Energy level density

Forst W 1971 Methods for calculating energy-level densities Chem. Rev. 71 339-56... 

The energy level density is not important in determining the magnitude of the isotope effect at high pressure. At the low pressure limit, again for thermal activation,... 

This density of states is probably a minimum at the bottom of the conduction band and increases to a maximum in the center of the band. When x in Na WO is small, optical excitation would be to the bottom of the conduction band, where the energy level density is small. Any finite number of transitions would necessitate use of several adjacent levels, which would be significantly spread out on an energy scale. When x in Na WOs approaches unity, the band is well populated and the Fermi energy is in a region where there are many states of almost identical energy. Any finite number of transitions would require a smaller spread between the adjacent levels, and hence the optical absorption curve would be narrower. 

Franck-Condon factors, rather than energy-level density, are primarily responsible for the variation in nonradiative rates. 

The photodynamics of linked systems are thus a sensitive function of their structure, and the excess energy dependence of the electron transfer depends on the details of the intramolecular dynamics. IVR and electron transfer are two important processes that may compete with each other or, conversely, operate in harmony. One way to check the role of IVR without significantly changing the electronic structure of the molecule is by isotopic substitution. The main change is in the vibrational energy-level density. Itoh and co-workers [31] applied this method to the 9-An-w-DMA system mentioned above. It was found that the Si vibrational energy thresholds for formation of the exciplex were considerably smaller in the deuterated molecules than those for the respective protonated molecules. This result is consistent with the assumption that the transition from the locally excited state (the one is initially excited) to the exciplex state, is aided by an increase in the energy level... 

The energy level density may be replaced by its classical limit for most complexes (see, however, the comments of Section IV.G when H atoms are present)... 

Figure 7. Energy level density-of-states diagram of the interaction of the CO frontier orbitals 5cr and 2n with a transition metal surface. The arrows indieate the donation of charge from the 5a and the baek donation of charge into the 27t. The effect of the electrode potential is to shift the metal energy levels up with respect to the adsorbate and the solution as the potential becomes more negative. Reprinted with permission from M. T. Koper et al, J. Chem. Phys., 113, (2000) 4392. Copyright 2000, American Institute of Physics...

The high reflectivity of metals is also due to the free electrons. When light photons strike the metal surface, those electrons near to the Fermi surface can absorb the photons, as plenty of empty energy states lie nearby. However, the electrons can just as easily fall back to the lower levels originally occupied, and the photons are re-emitted. A detailed explanation of reflectivity of a metal requires knowledge of the exact shape of the Fermi surface and the number of energy levels (density of states) at the Fermi surface. 

The generalized representation of molecular excitations leads to a convenient and comprehensive treatment of all the various cases of interest, ranging from the small to the large molecular limits. This is shown in Section II,E,3, where the typical dynamical modes are analyzed for excited molecules with various combinations of energy level densities, decay widths, and interstate coupling strengths. The general results hence obtained will form the basis for the discussion, in Section III, of specific examples for the time-dependent behavior of excited molecular systems. 

The absorption spectra show a clear picture of energy levels, density of states and allowed transitions in the materials. In case of nanocrystallites, the electrons, holes and excitons have limited space to move and also limited energy states. Thus, their energy spectram is quantized. As the size of crystal is decreased below Bohr exciton size, the electronic states are descretized and result in widening of band gap and increase the oscillator strength. The phenomena of radiation absorption in a material is considered to be due to inner shell c, valence band e", free carriers and electron bound to localized... 

Alternatively, analytical expressions for the energy-level densities can be obtained by inverse Laplace transformation of the corresponding partition function. This works well for the rotational degrees of freedom. For example, for a single rotor having a symmetry number equal to a, one has simply (except at very low energies) ... 

However, for a collection of oscillators, the set of energy levels is not dense enough and the energy-level density has to be numerically calculated by the steepest-descent method implemented by Forst. Nevertheless, an approximate closed-form expression involving an empirical correction for the effect of the zero-point vibrational energy has been developed by Whitten and Rabinovitch. For a system of n oscillators having frequencies one has ... 

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