Toughness and Brittleness of Plastics by Deanin R.D., Crugnola A.M., Gould R.F. (eds.)

By Deanin R.D., Crugnola A.M., Gould R.F. (eds.)

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Voit, cond-mat/0005114. This page intentionally left blank Chapter 4 The Jellium Model For some metals the valence electrons are very delocalized and do not participate in the formation of directional bonds between nearest neighbours. This is the case for s metals like Na, K, and Cs, but less for Au and Ag, and certainly not the case for metals with 3d or 4f valence electrons. When the valence electrons are very delocalized, the precise positions of the nuclei become less important and one may, accordingly, as an approximation study the hypothetical case that the nuclei and the core electrons are smeared out to a homogeneous medium with a constant density, the so-called jellium, in which the valence electrons move.

5. Conclusions In this section, we have briefly outlined the main scenario for single-particle descriptions of the properties of quasi-one-dimensional systems. We have seen that distortions that open up a gap at the Fermi energy are very important and will ultimately change any truly one-dimensional metallic system into a semiconductor or an insulator. , a structural distortion, is the most prominent example, but modifications of this can also be found. , a half-filled band for both spin components changes into two bands, one for each spin direction, with one being completely filled and the other completely empty.

FN ð~ x1 Þ   fN ð~ x2 Þ   , ..  . 15) 24 Chapter 3. Many-Body Properties where each electron occupies one orbital. 18) that is independent of the solutions ffk ; k ¼ 1; 2; . . 16). 20) p¼1 where only the expansion coefficients cpl are optimized. 22) i¼1 n;q¼1 and O contains the overlap matrix elements Opm ¼ hwp jwm i. 3. Density-functional theory approaches 25 We have here defined h^2 ð~ x1 ; ~ x2 Þ ¼ e2 . , any electron moves in the mean field of all the others. 15). This is, however, beyond the scope of the present work, as it hardly has been applied to the systems of our interest.

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