Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations

After giving a concise overview of the current knowledge in the field of quantum mechanical bonding indicators for molecules and solids, we show how to obtain energy-resolved visualization of chemical bonding in solids by means of density-functional electronic structure calculations. On the basis of a band structure energy partitioning scheme, i.e., rewriting the band structure energy as a sum of orbital pair contributions, we derive what is to be defined as crystal orbital Hamilton populations (COHP). In particular, a COHP(E) diagram indicates bonding, nonbonding, and antibonding energy regions within a specified energy range while an energy integral of a COHP gives access to the contribution of an atom or a chemical bond to the distribution of one-particle energies