States and its Analysis

In practise, to determine the DOS of a system, the k-dependent Hamiltonian is diagonalized for a fine mesh of k points in the Brillouin zone. This leads to a histogram of energy values, which is then numerically smoothed using a set of appropriate functions, for instance, Gaussians, leading to the DOS of the material. The finer the mesh of k points used, the more precise will be the DOS. 

The electronic structure of solids can be discussed solely on the basis of their DOS curve. The DOS of a real solid can have a quite complex shape. Thus, it is important to develop a qualitative way to analyze this type of plots [10,11]. The ftf(e) curve for a single band i satisfies the normalization condition 

The electron distribution in this molecular orbital is given by the normahzation condition 

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. 

Note that although these tools are mostly employed in a qualitative way, the use of COHP may be advantageous because it allows the weighting of the role of the contribution of different pairs of atoms to the bonding. 

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