Dispersion interactions in DFT

Since the silence has to be broken somehow, this time it's going to be a post about the practical aspects of computational chemistry.

It is well-known that description of long-range correlations leading to London dispersion forces (better known as "van der Waals forces", although it's only one of the multiple interactions falling into this category) is notoriously hard for quantum chemistry tools. Basically, until recently, to get reasonable description of dispersion interactions in weakly bound systems, one would have to either use high-level correlated ab initio methods (for which, until recently, computing resources adequate for simulating systems of any reasonably interesting size had been effectively unavailable), or augment their quantum chemistry (most often, DFT) with empirical classical interatomic potentials - sort of undermining the whole idea of a "first-principles" calculation. The latter approach can also be described as "atom-atom" (as opposed to the "electron-electron" ab initio approach).

There's been a recent improvement in the form of a fully nonlocal density functional which appears to describe many systems fairly well. I've tried it myself, using the JuNoLo code which gave me a mere 3% error for the c lattice constant of graphite. This is actually very impressive, and since this functional is now starting to get included in standard DFT codes (most notably, SIESTA), there's clearly a big future for this approach (although it is known to fail for some systems: I've heard it fail for Ni on graphene). Finally, there's also another first-principles approach employing exact exchange and RPA correlation, somewhat similar in the approach (i.e., nonlocal) also appearing to give good results.

Now, what I want to write about is a recent proposal which includes nonlocal interactions in a very peculiar way, that is, locally. The title of the paper describing the approach is Accurate and efficient calculation of van der Waals interactions within density functional theory by local atomic potential approach, and it appears that it really is accurate and efficient. What the authors did was identify that dispersion interactions can be described in the "atom-electron" way using a local component added to the pseudopotential. It's as simple as that: just take the modified pseudopotential, and dispersion interactions come free of charge.

While this is, strictly speaking, an ad hoc semiempirical correction, and the first obvious question that comes into mind is that of transferability. Luckily, the experience of classical interatomic potentials suggests that dispersion interactions are not extremely sensitive, and the vdW parameters in such force fields as OPLS seldom need fine tuning. The paper cited above appears to suggest that the accuracy of this new DFT+LAP method is extremely good for a huge range of C,H,N,O compounds. However, the authors only list interaction energies and no forces nor geometries. Therefore I decided to check myself how well it would perform for fcc C60 fullerite. Using the setup from the above paper gives a lattice constant of 1.4118 nm which, compared to the experimental value of 1.417 nm, is just amazingly good: the error is a mere 0.37% (!!!), and even if we subtract the radius of C60 and look only at the nearest-neighbor intermolecule distance, it's still only 1.3% off! What's further encouraging is that the bulk modulus also comes close to recent experimental results: the error is +25% for the modulus and -25% for the dB/dP, which can be considered quite good an agreement for elastic properties - mind also that these values have been calculated using Murnaghan fit, which is not well suited for such systems (dB/dP != const).

Some more open questions remain from the no-free-lunch side. First, it has yet to be demonstrated that (if) this approach works for other systems such as those containing metal atoms. Second, since it is an "atom-electron" approach, it has to contain the notion of an atom in some way or another - this time it's the pseudopotential; real systems don't have well-defined atoms, hence the "purity" of the approach again suffers somewhat. Interestingly, I'm more or less sure that DFT+LAP can be used to describe core electrons exactly, in a "semicore"-like manner, but someone has to test this.

Finally, I want to note that this approach seems to redefine the physical meaning of the pseudopotential: while the latter originally is interpreted as describing the "effective interaction" of valence electrons with core electrons, vdW-DF calculations suggest that it is unnecessary to include the core charge density in the DFT calculation to get the correlation energy responsible for dispersion attraction right. This seems kind of funny.

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