Energy derivatives, electron number

Fig. 9. Calculated relative energies (in kK) of the most important MO s (a) and spectral excitation energies derived from the electronic absorption spectrum (b) of ClFe(Et2

Table 1 Molecular parameters of the diatomic oxides and sulfides of carbon and silicon derived experimentally (force constant f and bond energy BE) and theoretically (bond distance d, charge Q, and Shared Electron Number SEN).

In particular, is it possible to determine the chemical potential (which obviously depends on how the energy responds to variations in the number of electrons) from the variation of the electron density at fixed electron number Parr and Bartolotti show that this is not possible the derivatives in Equation 19.8 are equal to an arbitrary constant and thus ill defined. One has to remove the restriction on the functional derivative to determine the chemical potential. Therefore, the fluctuations of the electron density that are used in the variational method are insufficient to determine the chemical potential. 

The effect of external field on reactivity descriptors has been of recent interest. Since the basic reactivity descriptors are derivatives of energy and electron density with respect to the number of electrons, the effect of external field on these descriptors can be understood by the perturbative analysis of energy and electron density with respect to number of electrons and external field. Such an analysis has been done by Senet [22] and Fuentealba [23]. Senet discussed perturbation of these quantities with respect to general local external potential. It can be shown that since p(r) = 8E/8vexl, Fukui function can be seen either as a derivative of chemical potential... 

FIGURE 25.1 Energy derivatives are defined by increasing the order of perturbation from 0 to 3. Left arrow represents derivative with respect to number of electrons while right arrow designates derivatives with respect to external potential. (Reprinted from Senet, P., J. Chem. Phys., 107, 2516, 1997. With permission.)... 

This chapter will be concerned with computing the three response functions discussed above—the chemical potential, the chemical hardness, and the Fukui function—as reliably as possible for a neutral molecule in the gas phase. This involves the evaluation of the derivative of the energy and electron density with respect to the number of electrons. 

The application of ab initio molecular orbital theory to suitable model systems has led to theoretical scales of substituent parameters, which may be compared with the experimental scales. Calculations (3-21G or 4-31G level) of energies or electron populations were made by Marriott and Topsom in 1984164. The results are well correlated with op (i.e. 07) for a small number of substituents whose op values on the various experimental scales (gas phase, non-polar solvents, polar solvents) are concordant. The nitro group is considered to be one of these, with values 0.65 in the gas phase, 0.65 in non-polar solvents and 0.67 in polar solvents. The regression equations are the basis of theoretical op values for about fifty substituents. The nitro group is well behaved and the derived theoretical value of op is 0.66. 

The small number of fundamental mass spectrometric studies on Ge, Sn and Pb derivatives also accounts for our poor knowledge of their thermochemistry. Heats of formation, ionization energies, bond energies and electron affinities of even simple Ge, Sn and Pb species are still scarce and subject to considerable uncertainty, as illustrated in the most recent NIST database5. 

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