Energy-level separation

The frequency of the electromagnetic radiation that can be absorbed by the nuclear system is easily calculated by equating the energy of a photon and the energy level separation ... 

We will now do the same for a system with an infinite number of equidistant energy levels, separated by Ae. For such a system the partition function becomes the following mathematical series with a well-known sum ... 

We thus obtain a set of energy levels separated by an energy gap AE = hv and bounded by the potential function 3.2 (figure 3.1). 

The charge transfer, - Qde, which accompanies a given atomic energy-level separation, AE, in the binary AB alloy may be obtained by filling the local densities of states up to the Fermi level as shown in Fig. 7.13. For the skew rectangular local densities of states this gives... 

The electronic partition function can be evaluated by summing over spectroscopically determined electronic states, but as the electronic energy-level separations are large, the number of molecules in excited electronic states is negligibly small at ordinary temperatures and the electronic partition function is unity and will be ignored henceforth. 

In the latter case (cou i S>2 V), the perturbation V is much smaller than the energy level separation cou j, and the maximum probability that state u can be reached is 2V2 ci / 2TC l, that is, the level u is never reached. 

Fig. 7.14. The intensity ratios of Ne-like 7D to 6C transitions as a function of energy level separation. Calculations are shown as dots, measurements are represented as asterisks...

Although the energy level separations are little affected by ligand, nevertheless they are not the same in all complexes. Careful study of the Fq separation in a number of... 

Figure 1 Potential wells for an electron trapped by polarization of solvent or ligand environment in a dinuclear complex (A- B). V = electron potential energy, r = distance along the A-B axis, (a) Ground state p(A+- B) with electron localized mainly at site B, excited state s (A - B ) with electron mainly transferred to site A. (b) The energy wells adjusted to equal depth by solvent and ligand motion. The electron is delocalized with two energy levels separated by 2Hab- (c) The reverse polarization, ground state i(A- B ), excited state -B)...

These form a sequence of equidistant energy levels separated by A = /ivg and bounded by the potential energy curve V = Vik rf, as shown in Fig. 2.26. The lowest (ground-state) level with n = 0 has an energy 0 = Vi/ivg, known as the zero-point energy. The vibrational eigenfunctions are usually interpreted in terms of probabihty density functions I i j I of the type shown in Fig. 2.26. 

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