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What's the crystal orbital Hamiltonian population (COHP) or the crystal orbital overlap population (COOP)? What's the relation between the bandstructure or density of states (DOS) and COHP/COOP? Why we can read the information about bonding or antibonding information from COHP and COOP?

A clear physical picture will be appreciated.

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There is a great description given of COOP in Roald Hoffman's Solids and Surfaces: A Chemist's View of Bonding in Extended Structures. It is sometimes referred to as the Overlap Population Weighted Density of States (OPWDOS) which makes the meaning a bit clearer: its the density of states, weighted by the overlap for a given bond ($c_ic_jS_{ij}$). This results in a signed DOS, as the overlap population can be positive or negative. This quantity is similar (though not exactly equivalent) to the molecular concept of bond order, where a positive COOP denotes a favorable/bonding interaction and a negative COOP indicates an unfavorable/antibonding interaction. We can see an example of this below from Hoffman's book, giving an example for a simple hydrogen chain.

COOP plot of H atom chain

COHP, as mentioned in Kevin J.M.'s link is a variation on the same concept, where the weighting is now done based on off-diagonal Hamiltonian elements as opposed to off-diagonal overlap elements. There are apparently advantages to describing binding this way, but I haven't gotten to look at the original COHP paper to see why it is better than COOP. One difference to look out for is the COHP plots are generally actually -COHP to make them more comparable with COOP plots. This is because a negative Hamiltonian element would correspond to a favorable interaction.

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