Half-filled band, energetics

Table 1. Energetics of Half-Filled Band Possibilities (12)...

The fundamental excitations of the half-filled band Peierls distorted chain are known to be phase kinks, or solitons, in the pattern of the bond alternation. This was shown for polyacetylene [5,6] to take the form of the bond alternation defects shown in figure 2. An important insight into the nature of these excitations from the work of Su et al [6] is that the bond alternation defect is not localised at a single carbon site, as indicated for convenience in the schematic representation in figure 2, but is spread over some 10 to 15 carbon sites. This delocalisation is crucial to the energetics of the stabilisation of the soliton, and is clearly demonstrated experimentally. For this situation, it is possible to use a continuum model for the polyacetylene chain, within which various simple analytic results are found. Thus, the gap parameter, A varies through the soliton as... 

For the trimerization, 38, it is the sixth moment (Table 5) which distinguishes it from the undistorted chain. Since the sixth moment decreases on distortion, the undistorted structure will be more stable at the half-filled point. Figure 26 shows a computed energy difference curve for this distortion too. Notice that the trimerization is predicted to be energetically favorable at the third or two-thirds full band. Here the distortion is the one... 

In its metallic state, Eu is divalent in order to achieve the energetically favourable half-filled shell (4F) configuration. Apart from the presence of the 4f electrons, Eu is isoelectronic to the alkaline earth metal Ba the influence of the d-bands on the conduction electron energies is largely responsible for the... 

We find that the 5d bands are 7-8 eV wide for the trivalent metals and somewhat narrower, 6—7eV, for divalent Eu and Yb. The 4f complements of Eu and Yb are larger by one than trivalency would imply (a consequence of the energetic favora-bility of a half-filled or filled 4f shell), and the relatively smaller effective nuclear charge is responsible for larger lattice constants and correspondingly narrower 5d bands. Our 5d bandwidths are in reasonable agreement with those of conventional band structure calculations (see the review by Liu (1978)), even though the methods of potential construction are quite different. 

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