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I am trying to calculate the binding energy of a small molecule with an underlying surface. I have used B3LYP-D3BJ (as implemented in ORCA) at def2-TZVP basis set to optimize the geometry of the VdW complex, and then performed a single point Binding Energy calculation using RI-MP2 at def2-TZVP basis set. However, I am concerned about the accuracy of the binding energy that I have obtained from RI-MP2 calculations. Should I calculate the binding energy using DFT-D3 or will the energies from RI-MP2 be more accurate?

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  • $\begingroup$ +1 but it will depend on which functional is being used. You have told us that the D3 part is BJ, but what about the base functional? $\endgroup$ Commented Aug 10, 2023 at 12:25
  • $\begingroup$ @NikeDattani Prof. Dattani, I have updated the question to include that information. $\endgroup$ Commented Aug 10, 2023 at 14:08
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    $\begingroup$ That was an important update, because if for example it was B2PLYP (which is designed to be an improvement over MP2), then the answer would clearly be that the DFT-D3 calculation is more accurate than the RI-MP2 one. $\endgroup$ Commented Aug 10, 2023 at 14:12
  • $\begingroup$ From ORCA Input Library, I see that B2PLYP calculations are very expensive. How bad will the regular RI-MP2 energies be, in comparison to B2PLYP ones? Especially if we are interested in relative energies? $\endgroup$ Commented Aug 10, 2023 at 14:16
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    $\begingroup$ In the answer that I recently posted for this question, B2PLYP is included within "double hybrid functionals" and is significantly better than MP2 (and therefore also RI-MP2, which is an approximately of MP2). B2PLYP will not cost much more than MP2 since the dominant part of the calculation is the MP2-like part. At the end of my answer, I suggested that you can try RI-B2PLYP-D3, which will have a similar cost to RI-MP2, but will be more accurate. I still recommend just to use B3LYP-D3 though since its much easier to justify (see below). $\endgroup$ Commented Aug 10, 2023 at 17:45

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Summary of my recommendation

If my choices are B3LYP-D3 and RI-MP2 for calculating a binding energy at a molecule whose geometry was optimized with B3LYP-D3, I would find it easier to justify using B3LYP-D3 for the binding energy. B3LYP-D3 was found in the study summarized below, to be more accurate than RI-MP2 for "basic properties" such as atomization energies, and that is without the RI approximation for MP2, and it's for extrapolated CBS estimates for MP2 rather than the single def2-TZVP basis set that you're using.

If somehow for your specific system's binding energy, RI-MP2/def2-TZVP is more accurate than B3LYP-D3/def2-TZVP and def2-TZVP is the biggest basis set that you can use for either of them, even if you were to do a (def2-TZVP,def2-DZVP → CBS) extrapolation for both RI-MP2 and B3LYP-D3, the results below show that other dispersion-corrected hybrid functionals with a similar cost to B3LYP-D3 are likely to beat MP2 by quite a lot (and therefore also RI-MP2 unless something fortuitous and unpredictable happens) in every category presented in the summarized results.

Results from Goerigk and Grimme (2011)

As summarized in my answer to What are some recent developments in density functional theory?, a 2011 study involving 841 relative energies and comparing more than 20 different hybrid functionals, for a variety of different properties, found that overall B3LYP-D3 was slightly worse than the average hybrid functional calculation (all hybrid calculations included the -D3 correction but the suffix was dropped for diagram), which had an average discrepancy of around 3.3 kcal/mol with the benchmark energy differences (mainly coming from experiments or CCSD(T)/CBS estimates):

                            

It would be great if we could know where MP2 lies on a histogram for exactly the same dataset. In fact the original paper has the following comparisons between MP2 and DSD-BLYP-D3:

enter image description here

DSD-BLYP-D3 is a "dispersion-corrected, spin-component-scaled, double-hybrid (DSD)" functional, and since you're using B3LYP-D3 which is a single-hybrid functional, it would be prudent for you to ignore the DSD-BLYP-D3 results in the above histogram. Instead let us compare the MP2 numbers in the above histograms with the B3LYP-D3 numbers in the histogram below (again, all calculations included a -D3 correction, but the suffix was dropped in the labeling of the functionals):

enter image description here

This leads me to the following summary for average discrepancies with the benchmark numbers:

Method Basic Properties Reaction Energies Non-covalent interactions Complete Set
MP2 5.7 kcal/mol 3.6 kcal/mol 0.90 kcal/mol 3.6 kcal/mol
B3LYP-D3 5.0 kcal/mol 4.7 kcal/mol 1.10 kcal/mol 3.7 kcal/mol

My first observation is that B3LYP-D3 is worse for everything except for "basic properties".

