For those of you interested in learning about dispersion corrections for density functional theory, I recommend Grimme’s latest review article.1 He discusses four different approaches to dealing with dispersion: (a) vdW-DF methods whereby a non-local dispersion term is included explicitly in the functional, (b) parameterized functional which account for some dispersion (like the M06-2x functional), (c) semiclassical corrections, labeled typically as DFT-D, which add an atom-pair term that typically has an r-6 form, and (d) one-electron corrections.
The heart of the review is the comparison of the effect of including dispersion on thermochemistry. Grimme nicely points out that reaction energies and activation barriers typically are predicted with errors of 6-8 kcal mol-1 with conventional DFT, and these errors are reduced by up to 1.5 kcal mol-1 with the inclusion fo the “-D3” correction. Even double hybrid methods, whose mean errors are much smaller (about 3 kcal mol-1), can be improved by over 0.5 kcal mol-1 with the inclusion of the “-D3” correction. The same is also true for conformational energies.
Since the added expense of including the “-D3” correction is small, there is really no good reason for not including it routinely in all types of computations.
(As an aside, the article cited here is available for free through the end of this year. This new journal WIREs Computational Molecular Science has many review articles that will be of interest to readers of this blog.)
References
(1) Grimme, S., "Density functional theory with London dispersion corrections," WIREs Comput. Mol. Sci., 2011, 1, 211-228, DOI: 10.1002/wcms.30
Qadir Timerghazin responded on 06 Dec 2011 at 12:06 pm #
It’s great to see that new developments in the DFT field that actually can end the ‘B3LYP reign’, which lasted for almost two decades already…
Also, many nice reviews in WIREs Comput. Mol. Sci., thank you!
Henry Rzepa responded on 07 Dec 2011 at 2:34 am #
It might be useful Steve if you could list the codes that implement the various dispersion corrections noted in your post. Thus ORCA is a reference implementation for much of this, but it lacks many of the more useful practical codes that are needed for routine calculations.
I might add that as we move into the realm of calculations on systems of between 100-250 atoms, dispersion corrections are an absolute must to get anything remotely resembling reality.
On a pedagogic note, when I was asked to write a lecture course on conformational analysis, I factored a dispersion corrected method (actually wB97XD) into all the examples.
Steven Bachrach responded on 07 Dec 2011 at 8:56 am #
I think a repository of available functionals within each major program would be a great idea – but I am not the one to undertake this!
Qadir Timerghazin responded on 07 Dec 2011 at 12:38 pm #
While the more advanced methods pick up in the current software, one-electron corrections that hijacking the existing ECP functionality found pretty much in any code out there, is perhaps the easiest and the most universal way to get poor man’s dispersion in DFT. It also can be combined with any functional too, if one bothers optimizing couple of parameters…
Holger responded on 08 Dec 2011 at 2:01 am #
At least with DFT-D3 I can help. It is currently implemented in:
dftd3 stand-alone code (from Grimme’s homepage)
ORCA 2.8 (next release before xmas will include all improvements and a vdW-DF style correction )
GAMESS-US from Okt. 2010 release (thought maybe not up to date)
TURBOMOLE 6.3 (up to date)
ADF 2010 (same as gamess)
NWCHEM 6.1 (details unknown)
(VASP) (periodic vasp implementation can be obtained from the Grimme group)
Gaussian is planning to implement it. I think they want to re-write all code. They have to keep the strict F77 style…. (it has the old DFT-D, though)
If I may mention it, even Truhlar’s functional (M05-2X, M06-2X) benefit from DFT-D3, especially in the long-range region, which is of course needed more large molecules.
Single-point energies are very easy to get with the dftd3 stand-alone code.
Eugene responded on 08 Dec 2011 at 10:41 am #
So what do you think the best options within Gaussian 09 are? I’ve been using M06-2X, but in light of this article, maybe there are better choices in some circumstances.
Steven Bachrach responded on 08 Dec 2011 at 10:55 am #
Eugene’s question might trigger a religious holy war – I am not convinced that there is close to a consensus as to a preferred functional.
As Qadir Timerghazin mentioned above, the B3LYP reign shoudl be over – with a tinge of regret in the sense that for a time we sort of had a de facto functional to call upon.
Personally, I have been playing with M06-2x and ωB97-XD and find both pretty reasonable. From Henry Rzepa’s blog one can infer that he has swung over to the ωB97-XD camp.
Others want to chime in?
Henry Rzepa responded on 08 Dec 2011 at 11:04 am #
As noted, I am a ωB97XD fan (with or without hyphen!). Although perhaps it over-estimates activation barriers, it seems almost unreasonably good for GIAO prediction of 1H NMR shifts and chiroptical properties, although I am less certain of UV-Vis properties using TD-DFT. As I noted, I have used it for systems of up to 250 atoms, where B3LYP would simply give absurd results.
Qadir Timerghazin responded on 08 Dec 2011 at 12:13 pm #
Looking at the current literature, it seems like the M06 family is set to replace B3LYP, for better or for worse. The purists might not be happy here, since the number of fitted parameters keep increasing.
Ragnar responded on 08 Dec 2011 at 2:44 pm #
I recommend a very recent paper from the Grimme group (http://pubs.rsc.org/en/Content/ArticleLanding/2011/CP/c0cp02984j) where they have compiled a huge database (GMTKN30) of maingroup thermochemistry data and then benchmark a fair share of the available DFT methods in the literature at the moment. In order to judge the functionals fairly, each functional has been combined with the DFT-D3 correction so that dispersion is described at pretty much the same level.
