I've been looking to use time-dependent density functional theory, but reading the literature I keep getting overwhelmed by how many different functionals there are. How should I go about selecting which functional to use?

  • $\begingroup$ @Dan - What properties are you most interested it? $\endgroup$ Jun 5 '12 at 2:45
  • $\begingroup$ @Richard Terrett: I suppose the "time-dependent" part is the most important; I've heard many functionals lose a lot of accuracy when calculating the response of the molecule to some time-dependent forcing. $\endgroup$
    – Dan
    Jun 5 '12 at 7:13
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    $\begingroup$ @Dan, it really boils down to the literature when it comes to DFT. I would start by looking papers which benchmark DFT with ab initio methods. DFT should never be used without some sort of verification from another method or experiment. You could try finding Christopher Cramer's Computational Chemistry book which has a nice table outlining the various functionals on standard datasets and go from there. $\endgroup$ Jun 5 '12 at 13:31
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    $\begingroup$ A useful review of many functionals and how they came to be is "Perspective: Fifty years of density-functional theory in chemical physics" by Axel Becke, J. Chem. Phys. 140, 18A301 (2014). $\endgroup$
    – TG3D
    Oct 2 '16 at 12:32
  • $\begingroup$ A newer question partially overlaps with this one: chemistry.stackexchange.com/a/27418/5017 $\endgroup$ Feb 1 '18 at 21:12

For Structures and Energies: Answer Hazy, Try Again Later

People can talk on this subject for literally days.

It mostly comes down to computational expense vs accuracy - if you have a larger system, you can't afford the fancier functionals. The absolute highest accuracy state of the art functional-wise would probably be those using the Random-Phase Approximation (e.g.), and also the use of more complex range separation techniques (such as the Coulomb-Attenuated Method mentioned below).

Having said that, a lot of people just use B3LYP for everything. B3LYP is parametrised for low-Z main-group chemistry, and so does reasonably well there. It's a hybrid functional (i.e. it includes the exact Hartree-Fock form exchange operator), so it's not the cheapest. I tend to use the series of PBE, PBE0, TPSS - their only parameters are physical constants, so they should never give surprisingly bad results.

A couple of basic guidelines, though (which should be taken as "as far as I know"s):

  • If you have a delocalised system, you want exact exchange (so, a hybrid functional like PBE0, B3LYP, M06-2X, etc). Without this, most functionals will over-delocalise the orbitals.
  • If you have a system in which dispersion forces are important, worry. Then use something like $\omega$B97X-D which includes empirical dispersion corrections. Some packages can also apply Grimme's empirical dispersion corrections to any functional.
  • If you have a periodic system, you probably want to use screened exchange rather than full exact exchange - something like HSE (which tails off the exact exchange past a certain range) rather than PBE0 should be faster while not significantly less accurate.

For TDDFT: Probably CAM-B3LYP

Fortunately, this is a bit easier.

Firstly, you want something that incorporates exact exchange (a hybrid functional), which quickly rules out many functionals. Pure GGAs and LDAs give qualitatively wrong answers for states involving charge transfer. Secondly, functionals that include long-range exchange corrections, such as CAM-B3LYP, also give better results.

Also, look out for triplet instabilities, which can be a problem with the introduction of HF exchange.

(David Tozer is my go-to author for TDDFT testing, though I would warn that despite the above answer, I've never used TDDFT in "production".)

(Now, bring on the functional flamewar.)

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    $\begingroup$ Be very careful when characterizing systems with delocalization and dispersion. When doing so, I highly recommend checking the literature before supporting the data various DFT methods will give. Sadly, even using a slew of functionals won't help you determine a proper answer without reverting to ab initio methods. Here is a great paper illustrating how badly DFT is when describing hydrocarbon/water interactions. $\endgroup$ Jun 6 '12 at 14:40
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    $\begingroup$ And maybe this paper is of any help. One should try to climb from bottom to top. I usually start with BP86 (very robust), always try to skip B3LYP (it is a pain quouting and a very lazy functional), continue via PBE0 and unfortunately end up at the Minnesota functionals. (BTW, I'd be delighted to enjoy a good flamewar :D) $\endgroup$ Apr 14 '14 at 11:07

This is a loaded question.

Some groups focus on precisely cooking a recipe from known ingredients to produce useful functionals, the Minnesota functionals being quite popular.

In general, you will have to benchmark available functionals against your property and known analogues to your target of choice and ensure that you are capturing the relevant physics. This requires that you familiarize yourself with the respective assumptions in functional design, e.g., the homogeneous electron gas approximation.


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