Average excitation energy approximation

Alternatively, recourse may be made to the average excitation energy approximation, in which the several triplet excitation energies are replaced by an average value AE. The coupling is then given in terms of P spSm total MO bond order between the s... 

Finally, dispersion energy is obtained from an approximate London-type expression, with local static polarizabilities and average excitation energy of the monomer, evaluated using Koopman s theorem. An empirical correction factor is then applied to take into account the error in the evaluation of the average excitation energy and the approximate character of the London expression. 

E is the "average excitation energy," frequently approximated as AE, the difference in energy between ground state and the first maximum in the electronic spectra, (r 3)2po is the inverse of the mean volume of 2p orbitals on oxygen, and Qox is the charge density bond order matrix. Even though these terms may be interrelated, a number of empirical correlations between NMR chemical shifts and other data taken to represent various terms in the Karplus-Pople expression have been reported [8]. 

Figure 12 Boxes fringe visibility as a function of Bragg excitation frequency. Error bars uncertainty due to four measurements. We observe a clear double-peaked spectrum, which is finite-time broadened. Solid line double peaked Gaussian fit. The peaks are found at 139 10 Hz, near the expected Bogoliubov local density approximation average excitation energy (138 5 Hz).

Equation (10) is often simplified by replacing the excitation energies by a mean value, A , to give the Average Excitation Energy (AEE) approximation. Since overlap is neglected in the semi-empirical... 

Platzman (1967) has emphasized that most direct ionizations in molecules leave the positive ions in an excited state. Based on crude DOSD, he estimated that in water the average positive ion will have about 8 eV excitation energy. Later, the less approximate calculation of Pimblott and Mozumder (1991) reduced that figure to about 4 eV The chemical role of this excitation energy is unknown, although it may have some effect in the radiolysis of highly concentrated solutions. 

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