In the paper they then look at GGAs, hybrids, meta-GGAs and double-hybrid separately and find the best functional in each family. Interestingly the performance of each family is nicely correlated with Perdew’s hierarchy of functionals (Jacob’s ladder).
This extensive benchmarking confirms the accuracy of M06-2X and wB97X-D that have been mentioned already, but also show that double-hybrid functionals offer a significant step forward in accuracy (also when comparing to MP2) if one can afford the increased computing cost (which can often be made tractable by RI approximations) and basis set dependence.
Other recent interesting papers:
M11, the latest Minnesota functional, improves upon M06-2X by range-separation:
http://pubs.acs.org/doi/abs/10.1021/jz201170d
Comparison of nonlocal vdW-DF methods and DFT-D3 corrections for the same GMTKN30 database:
http://pubs.acs.org/doi/abs/10.1021/ct200644w
Most recent double hybrid from the Martin group (seems to improve upon DSD-BLYP-D3 which was the best performer in the Grimme-Goerigk study):
http://pubs.rsc.org/en/content/articlelanding/2011/cp/c1cp22592h
My contribution to availability of functionals in different codes:
NWChem : M06 series, DFT-D3 correction (next release), double-hybrids
Orca: DFT-D3, almost any double-hybrid can be defined (analytical gradients and efficient RI approximations available)
Holger Kruse responded on 09 Dec 2011 at 2:55 am #
Coming from Grimme’s group I am obviously biased, but as Grimme put it at the WATOC2011 talk this year:
“Any dispersion-correction is better than none”
To support my comment on the bad performance of M06-2X for long-range interactions, pls see DOI: 10.1002/cphc.201100826 (e.g. Figure 5).
One comment on the computational cost (not scaling) of double-hybrids:
For single-points it is often the same as for hybrid-functionals. Why? Because with an efficient RI-MP2 code the SCF iterations still takes far more time. The crossover point with Turbomole (using RIJK) is about 4000-5000 basis functions. (Gradients is more involved, but optimizations were never the purpose of double-hybrids)
Henry Rzepa responded on 11 Dec 2011 at 4:26 am #
“but optimizations were never the purpose of double-hybrids”. Indeed, transition state location using these for > 100 atoms is likely still some time away. I re-iterate that anyone studying a system of this size (very common nowadays in catalytic studies) should adopt one of the “single hybrid” “D” methods cited above.
Eugene responded on 12 Dec 2011 at 1:12 pm #
Thanks for the information! It’s hard to know what to make of a lot of these benchmarks. For example, I’ve been looking at how well the various DFTs do at predicting endo/exo ratios in Diels-Alder reactions lately, and it doesn’t look like any of them do that well. Certainly, it’s a tough problem, because you have to get dispersion, solvation, and probably a lot of other things right. What surprised me was that you can have B3LYP getting the secondary isotope effects right, but get the endo/exo ratio totally wrong. For example, if you look at the Houk work on the MacMillan Diels-Alder catalyst, you’ll see that both endo/exo ratio and ee are wildly overpredicted. One thing I’ve been looking at is using focal point methods–you’d think CBS-QB3 would do OK. But it doesn’t do much better. Maybe it’s solvation, maybe it’s errors in the geometry because of dispersion…who knows? If the best calculations don’t understand secondary orbital effects, or whatever is controlling these ratios, I don’t think I have a chance of doing it, either. Thoughts?
Henry Rzepa responded on 12 Dec 2011 at 1:54 pm #
Steve has noted on this blog how dynamic effects may also matter. Although not QD proper, I did an IRC for a simple ring opening and was quite surprised at how much went on after the transition state.
Aloke responded on 17 May 2012 at 7:48 am #
I find that M05-2X and B97-D functional give better performance than M06-2X and wb97x-D in the calculations of non-covalently bonded complexes. Any comments???
Hans Horn responded on 25 Sep 2012 at 2:56 pm #
What is the expert’s opinion: can / should the latest Minnesota functional M11 be used with D3?
thx,
H.
Computational Organic Chemistry » Benchmarking conformations: melatonin responded on 12 Apr 2013 at 4:23 pm #
[…] correction, Grimme’s D2 or D3 variety or the Vydrov-van Voorhis (VV10) non-local correction (see this post for a review of dispersion corrections), reduces the error substantially. Among the best performing […]
Computational Organic Chemistry » Acene dimers – open or closed? responded on 28 Oct 2013 at 9:06 am #
[…] conformer. B3LYP-D3 and B3LYP-NL, two different variations of dealing with dispersion (see this post), do a reasonable job at mimicking the LPNO-CEPA results, while MP2 indicates the stacked conformer […]
Flash responded on 26 Oct 2014 at 8:39 am #
For a Ir-catalyzed reaction I am studying now, I used B3LYP to optimize the intermediates and transition states. The energies were then corrected by the Grimme’s D3 correction. I also used M06 to do the single-point energies. Interestingly, the results calculated by B3LYP-D3 and M06 give somewhat different conclusions, and B3LYP-D3 was found to be consistent with experimental results. I am wondering which one should be trusted? It is possible that B3LYP-D3 is consistent with experimental results because of more accuracy, but also because of wrong reasons, such as the mechanism is not the right one.
narges responded on 03 Mar 2015 at 1:08 am #
Hi every body
I am working in crystal engineering area and want to calculate interaction energy in some Hg complexes. so I am looking for the best functional and basis set that introduce dispersion correction. I read your explanation about dealing with dispersion but I cant distinguish between them! ( I am not a physical chemist). I would be grateful if any body help me in this regard.