COHP: Crystal Orbital Hamilton Population
Definition:The COHP technique is a quantum-chemical bonding indicator that allows to identify bonding (stabilizing), nonbonding and antibonding (destabilizing) contributions to the electronic band structure of a solid.
Explanation:A central concept in computational materials science is the electronic band structure: that is, the quantum-chemically computed energy eigen values. They are routinely visualized using density of states (→DOS) plots, the solid-state chemists’ analogue to a molecular orbital diagram. Despite their usefulness, the DOS plots lack a crucial information: the interaction between pairs of atoms, which translates into the notion of “chemical bonding” [1]. In particular, an atomic resolved DOS may indicate where the electronic levels are, but not whether they stabilize or de-stabilize a solid structure. The latter information can be recovered by weighing the DOS matrix elements with the corresponding expectation values of the Hamiltonian. The result is called COHP [2], and usually plotted along with the DOS.

COHP curves are used to identify bonding and antibonding contributions to the band structure. Diamond (crystalline carbon) may be the simplest example: all occupied states are bonding, and the antibonding states above εF are not filled, as in Fig. 1a. In the theory of itinerant magnetism, the COHP serves a special role: it can be used to explain and predict the onset of phenomena such as ferromagnetism [3]; this is exemplified in Fig. 1b for body-centered cubic (→bcc) α-Fe.
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Figure 1: (a) COHP analysis for α-Fe. Ferromagnetism arises because by lifting the degeneracy of “up” and “down” spin channels (solid and dashed lines, respectively). The crystal may reduce unfavorable antibonding interactions at the Fermi level εF. (b) Band structure, DOS, and COHP plots for crystalline diamond.
SFB-Link:The COHP technique is applied by subproject A1 to different structures of SFB material in order to understand bonding, magnetism, and stability.
References:[1] R. Hoffmann, Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures. John Wiley & Sons, New York (1988).
[2] R. Dronskowski, P. E. Blöchl, J. Phys. Chem. 97, 8617 (1993).
[3] G. A. Landrum, R. Dronskowski, Angew. Chem. Int. Ed. 39, 1560 (2000).