Energy Levels in Solids

It is evident that in representing energy levels in solids extensive use is made of momentum (reciprocal- or k-) space rather than the real-space representations which theoretical chemists frequently employ for the description of isolated molecules. One of the obvious advantages in so doing is that optical and spectroscopic properties are concisely illustrated and the various symmetry-allowed transitions clearly identified with reference to such E/k plots. 

One factor affecting the dielectric strength is the electronic structure of the polymer, and in particular its band gap. In quantum mechanics [29], each electron in a molecule can only occupy one of a discrete set of allowed energy levels. In solids, the overlaps between different repeating units of the material (for example, the repeat units in quasi-one-dimensional systems such as polymer chains [29-31]) cause these discrete energy levels to broaden into bands. The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. (In terms which are equivalent but more familiar to chemists, the band gap is... 

Fio. 10. Gibbs free energy profiles for the formation of tyrosyl adenylate and pyrophosphate, as defined in Eq. (2), by wild-type (energy levels in dashed lines) and mutant (energy levels in solid lines) tyrosyl-tRNA synthetases, using standard states of 1 W for tyrosine, ATP, and pyrophosphate. [Reprinted with permission from Ref. (25/).]... 

It is worth noting that the binding energies (BE) of energy levels in solids are conventionally measured with respect to the Fermi level of the solid, rather than to the vacuum level. This involves a correction to the equation given above in order to aceoimt for the work function (Og) of the solid ... 

This representation is meant to be schematic. Actually, the energy levels in solids form bands of available states and are not discrete as is the case for individual atoms. 

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