Chem Phys 13:6670), that is better because dispersion may be important when you increase the length of the acene. I just suggested $\omega$B97XD first because it already includes Grimme's D2 correction and range separation. Also note range separated hybrids give better molecular geometries than normal hybrids (e.g., B3LYP) in large conjugated systems (see, e.g., Jacquemin D, Adamo C (2011) J Chem Theory Comput 7: 369 and references therein). Furthermore, range separation is necessary for calculating higher-order polarizabilities since normal hybrids and GGAs largely overestimate these quantities (many works on this by B. Champagne, D. Jacquemin, and others; I can elaborate if you need it, but it seems like you are interested only in first order polarizabilites).

Also, remember to use a basis set having polarization functions.

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  • $\begingroup$ Thanks for your advice. I don't plan on changing functionals; DFT is not my area of expertise, and I'd rather understand the performance of one or two functionals instead of using a different one for each situation. Still very helpful though. $\endgroup$ Commented Nov 26, 2013 at 1:31
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For static polarizability calculations it seems that both B3LYP and PBE functionals do a pretty good job; for benzene and napthalene I am getting numbers within a few percent of experimental values. What is much more important is the basis set. In particular, it's absolutely necessary to include diffuse functions. For benzene it's so extreme that AUG-cc-pVDZ is closer to basis-set convergence than cc-pVTZ, cc-pVQZ, or even cc-pV5Z.

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