Electronic Term Values

Just as in the ground electronic state a molecule may vibrate and rotate in excited electronic states. The total term value S for a molecule with an electronic term value T,... 

The vibrational term values for any electronic state, ground or excited, can be expressed, as in Equation (6.16), by... 

If a sufficient number of vibrational term values are known in any electronic state the dissociation energy Dq can be obtained from a Birge-Sponer extrapolation, as discussed in... 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

In Figure 7.25 are shown stacks of rotational levels associated with two electronic states between which a transition is allowed by the -F -F and, if it is a homonuclear diatomic, g u selection rules of Equations (7.70) and (7.71). The sets of levels would be similar if both were states or if the upper state were g and the lower state u The rotational term values for any X state are given by the expression encountered first in Equation (5.23), namely... 

Screening Constants for Many-electron Atoms. The Calculation and Interpretation of X-ray Term Values, and the Calculation of Atomic Scattering... 

The screening constants for neutral atoms are constant so long as no additional screening electrons are introduced, as is strikingly shown by the energy screening constant for X-ray term values. But this con-... 

In a fluid model the correct calculation of the source terms of electron impact collisions (e.g. ionization) is important. These source terms depend on the EEDF. In the 2D model described here, the source terms as well as the electron transport coefficients are related to the average electron energy and the composition of the gas by first calculating the EEDF for a number of values of the electric field (by solving the Boltzmann equation in the two-term approximation) and constructing a lookup table. 

Pauling L. and Sherman J. (1932). Screening constants for many-electrons atoms The calculation and interpretation of X-ray term values and the calculation of atomic scattering factors. Zeit. Krist., 81 1-29. 

A point that initially surprises some is that many of the off-diagonal terms in Eq. (5.89) are complex-valued, even when the r-space basis functions and expansion coefficients are all real. However, the momentum density is always real because each off-diagonal ij term in Eq. (5.89) is the complex conjugate of the corresponding ji term. The electron density can be written as... 

Although, from a purely chemical point of view, learning how to create these complicated supramolecular structures has its own value, there are plenty of more practical reasons to investigate this chemistry. In the short term, these include catalysis and sensor applications, and in the long term, molecular electronics and molecular machines. With perhaps the exception of catalysis, all these applications will require some sort of signal transduction to allow for communication with the supramolecular device. This, of course, is one of the main reasons that electrochemistry is useful for supramolecular chemistry. Electron transfer provides a well-understood and very sensitive method to both communicate with supramolecular assemblies and control their structure.8... 

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