Chemistry and Physical Properties by Manes L. Actinides

By Manes L. Actinides

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14a, b. Hubbard sub-bands for the localized (~ or ~) and polar states in a narrow band solid a) band spread as a function of interatomic distance: at ac, the Mott-Hubbard transition occurs. M. Fournier and L. Manes We take the model of a monovalent element containing just one electron in its outer shell (the "hydrogen" lattice described above). We consider first (Fig. 14 a) what happens at very large distances. The Hamiltonian (11) (without the correction (35)) would then give rise to a very narrow band (a level).

The Stoner Parameter I and Spin-Polarization Let us resume here the results of the model. A Hamiltonian such as (11), obtained after all the approximations of the electron interaction described in LDA, provides a ground state energy for the electron system which we term E°(n) (we have omitted for brevity the k-dependence, giving rise to the band spread, and indicated explicitly the fundamental dependence on the charge density n(R)). However, Wohlfarth 32), already in 1953, had analyzed the quantum mechanical derivation of the total energy of a d narrow band (using the so-called "tight-binding" approximation (see23)), proper for atomic-like wave functions such as the d wave functions) and found, in the solution, Coulomb and exchange terms dependent on the spin-polarization, and leading to a lowering of the total energy.

Conversely, the state does not help at all to define the Fermi level by means of (14). This is essentially an atomic localized level. Different is the case for a state (a resonant state) as 1 in Fig. 12 a, lying very close to the Fermi level (E very close to EF). For this state, (13) gives a probability of occupation which is strongly temperature dependent. How much it determines the position of the Fermi level depends on the contribution which, together with the population of the broad (s-d) conduction band which we have super-imposed in Fig.

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