Mott-Hubbard correlation energy

In discussing the issue of interparticle interactions, it is generally assumed that an individual metal particle will remain electrically neutral. This innovation, originally proposed by Kubo, " has its atomic counterpart in the Mott-Hubbard correlation energy, U, for macroscopic systems (Fig. 5). For our present purposes... 

Figure 5. The metal-insulator transition in the doped semiconductor (Si P) and a divided metal. Here t/jc is the Mott-Hubbard correlation energy in the doped semiconductor, and t/dus is the corresponding charging energy of the divided metal.

Figure 7.1. The band gap is determined by the d-d electron correlation in the Mott-Hubbard insulator (a), where A > I/. By contrast, the band gap is determined by the charge transfer excitation energy in the charge transfer insulator (b), where U > A.

To put it on a more quantitative basis, Johansson uses the expression for the critical point of the Mott transition as reformulated by Hubbard in terms of the bandwidth W[ and the polar state formation energy Uh (or effective intra-atomic correlation) (Eq. (36)). 

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