Two recent papers

  1. A review on computational studies of carbon nanostructures and related materials, part of a special issue of Advanced Materials dedicated to the centennial of Rice University. Unfolding the Fullerene: Nanotubes, Graphene and Poly-Elemental Varieties by Simulations. E. S. Penev, V. I. Artyukhov, F. Ding, and B. I. Yakobson. Adv. Mater. 24, 4956-4976 (2012).
  2. A paper in PNAS investigating the atomistic mechanisms of graphene synthesis viewed as a crystal growth process. Equilibrium at the edge and atomistic mechanisms of graphene growthV. I. Artyukhov, Y. Liu, and B. I. Yakobson. Proc. Natl. Acad. Sci. U.S.A. 109, 15136-15140 (2012).
The second paper is Open Access, and here is the official Rice News release:

Every atom counts in graphene formation

Rice University lab’s nanoreactor theory could advance quality of material’s growth

HOUSTON – (Sept. 4, 2012) – Like tiny ships finding port in a storm, carbon atoms dock with the greater island ofgraphene in a predictable manner. But until recent research by scientists at Rice University, nobody had the tools to make that kind of prediction.
Electric current shoots straight across a sheet of defect-free graphene with almost no resistance, a feature that makes the material highly attractive to engineers who would use it in things like touchscreens and other electronics, said Rice theoretical physicist Boris Yakobson. He is co-author of a new paper about graphene formation to appear this week in the Proceedings of the National Academy of Sciences.


Paper on graphene fracture in Nano Letters

Ripping Graphene: Preferred Directions

This is a joint paper where we work together with experimentalists to explain unusual observation of tears in graphene going almost exclusively in the zigzag or armchair directions of the crystal lattice (Fig. 1), using fracture theory and molecular dynamics simulations (Fig. 2). 

Fig. 1. A crack in graphene as seen in a transmission electron microscope and the distribution of cracks by orientation with respect to lattice (zigzag is blue and armchair is red in the left panel).

Fig. 2. Snapshots from MD simulations showing straight crack propagation in the armchair and zigzag orientation and crack redirection when started at an intermediate orientation with respect to the lattice.

A couple of videos from MD simulations:


Some teaser videos

from an upcoming paper:


Charge-shift bonding

A yet another theory post, h/t Steven Bachrach.

Everyone remembers the two fundamental chemical bond types: covalent and ionic. Recently, a third one has been proposed, which is called "charge-shift bonding". The valence bond wavefunction that describes the system, e.g., a fluorine molecule, is a linear combination of different charge shift states, e.g.:

Ψ(F2) = C1*φ(F-F) + C2*φ(F+F-) + C3*φ(F-F+)

Now, the fluorine molecule stands here as an example because the energy contribution of the covalent term is positive, meaning that the system exists in a "superposition" of two resonant states, F+F- and F-F+, while the covalent contribution actually destabilizes the molecule. This is a very interesting phenomenon, particularly because it is reminiscent of the Mott transition. For more details on charge-shift bonding, see the review in Nature Chemistry, and the blog post for a more strict explanation of the concept.

While this is an interesting explanation of why the fluorine molecule falls apart so happily, it has been suggested that a similar mechanism can be behind the differences in energy of linear vs. branched alkanes. Basically, the latter have more available options for second-atom "resonances" (C+CC- and C-CC+). Here's the paper and the blog post

Now, this is a very interesting explanation of a long-standing problem. On the other hand, though, the fact that even such seemingly simple and familiar systems as alkanes sometimes have to be treated using multi-reference methods is, in my view, somewhat disencouraging...


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.