So what are "basic properties"? They are described in the paper as "atomization energies, electron affinities, ionization potentials, proton affinities, SIE related problems, barrier heights".

You seem to be interested in "binding energies", which are similar to "atomization energies", which is where B3LYP-D3 wins against MP2, and would probably win even more after we consider:

  • that the MP2 results in the above histograms are for CBS estimates and your MP2 calculations are using just the def2-TZVP basis set with no extrapolation, and
  • that the MP2 results in the above histograms are from full MP2 rather than the RI-MP2 approximation to full MP2 (and you are using the latter),
  • that you optimized the geometries with B3LYP-D3, so your B3LYP-D3 binding energies would most likely have an inherent advantage over your MP2 ones.

I think it would be harder to justify using RI-MP2 for the binding energy after optimizing the geometry with B3LYP-D3 rather than maintaining consistency by using B3LYP-D3 for both the geometry optimization and the binding energy calculation. I guess you chose to use RI-MP2 because it's a more expensive method, with a formal scaling of O(N^5) as opposed to B3LYP-D3 whose cost is probably dominated by the HF part which has a formal scaling of O(N^4), but B3LYP-D3 according to this 2011 study, B3LYP-D3/(aug-)def2-QZVP is more accurate than MP2/CBS for "basic properties", and some of the other dispersion-corrected hybrid functionals that cost almost the same as B3LYP-D3, beat MP2 in every single category in this study.

Other findings

When I searched DFT vs MP2 on Google, the first page of results gave me the following 10 results, in order:

When I searched MP2 kcal/mol accuracy on Google, the first page of results gave me the following 10 results, in order:

Related MMSE posts

Ideally these would appear in the "Related" section in our sidebar, but at the moment they don't:

RI-B2PLYP-D3 is mentioned in the last of these, and in theory it would have a similar cost to RI-MP2 since the dominant-scaling part of B2PLYP-D3 is the MP2-like calculation. Since in this comment you were worried about the cost of B2PLYP, RI-B2PLYP-D3 might be a good option for you too.

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  • $\begingroup$ I agree with this answer except that you say binding energies are similar to atomization energies. Binding energies are most comparable to the non-covalent interaction portion of the table you show since the binding energy separates a system into molecules, not atoms. In that case, MP2 would be a better choice and in general MP2 is quite good for vdw complexes. For vdw complexes though, I think including more diffuse functions in the basis is going to be important for OP. Perhaps def2-tzvppd would be a better choice of basis if possible. $\endgroup$
    – jheindel
    Commented Aug 10, 2023 at 23:26
  • $\begingroup$ @jheindel Thanks! For a molecule, like H2, the "binding energy" of the first vibrational energy, is literally the atomization (or dissociation) energy, but I trust that for vdW complexes, "binding" energy means what you say it means. Even if "binding energies" were/are literally the same as the "non-covalent interactions" studied, then MP2/CBS would have an average discrepancy of 0.9 kcal/mol and B3LYP-D3/(aug)-def2-QZVP would have an average discrepancy of 1.1 kcal/mol. When you switch from MP2/CBS to RI-MP2/**def2-TZVP** (which is what OP used) the 1.1 kcal/mol could become 0.9. $\endgroup$ Commented Aug 10, 2023 at 23:52
  • $\begingroup$ So for those reasons, I'd recommend to just calculate the properties with the same method as the method used for geometry optimization, so that no extra discussion needs to be provided about how much the optimal geometry might have changed when switching methods. $\endgroup$ Commented Aug 10, 2023 at 23:53
  • $\begingroup$ Great answer! A small comment: by def2-DZVP, do you mean def2-SVP? I've never heard of def2-DZVP, and I cannot find it in the BSE. $\endgroup$
    – wzkchem5
    Commented Aug 11, 2023 at 7:28

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