Crystal orbital Hamilton populations

Similar to the COOP method, this approach has been called crystal orbital Hamilton population (COHP) analysis [91]. Given a short-ranged orbital basis set, the sum of all pairwise interactions rapidly converges in real space, similar to the COOP formalism. In fact, such energy-partitioning schemes have a long... 

Fig. 2.22 Semiempirical band structure, density-of-states, and crystal orbital Hamilton population for a two-dimensional square lattice of iron atoms spaced at 2.2 A.

In addition, let us quantum-chemically analyze the electronic structure of this simple material in terms of chemical bonding. This is very easy to do because the above-mentioned TB-LMTO-ASA method operates with an extremely short-ranged basis set, such that electron and energy-partitionings are straightforward. Figure 3.3 shows the results, namely the band structure, the density-of-states, and the crystal orbital Hamilton population analysis. 

Fig. 3.5 Density-of-states (DOS) including local 3d projections (a) and the crystal orbital Hamilton populations (COHP) for the M-N interactions (b) and the M-M interactions (c) in MN, adopting the sodium...

A difficulty often associated with the use of overlap populations is that it is not sensible to compare values for different pairs of atoms. A useful tool derived within the DPT scheme is that of the crystal orbital Hamilton population (COHP) analysis [14]. In that case, what is partitioned in bonding, nonbonding, and antibonding contributions for a certain energy window is not the number of electrons (COOP) but the band energy (COH P). Except for the obvious fact that the two kinds of curves show opposite sign behavior, they usually lead to the same qualitative analysis. 

FIGURE 36 Crystal orbital Hamilton population (COHP) diagram Fot homoatomic (Y-Y) and... 

---