Electronic energy levels partition function

In most cases, excited electronic energy levels lie high above the ground-state energy relative to ksT, and the population in the upper levels is negligibly small. In these cases the electronic partition function reduces to one term ... 

In some instances, multiple electronic states of a molecule are possible, and an electronic partition function must be evaluated. One would use an explicit summation over electronic energy levels, as in Eq. 8.50. No simple general theory is available to account for all the manifold of electronic energy states. 

Thus, even in this very high temperature example, excited electronic energy levels make a negligible contribution to the electronic partition function. 

All calculations will be done for the standard pressure of 1 bar and, unless otherwise noted, at T = 298.15 K for one mole of gas. Table 8.1 lists the calculated molecular partition function, thermal energy (energy in excess of the ground-state energy), heat capacity, and entropy. The individual contributions from translation, rotation, each of the six vibrational modes, and from the first excited electronic energy level are included. 

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. 

When the total energy of a system is the sum of the energies from the different degrees of freedom, for example, translation, rotation, vibration, and electronic, then the partition function for a combination of the energy levels is the product of the partition functions for each type. Thus,... 

Finally, the electronic partition function is considered. The zero of energy is chosen as the electronic ground-state energy. The spacings between the electronic energy levels are, normally, large and only the first term in the partition function will make a significant contribution that is,... 

Since a molecule has translational, rotational, vibrational and electronic energy levels it is possible to define q for all four cases. Vibrational energy e is given hy e = hv, where h is Planck s constant, and V the frequency of vibration. The vibrational partition function q is then obtained by taking the sum over all tihe vibrational energy levels defined by the vibrational quantum number v. This is... 

The Information on electronic energy levels and quantum weights given by Moore (4) Is Incomplete because many theoretically predicted levels have not been observed. Our calculations Indicate that any reasonable method of filling In these missing levels and cutting off the summation In the partition function (5) has no effect on the thermodynamic functions to 6000 K. This Is a... 

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