As others have pointed out, there is no definitive answer to this question yet because the exact exchange-correlation functional is non-analytic and, more importantly, completely unknown! However if you let us know which particular properties and chemicals/materials you are interested in, what accuracy you need, and perhaps even which DFT program, I'm sure we could offer some relevant advice.

Having said all this, I will attempt to give some general guidance here:

1. You need to think about how *predictive* you want your results to be. Using a semi-empirical functional like B3LYP will give good agreement with post-DFT methods for systems and properties close to those for which it was fitted (e.g. organic molecules) but fail spectacularly outside of this regime (e.g. ZnO). More general functionals such as PBE will give greater predictive power across all simulations and properties, but are less likely to achieve the accuracy of a semi-empirical functional within its range of applicability.

2. You need to consider the self-interaction error, in particular whether you: ignore it; mitigate against it (e.g. DFT+U or hybrid functionals like HSE06); or eliminate it (e.g. via the self-interaction correction of Perdew & Zunger).

3. At some point you'll need to think about computational cost. In a localised basis set the cost of a real-space Fock operator is fairly low, so hybrid functionals are reasonably cheap; in a plane-wave basis the Fock operator is expensive, so hybrid functionals need to be used with care. For a periodic crystal the Fock operator is particularly expensive, since it involves a double-summation over Brillouin zone sampling points (k-points). Needless to say, double-hybrid methods are even more computationally demanding.

4. If you're using a pseudopotential method, you should ensure the pseudopotentials are generated with the same exchange-correlation functional as your main DFT calculation (or at least a closely-related functional). This is actually a very difficult problem with Hartree-Fock and hybrid functionals, as they are extremely ill-conditioned for isolated atoms.

5. Strictly speaking, excited states are not described by DFT, and you need TDDFT (at least) to compute them. Unfortunately, functional development for TDDFT is at least a decade behind that for ordinary DFT (TDDFT requires you to know the time/frequency-dependence of the functional as well as the spatial-dependence). See, for example, the recent work of Rex Godby for more insights on the nature of the "true" TDDFT functional.

More practically, if all you want is a density-of-states or an optical spectrum, then it is often found that DFT is "good enough" once you have accounted for HOMO-LUMO/band-gap error.

6. Some properties are notoriously difficult to predict. Charge-transfer reactions and Coulomb-blockades are very sensitive to self-interaction error, as are the positions of defect levels and the localisation of polarons. Van der Waals bonding is completely missing from almost all density functionals, and if it's important for your system it would need to be added in (see e.g. the work of Tkatchenko and Scheffler).

I hope that's been of some help, but like I said at the start if you give us more information I'm sure we can offer some more specific advice.

All the best,

Phil

It cannot be picked a priori, as performance of a functional depends on the problem you study. If you have good reference data for the system of interest or similar ones, I'd suggest to perform a benchmarking study using different functionals and see what works best for you.

Unfortunately, that's impossible to tell without knowing the specific application or at least the rough kind(s) of molecule(s) involved.

Well, I want to run geometry optimization of some heterocyclic compounds with one or more aromatic rings.

You could also look up literature -- maybe someone has already found a computational approach suitable for your research problem. Besides, you can try some general-purpose functionals like ωB97X-D and M06-2X to see if the results make sense to you.

If for oxide compounds, hybrid functional of HSE06 may be a good choice.

The pragmatic approach is to test different functionals for some of the properties of interest that are well known for the systems of interest. You also need to take into account the basis set and whether you will be using a pseudopotential or an all-electron approach.  You can narrow down your possibilities by using functionals that have been sucsessful for systems that are similar to yours.

The best exchange-correlation functional does not exist, because the DFT nature is pure semi-empirical. There is a whole zoo of various functionals and a proper choice is a bit tricky. From a general viewpoint, however,  hybrid ex.-corr. functionals should be better.

This is indeed a never end question: is there any universal DFT approach? No. It strongly depends on your system and the property you are looking for. In the TDDFT case, I suggest you any of the recent benchmark paper by Jacquemin and Adamo, e.g. Chem. Soc. Rev.,2013, 42, 845, a nice tutorial where these very well-known authors deals with that question.

Hope it helps. Best,

Jose

Thanks all for the replies.

You could try the 5-th rung functionals (mPW2PLYP, or B2PLYP), containing non-local correlation part. If you have a new system, with little knowledge of its characteristics, these functionals give you high chance of good performance. Unfortunately, they are costly (scale as N^5), which makes them inapplicable for larger molecules.

Alternatively, you can use such cons-conscious methods as MP2 or CC2 (scale also as N^5) and cautiously use the results as benchmark to test various functionals.

