Degeneracy of energy level

Loss of degeneracy of energy levels of molecular entities due to lower site symmetry created by a crystalhne environment this term is not synonymous with hgand field splitting. See Ligand Field Splitting Comm, on Photochem. (1988), Pure and Appl. Chem. 60, 1055. 

Harris and Bertolucci [16] illustrated the relationship between symmetry and degeneracy of energy levels with a simple and attractive example. There are three parrallelepipeds in Figure 6-2. Each of them has six stable resting positions. The potential energy of these positions depends on the height of the center of the mass above the... 

This correlation between symmetry and degeneracy of energy levels is fundamental to understanding the electronic structure of atoms and molecules. This relationship is valid not only when increasing symmetry renders the energy levels degenerate but also when energy levels are split as molecular symmetry decreases. 

Loosely speaking, we attribute to MOs a property (degeneracy) of energy levels. 

Since the roots are in general different, the degeneracy of energy levels is (partially) removed. 

The dimension of a space-group full representation (degeneracy of energy levels in a crystal) for a given k is equal to the product of the number of rays in the star k and the dimension of the point group irreducible representation (ordinary or projective). In particular, for the space group under consideration at the X point the dimensions of full representations are 6 and at the W point - 12. As to each of the... 

Electronic spectra rarely give direct information about molecular structures. Because a typical molecule has many electrons in different energy levels, together with a large number of unoccupied levels, and excitation can occur from each of the occupied levels to many or all of the unoccupied levels, the spectra are in principle complicated, so that assignment can sometimes be difficult or impossible. But symmetry, degeneracy of energy levels and selection rules aU simplify matters, and if we understand all of these, then we will usually be able to extract very useful information. 

In eq 13, gk is the degeneracy of energy level k and the summation is over all molecular orbitals k. It is convenient to tabulate orbital energies as Ek = Ek — a, such that... 

There is no degeneracy of energy levels in harmonic oscillators (g,- = 1). The partition function can then be written as shown in Eq. (2). Equation... 

Figure 28.15 The Degeneracy of Energy Levels in the Free-Electron Theory. From N. B. Hannay, Solid-State Chemistry, Prentice-Hall, Englewood Cliffs, NJ, 1967, p. 26.

The energy difference associated with excitation of the electronic structure of atoms and molecules is typically 20,000 cm i and above. Assuming no degeneracy of energy levels, find the ratio of the population of an excited state at 20,000 cm" to the population of the ground state at 300 K. Next, find the temperature at which this ratio becomes 0.1. 

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