# Can PBE (and LDA) actually be a better choice sometimes?

Part of my work as an inorganic chemist is to investigate the magnetic coupling between metallic centers in coordination compounds. After some time, I've noticed that the classic PBE functional is the one giving me the best results (better than B3LYP, PBE0 or even M06) and, at first, I was convinced that this was a mere coincidence.

The cases in which PBE keeps giving me better results are adding up, so, I've decided to perform a quick test using the well known $\ce{[Mn(III)2O2(NH3)8]^{2+}}$ that have a reported experimental $J_{AB} = -186.5~cm^{-1}$.

My benchmark showed this:

To me, the results are that the Local and Gradient Corrected Functionals like PBE and LDA are, actually, better for this kind of properties in which orbital superposition and spin delocalization are important.

My point here, I think, is that I struggle to believe that such simple and "old" functionals like PBE and LDA are actually better describing a complicated phenomenon like magnetic coupling.

I'd love to hear what you, guys, think.

P. S. 1: I'm using ORCA, that gives me J calculated using 3 different formulas, that's why I have 3 J values.

P. S. 2: Sometimes I'm using 2 basis sets, a bigger one for Mn and a smaller for O, N and H.

• I know this question is about density functionals, but I have to suggest that you should also test "conventional" quantum chemical methods like HF and MP2. These should be definitely within reach in terms of CPU time. Nov 25, 2015 at 17:37
• @uLoop, actually, I did. HF gave me something like -36 cm**-1 and MP2 was comparatively bad. Nov 25, 2015 at 22:30
• I have never worked with transitional metal complexes, but AFAIK they have a tendecy to be nasty multireference problems. That would be consistent with HF and MP2 giving bad results. Unfortunately, multireference methods tend to be quite CPU intensive. Nov 27, 2015 at 14:11

Can PBE (and LDA) actually be a better choice sometimes?

Of course, they can. This is in fact one of the major problems with DFT: there is no systematic way of improving a functional, so we never know a priori which will work better for some particular problem. The only thing we know is that some functionals perform systematically better that the others for some cases (see a bit more on that at the very end).

The choice of a functional (and even more generally the level of theory) is dictated by which property has to be calculated with which accuracy and is usually based on extensive benchmark studies. A rather quick search by "magnetic coupling dft benchmark" terms found few papers claiming that hybrids indeed work worse than pure functionals for that particular property. For instance, here, it is explicitly claimed in the abstract that

The inclusion of exact exchange does not lead to improvements but worsens results drastically.

Exactly the same thing happens in your case, and this is not a big surprise for a number of reasons.

• First, hybrid functionals are primarily better for energetics, and not just for any property. Many of hybrid functionals were even crafted with that particular aim in mind, i.e. to improve the description of energetics. But for other properties hybrid functionals might provide almost no improvement comparing to pure functionals and the results can indeed be even worse.
• Secondly, the might be some cancelation of errors out there. In some cases you can get lucky and have a better results using a lower level of theory with a smaller basis set due to cancelation of errors.
• Finally, benchmark has to be extensive. When it is said that some functionals perform better, the meaning is that they perform better systematically, i.e. for a wide variety of cases at average they spit out "better" numbers. There is absolutely no guarantee that these functionals will perform better for each and every case.

So, I recommend to:

• Always start from the literature search for benchmark studies on the property of interest which were already done and reported. They very likely exist and can be of a great help.
• On the basis of extensive benchmarks choose just a few combinations of methods and basis sets which are known to perform systematically well for the property of interest and benchmark them on your system, or, even better, on a number of similar systems which you might want (or even planned already) to study in the future.
• Pick one or two methods and stick to them.
• Thank you for your answer. You're right: I'm searching for other benchmarks and as soon as I have something consistent I'll be sharing it here. Nov 25, 2015 at 23:44