Minnesota MN15 functional (and the others) – new challenge

As an attention seeker, I want to have more and more views for my blog. And you know what, the number of views of the MN15 posts (or DFT in general) is way higher than the other WFT posts. So today, I write (again) on MN15 and the other modern functionals.

Let’s milk the cow MN15

Of course, I will not choose some simple challenges for MN15 such as non-covalent interaction or simple reactions of organic molecules because (a) these things are easier for DFT and (b) many of them are in the test set when training the functionals.

The post today is inspired by the work of Truhlar (surprise!) on the vanadium dimers. In his paper, beside testing a bunch of functionals as usual, Truhlar tried to explain why many functionals give very different results for the dissociation energy of the vanadium dimer (V2). I quote from the abstract

The results show that the errors in estimates of the bond energy of vanadium dimer can primarily be related to the calculated energy gap between the 4s and 3dz2 atomic orbitals of the vanadium atom and especially to the 3dz2 orbital energy.

I don’t comment much on this explanation, but it’s like trying to explaining why the chicken cross the road.

Why my functional gives bad results?

OK, let’s see the results. I did all calculations with the same level of theory like in the paper of Truhlar. And I am able to reproduce his results.

The binding energy is calculated as De = 2E(V) − E(V2). E(V) is the ground state energy of the vanadium atom (4F). E(V2) is the ground state energy of the dimer (3Σg), calculated at the experimental distance 1.77 Å. Spin orbit coupling contribution to the binding energy is −1.83 kcal/mol, taken from the paper. The experimental binding energy De is 64.2 kcal/mol.

Well, the results are bad as I expected.


Functional De (kcal/mol)
B3LYP 37.4
MN15 40.5
SCAN0 0.7
ωB97M-V 8.3
M06-L 57.0

I’m disappointed again with the modern functionals MN15, SCAN0, and ωB97M-V. Among these three, MN15 gives the best results, but still has an error of 23.7 kcal/mol. SCAN0 gives me the worst result.

How about my random number functional? It gives 61 kcal/mol for the first try. It’s ultra-fast (5 seconds including opening the webpage), perfect, and beautiful.


So what should be the explanation of these bad results? I quote

It is usually assumed that these larger errors arise from high multireference character in transition metal compound since molecules containing transition metals often present multiconfigurational characteristics.

Exactly! I think this is the reason. It’s time for my baby to shine (coming up next week).


PS. Good news. If you try to search “Minnesota MN15 functional” on my favorite search engine, my page is now on the first page.



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