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A critical comparison among recently proposed methods for evaluating the condensed Fukui function neglecting relaxation effects is presented. The sign of the condensed Fukui function is discussed and arguments for a positive definite condensed Fukui function are given. Our numerical calculations in two series of molecules show that: (i) the condensed Fukui function can give, in general, valuable information about the site selectivity in chemical reactions and systematization in a family of molecules. In particular, it has been shown that the selectivity towards protonation in anilines and derivatives molecules can be correctly assessed by the electrophilic Fukui function described in this paper. Within this approach non-negative values for the condensed Fukui function are obtained for the relevant protonation sites in these polyfunctional systems; and (ii) the solvent effects on the condensed Fukui function are negligible, confirming a recently presented theoretical prediction.

The electron localization function (ELF) has been separated in its sigma and pi components. The topological analysis of the new ELFsigma and ELFpi functions has been used to quantify the concept of resonance. The highest bifurcation values of these functions describe in a correct way the aromaticity of classical ring molecules and some new aromatic compounds as B6CO6, Al4(2-), and N5-. In the case of Al4(2-), an important sigma delocalization contribution has been found, which is in agreement with previous interpretation.

Some exact conditions for the extremals of the electrophilicity index, ω = μ(2)/2η (Parr, R. G.; von Szentpály, L.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922), along an arbitrary reaction coordinate, have been carefully examined. Implications within the widely used finite difference approximation for the density-functional based reactivity descriptors, their relationship with the maximum hardness principle, and the reliability of the general relationships have been tested in the framework of computational evidence for some simple systems of chemical interest.

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Higherorder response theory based on the quasienergy derivatives: The derivation of the frequency dependent polarizabilities and hyperpolarizabilities Several third derivatives of the ground-state electronic energy E with respect to the electron number N and/or the external potential v, as defined in density-functional theory, are studied. These include the first derivatives of the hardness rt. Legendre transforms of rt [N,v] are constructed and corresponding Maxwell relations derived. Various new functions and relations are found. The derivative of the hardness with respect to the electron number at constant potential r is studied numerically for atoms and positive ions, and suggested values are displayed and discussed. Recommended values of r are positive for most spherical atoms, negative otherwise. Power series expansions of E(N) are not recommended for reasons given. Simple analytical representations are recommended instead.

In this work, the average bifurcation value of the electron localization function (ELF) of both σ (ELFσ) and π (ELFπ) contributions was used to construct an aromaticity scale for chemical compounds. We have validated the scale with a series of well-known molecules and then used it to evaluate global aromaticity on aluminum based clusters, which present σ aromaticity and π antiaromaticity. The proposed scaled predicts an overall antiaromatic character for the Al4(4)(-) moiety.