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COHP、pCOHP、COOP演化历史
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关注：
1） I am lucky, I have ties with the following people: Peter Blöchl and Richard Dronskowski，Roald Hoffmann
2) Can I translate it into an advantageous position in my institute?
History: The Misty Past and Some Venerable Codes
COHP was given birth at the end of the 1980s in the 
Max-Planck-Institute for Solid State Research at Stuttgart, Germany. Those were the good old days when computer hardware was slow but robust, computer software was unforgiving, and real programmers did not use Pascal (or C) but Fortran... Well, the good old days...
At that time, Peter Blöchl and Richard Dronskowski were heavily working on their PhD theses in the groups of Ole Krogh Andersen and Arndt Simon, respectively. Peter had just completed the first workable tight-binding LMTO-ASA program (running on a Cray X-MP monster), and it was Richard's job to add the COHP subroutines (written on a 6 MHz 80286 computer) in order to extract the chemical information from the k-dependent wave functions, following an idea by Ole Krogh Andersen borrowed from Roald Hoffmann. Peter and Richard eventually succeeded and received their PhDs! As a matter of fact, COHP was neither the main topic of Peter's thesis (full-potential LMTO & electronic structure theory of boundaries) nor Richard's thesis (oxides and arsenides containing condensed molybdenum clusters).
Funnily, COHP had been dubbed Hamilton-projected densities of states at that time; consequently, Richard's first COHP program was called NEWHPDS. The first calculations were performed on silicon (of course, what do you expect?) and on octahedral molybdenum clusters (still unpublished).
The first COHP paper was put together in 1992-3 when Richard had just returned from his postdoctoral time with Roald Hoffmann at Cornell university; the paper came out in the Journal of Physical Chemistry, dealing with silicon, its bonding properties and a number of technical questions (such as Euler rotations) which turned out to be fairly unimportant in the long run. In the meantime, however, a new TB-LMTO-ASA program had already been developed in the Andersen group (the code which is nowadays distributed worldwide) such that the old COHP code had to be adjusted to digest the newly calculated wave functions. This major renovation (reprogramming, in fact) of Richard's outdated computer code was skillfully mastered by postdoctoral candidate Florent Boucher from Nantes. Exactly, this is the COHP program for analyzing the LMTO wavefunctions you find within the popular TB-LMTO-ASA package; it is quite likely the basis of many COHP curves you find in published papers, also today.
Independently, in the 1990s, graduate student Greg Landrum at Cornell totally rewrote the extended Hückel computer programs by the Hoffmann group; the result was called YAeHMOP (Yet Another extended Hückel Molecular Orbital Program), and you can still get it today (for free). Wingfield Glassey, another member of the famous Hoffmann group, then added the COHP functionality.
More recently, COHP analysis has been implemented into the SIESTA code, an efficient order-N electronic-structure code that makes use of adjustable local-orbital basis sets. SIESTA is provided free of charge for academic research, and you can get it directly from the developers.
Finally, in the first decade of the 21st century, a totally new method to calculate COHPs (so-called projected COHPs) was eventually put together—please have a look at the next chapter!
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). LOBSTER is currently going through beta tests and will be available here very soon! 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.
RULES: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 have a few other ideas for more elaborate projection basis sets, which we will hopefully announce here soon. Stay tuned!
What is the difference between COOP and COHP?
Both COOP (crystal orbital overlap population) and COHP (crystal orbital Hamilton population) are partitioning methods for analyzing the (k-dependent) wavefunction. While COOP partitions the electron number, COHP partitions the band structure energy.
As a consequence, if you calculate the energy integral of a COOP curve, you get a number of electrons (like in the Mulliken scheme);
if you integrate a COHP curve, you get an energy value that hints toward the bond strength.
I have heard about the "wxDragon" visualization program. Is there a relationship between wxDragon and COHP?
Originally intended for viewing molecular-dynamics output, wxDragon has evolved into our favorite program to explore the results of COHP calculations (or any electronic-structure properties, for that matter). wxDragon has been developed by Bernhard Eck at Aachen and is available via http://www.wxdragon.de. While we are quite happy with it, the use of wxDragon is of course not mandatory; COHP data are provided as plain text files and in principle, you can use any suitable piece of software to view them.
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