Conduction band width

Fig. 3.1. The location of the donor and acceptor levels relatively to the crystal energy bands. The levels of valence band are shaded to underline their occupation, the levels of conductivity band are empty. The conductivity band width Ew and the value 5E (see formula (23) in the text) are shown.

The ionization potentials (IP), electron affinities (EA), fundamental gaps (AEg)t and valence- and conduction-band widths (8EV and 8EC, respectively) of... 

Table 2 Some one-electron properties of the investigated polyacetylene models IP (ionization potential), EA (electron affinity), fundamental gap (AE0)t valence band width (8EV), and conduction band width (8Ec), respectively, obtained from calculations up to the 28th neighbouring C2H2 unit (all values in eV)...

These numbers are to be compared with experimental values of 1° = 9.0 eV and A° = +0.5 eV for NaCl. They are not the same since they differ by one-half the band widths, as Figure 5.7 shows. The valence band width is 4.1 eV for NaCl," which makes I and 7° agree. The conduction band width needed to make + and A° agree is 3.6 eV. Actually this piece of information is not readily available from experiment. 

The a. i. method seems to be the best for the overall description and de-ficiences, in our opinion, are mainly connected with the omittance of the correlation (15) the conduction band width is too large and the effective mass as well as the density of states at Ep are therefore probably accidentally close to experiment. A 3D calculation using the a. i. SCF method is for numerical reasons out of the question today, but we think that our Fock matrix elements should be used in a 3D EH type work. Nevertheless, successes of a ID model indicate that - at least as far as stability of the chain, charge distribution, the deeper valence bands and the type of the wave function at Ep are concerned -3D couplings are unimportant. 

Method, model and Ref. Conduction band width (eV) meff (me> N(Ep) states eV spin molec. Charge transfer (e) Stability... 

Typically, is near to one for Ce systems with the bare f-level well below Ep. Note that the Anderson width A is much smaller than that conduction-band width, so that N (Ep) is indeed large when compared with the bare conduction-band DOS. On the other hand, it should be clear that singlet formation via an indirect exchange coupling cannot transfer much spectral weight from the bare local level up to Ep. Thus, a narrow resonance near the Fermi level of maximum height (jrAY and width k Tp < A arises. It should be emphasized that the local DOS considered here is not the quasiparticle DOS that is used in Fermi-liquid theory to express thermodynamic quantities via free-particle for-... 

Fig. 23. Calculated 4f contribution to the EDC of o-Ce for different values of the hybridization matrix element, V. The bare 4f level was placed at a binding energy of 2.5 eV, the f-f repulsive interaction, V, was SeV, and the elliptical conduction band width was 6eV with p at its center. The calculated spectra were convolved with a Lorentzian of full width at half maximum of 0.5 eV to simulate experimental broadening. (After Gunnarsson and Schonhammer 1985a,b.)...

It can be seen from Table 2.6 that the physically most important valence and conduction bands in the later ab initio calculations are much broader (0.435-0.789 and 0.245-0.820 eV, respectively) than those obtained by application of different semiempirical crystal-orbital methods. With the simple PPP-CO approximation, the corresponding values for the highest filled bands are 0.218-0.299 eV and those for the conduction band are about 0.109 eV. Energy-band-structure calculations for the base stacks taking into account the effect of the other valence electrons with the aid of the CNDO/2 CO method give again broader bands (valence bandwidths of 0.136-0.490 eV and conduction band-widths of 0.109-0.245 eV), while the MINDO/2 CO results indicate somewhat less-broad bands (valence bandwidths of 0.027-0.299 eV and conduction bandwidths of 0.027-0.163 eV). For futher details on the semiempirical crystal-orbital calculations see also Chapter 3. 

The Link between Conduction Band Width and Oxygen... 

Since the integral equation (52) is not separable, it ought to be solved numerically. An approximate solution is found by a decoupling procedure, valid Avhenever the Coulomb interaction strength is greater than the occupied conduction band width,... 

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