The Present: COHPs from Plane-Wave Output

The theory so far has built on local orbitals—recall the H chain or the orbitals of tellurium and iron, or even the very name of the method. So far, this has been fine, because COHPs have been implemented in frameworks such as tight-binding LMTO or the SIESTA method, which we have described on the previous page. Much to the contrary, a totally different method has been growing fast in the last two decades: the use of plane wave based DFT codes, instead of those with local-orbitals.

In fact, together with advanced theories such as the projector augmented-wave (PAW) method, plane waves have risen to the de facto standard in the solid-state sciences. Despite their undeniable power, plane-waves are (by their very nature) delocalized, and do not allow for COHP analysis at all. Luckily, a way out is available: by using a projection to a local, auxiliary basis, one can extract the chemical information. The underlying principle has been described a while ago, and it is used for Mulliken analysis up to the present day!

It should be possible to re-extract a COHP as well, shouldn't it? Indeed, we succeeded in developing such a method in 2010, and it was consequently dubbed "projected COHP". The central clue is that the COHP is a product of two matrices, density (where are the electrons?) and Hamiltonian (what do they do?), and one needs to develop a theory to retrieve both and then multiply their entries, just like one would do in "traditional" COHP analysis. (Admittedly, it always looks simpler afterwards.)

Once the knot had been broken, the next step was to extend the theoretical framework. Over the last two years, we have developed a more general, analytical scheme, but the general idea (as stated above) stays largely untouched. This new scheme has also been implemented into the LOBSTER program which calculates pCOHPs directly from your plane-wave output (as well as a number of other, valuable pieces of chemical-bonding information). Needless to say, this program is free of charge for any academic or non-profit research.

Finally, a word of caution is in order. A faithful description of the electronic structure requires a proper projection—just like a novel or other literary work must be translated by a specialist, not an online translating tool. Going back to chemistry, one requires that the original and the reconstructed wavefunction resemble each other as closely as possible; mathematically, one may even calculate a "spilling indicator" which ranges from one to zero; the lower, the better. To get this value low, and thus to calculate reliable pCOHP curves, a local basis of Slater type orbitals has proven quite successful. We also had a few other ideas for more elaborate projection basis sets, which are included in our software.