Density-of-states and Basic Electron Partitioning

The detailed discussion of band structures arising for three-dimensional materials is hardly ever attempted, due to their often incredibly high complexity it is difficult to think in terms of reciprocal space We will also leave the calculations of three-dimensional band structures and parts of their numerical analysis to fast (albeit dumb) computers. 

What is needed, at least in the electronic-structure theory of solids, is an appropriate tool, one which averages over the entire system to make the electronic structure transparent and which brings us back into real space there are at least two ways to accomplish this, either through averaging in real or in reciprocal space. 

In the second approach, one deliberately sacrifices all direction-related information to yield such energy-resolved indicators, and the strategy proceeds as follows. If we were interested in the number of one-electron levels in an infinitely small energy interval dE, we would introduce the density-cf-states P E) which, as solid-state physics teaches [53], behaves as the reciprocal gradient of the band structure. For the one-dimensional case, this is 

It also needs to be mentioned that there is a different style of DOS presentation in chemistry and physics. Within the latter community, it is customary 

12) Whether or not density-of-levels (DOL) or density-of-states (DOS) is the more appropriate term depends on the perspective. In the first case, the one-electron picture (orbitals) prevails whereas, in the second, the calculation of a many-body wave function would be necessary in practice, the term IX)S is used throughout, even if the construction of a many-body wave function is not attempted. 

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