Application of the MV-3 Model

Consider two different sites, M+ and M, in a disproportionated system. We first assume symmetric geometry of the enviromnent, so that M+M has the same energy as M M+. Since the spin-coupled state MM is unstable, two electrons may be transferred at the same time from M to M+, forming M+ and M. This is one of the rare situations when a transfer of electron pairs is possible (and, in fact, the only possibility) in a chemical system. 

We may choose Hjj and Qo to fit previously calculated PES. If the ground state is the MM state with Q = 0 as the equilibrium point, we are talking about a spin-coupled ground state, as for example in CuO, NiO, or in the cuprates. This is the antiferromagnetic state, sometimes referred to as the spin density wave (SDW) state. 

In another ch ical situation, the ground state may correspond to site occupation different in two electrons for example -1-3 and -El. In this case, the outer parabolas form the ground state. We call this state the charged state or charge density wave (CDW) state. In this case, U is small, but not necessarily negative. 

We call the region from U = A, to U = 0 the state overlap region. Electron pair transfer is only possible nnder the additional condition that the charged state is the ground state. 

What is causing the coupling between the M M+, MM, and M+M states There is also a coupling to the vibrations, but we suspect that this coupling may be derived from the correction terms to the Bom-Oppenheimer approximation. 

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