Mott-Hubbard energy

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

Figure 17 is a clear illustration of the Mott-Hubbard transition in the actinide series the 5f emission occurs, for a-Pu, at Ep, indicating a high 5f-density of states pinned at the Fermi-level, whereas the 5 f emission occurs at lower energy for americium metal. In this case, therefore, a theoretical concept deduced indirectly from the physical properties of the two metals, finds direct (one might even say photographic ) confirmation in the photoemission spectra. 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

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.

Unlike the Mott-Hubbard insulator MnO described above the band-gap in the isostruc-tural oxide NiO is much smaller than expected from intrasite Coulomb repulsion. Fujimori and Minami showed that this is owing to the location of the NiO oxygen 2p band - between the lower and upper Hubbard sub-bands (Fujimori and Minami, 1984). This occurrence can be rationalized by considering the energy level of the d band while moving from Sc to Zn in the hrst transition series. 

For transition metal oxides such as NiO the Mott-Hubbard model gives much better agreement with experiment localization of the electrons in this way explains the anh-ferromagnetic ordering observed in NiO and its electrical insulator proper-hes [112]. The terms required to calculate the electron-electron interachon energy on a site, Fmh can be written in terms of the d-electron occupahons, using a UHF approach ... 

The ARPES spectra signal for the sulfur compound (TMTTF)2PF,5, displays a rigid shift of the leading edge near the Fermi energy to about 100 meV. This value is consistent with the charge gap of 900 K obtained from transport experiments DC or 800 cm from optical conductivity of (TMTTF)2PF6, Within a onedimensional frame of interpretation, this gap has been ascribed to a Mott-Hubbard localization gap [99],... 

Instabilities in a 1-D system, driven by a strong on-site electron-electron Coulomb repulsion U, lead to a Mott-Hubbard insulator [161], particularly for p = 1 systems this causes charge localization, and the crystal becomes insulating. For a chemist, a Mott-Hubbard insulator is like a NaCl crystal, where the energy barrier to moving a second electron onto the Cl site is prohibitively high, as is the cost of moving an electron off a Na site. 

When p = 1 (one electron per molecule) the electrons (or holes) are localized [23] any transport of charge puts two electrons on the same site, at a huge cost in energy thus a p=l system is a Mott-Hubbard insulator [161]. If Em + Id Aa 0 then interesting properties become possible [48]. 

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... 

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