I have been reading a handful of review articles about the various types of DFT methods and their accuracies but my scope of knowledge is not very well versed enough in computational chemistry to fully understand the finer details. Most notably I'm interesting in the popular functionals B3LYP, WB97XD (ωB97X-D), and MP2.
As far as I understand the main differences between B3LYP and WB97XD are the addition of a semiempirical dispersion term that accounts for the weaker london forces. This results in greater accuracy in geometries of optimized structures using the respective functionals. For example in DOI: 10.1021/jo4018974 the author found that WB97XD had greater accuracy than B3LYP in predicting proton affinities of various amines using a relatively small basis set.
Now my biggest question lies in methods of DFT vs MP2. If I am not mistaken, MP2 methods attempt to solve the wavefunction, thus include the effects of dispersion but at great cost. At this point is the MP2 method still more accurate than WB97XD?
For example I am going under the suggestion of S. Grimme stating that "Any dispersion correction is better than none" but is it still beneficial to use a hybrid energy-geometry method such as MP2//WB97XD?
http://pubs.acs.org/doi/abs/10.1021/jo4018974
Dear Patrick,
It is not true that MP2 is more accurate than DFT, but their energy is more approximated and "real" than DFT.
DFT methods have the problem that change their tendency, results, values and capability to give reasonable energy depending on system. Every system could need different functional to describe it and DFT methods have a lot of problematic systems that you can find in all computational books.
On the other hand, with a system which a concrete DFT method is known that gives good description, it could be better than MP2. Even so, MP2 is useful to know if one DFT methods describes correctly a system. MP2 gives "true approximate energies" always, at every system "taking into account their peculiarities".
In summary, MP2 is useful to see the real tendency of a system and compared with a DFT. Is DFT gives the similar energy than MP2 that could imply that DFT describes properly the system and it could gives better results than perturbative method.
DFT are very useful but you must be sure that you are using the correct functional for every system and every property and, in my point of view, their application should require validations, comparison and clear evidences about capabilities of DFT to describe the system studied.
I hope it helps you,
Joaquim
From the theoretical point of view the biggest difference is the approach: variational (DFT) versus perturbation-based (MP2). This has some serious implications concerning the obtained results.
MP2 is also ab initio in the sense, that the equations are derived in a strict way. This is not true for modern DFT functionals, as parts of the functionals are fitted to experimental data.
If you want to get an accurate description of dispersion, some modern DFT functionals may be, however, actually better than MP2. Unfortunately ths can vary a lot between the specific systems: see e.g. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3477180/
The difference between B3LYP and WB97XD is not only the empirical D correction. WB97XD is also a long range corrected funcional (like CAM-B3LYP). The main difficulty with DFT is that modern functionals are mainly local or semi-local with incorrect asymptotical behavior (i.e. they depend only on density and its gradient), while HF solution has correct asymtotics (so MP2 inherits this). So the "simple" solution implemented in long range corrected functionals is to increase the ammount of HF-exchange as the distance increases.
Mr. Batoon,
Please pay attention to following [Ref. 1(a)] about perturbation theory in all orders. It unfortunately do not include the more recent developments in DFTs by Truhlar's and Grimme's, but it has involved the fundamentals of DFTs [Ref.1(b)].
[Ref.1] PvR Schleyer, P. Schreiner (Eds.-in-Chief), N. Allinger, T. Clark, J. Gasteiger, P. Kollman, H. Schaefer III (Eds.), Encyclopedia of Computational Chemistry, Wiley, Wiley (1998) West Sussex, Vol. 3 (a), pp. 1706-1735 and Vol. 1 (b) pp.679-700.
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