That is, of course, if there are no reliable experimental data for comparison ;)

What kind of accuracy are you hoping to achieve, and in what properties? For example, if you are interested in accurate bond lengths, atomization energies, etc.,, M06-2X is optimized for organics.  If you are interested in excited states, uv spectra, etc., this may not be the best chioce.

following articles can help you:

"Why does the B3LYP hybrid functional fail for metals? " http://scitation.aip.org/content/aip/journal/jcp/127/2/10.1063/1.2747249

" A Bird’s-Eye View of Density-Functional Theory" http://arxiv.org/abs/condmat/0211443

As others have pointed out, there is no definitive answer to this question yet because the exact exchange-correlation functional is non-analytic and, more importantly, completely unknown! However if you let us know which particular properties and chemicals/materials you are interested in, what accuracy you need, and perhaps even which DFT program, I'm sure we could offer some relevant advice.

Having said all this, I will attempt to give some general guidance here:

1. You need to think about how *predictive* you want your results to be. Using a semi-empirical functional like B3LYP will give good agreement with post-DFT methods for systems and properties close to those for which it was fitted (e.g. organic molecules) but fail spectacularly outside of this regime (e.g. ZnO). More general functionals such as PBE will give greater predictive power across all simulations and properties, but are less likely to achieve the accuracy of a semi-empirical functional within its range of applicability.

2. You need to consider the self-interaction error, in particular whether you: ignore it; mitigate against it (e.g. DFT+U or hybrid functionals like HSE06); or eliminate it (e.g. via the self-interaction correction of Perdew & Zunger).

3. At some point you'll need to think about computational cost. In a localised basis set the cost of a real-space Fock operator is fairly low, so hybrid functionals are reasonably cheap; in a plane-wave basis the Fock operator is expensive, so hybrid functionals need to be used with care. For a periodic crystal the Fock operator is particularly expensive, since it involves a double-summation over Brillouin zone sampling points (k-points). Needless to say, double-hybrid methods are even more computationally demanding.

4. If you're using a pseudopotential method, you should ensure the pseudopotentials are generated with the same exchange-correlation functional as your main DFT calculation (or at least a closely-related functional). This is actually a very difficult problem with Hartree-Fock and hybrid functionals, as they are extremely ill-conditioned for isolated atoms.

5. Strictly speaking, excited states are not described by DFT, and you need TDDFT (at least) to compute them. Unfortunately, functional development for TDDFT is at least a decade behind that for ordinary DFT (TDDFT requires you to know the time/frequency-dependence of the functional as well as the spatial-dependence). See, for example, the recent work of Rex Godby for more insights on the nature of the "true" TDDFT functional.

More practically, if all you want is a density-of-states or an optical spectrum, then it is often found that DFT is "good enough" once you have accounted for HOMO-LUMO/band-gap error.

6. Some properties are notoriously difficult to predict. Charge-transfer reactions and Coulomb-blockades are very sensitive to self-interaction error, as are the positions of defect levels and the localisation of polarons. Van der Waals bonding is completely missing from almost all density functionals, and if it's important for your system it would need to be added in (see e.g. the work of Tkatchenko and Scheffler).

I hope that's been of some help, but like I said at the start if you give us more information I'm sure we can offer some more specific advice.

All the best,

Phil

There's no "best" XC-functional.

It depends on the property you want to recover (structure? optical properties? vibrational frequencies?) and the system you want to simulate.

For example, for nanogold a recent benchmark paper (more than 20 functional tested!) is the following:

http://pubs.acs.org/doi/full/10.1021/jp411483x?prevSearch=francesco%2Bmuniz-miranda&searchHistoryKey=

As many have said already, there is no universal XC functional. For the ground state, B3LYP is still very used but for organic molecules I would suggest to try M06-2X that seems to behave better in many cases. For systems with transition metal, you have to look for previous studies as it will depend on the transition metal you have, and the properties you are looking for.

For excited states in TDDFT, you should look at benchmarks as the behavior of many functionals is quite different from their ground state performance.

Good luck!

B3LYP IS THE BASIC FUNCTIONAL CORRELATION. YOU TAKE THIS AS A FIRST OPTION, THEN INVESTIGATE THAT TYPE OF FUNCTIONAL HAVE BEEN USED FOR A COMPOUND SIMILAR TO YOURS AND COMPARES RESULTS. PERSONALLY I DO NOT THINK THAT THERE IS A FUNCTIONAL UNIVERSAL

Thanks all of you for the replies.

Philip, your detailed reply is really very helpful. Could you suggest some reference where I can find a summary about important features of popular DFT functionals?