The DFT-based reactivity descriptors “local softness” and “local hardness” are used as reactivity indices to predict the reactivity sequences (both intramolecular and intermolecular) of carbonyl compounds toward nucleophilic attack on them. The finite difference approximation is used to calculate local softness, whereas local hardness is approximated by −V el/2N, where V el is the electronic part of the molecular electrostatic potential. Both aldehydes and ketones, aliphatic and aromatic, have been selected as systems. Critical cases, e.g., C6H5CHCHCHO, CH3CHCHCHO, and CH2CHCHO, where a CC double bond is in conjugation with the CO group, are also considered. Two new reactivity descriptors are proposed, “relative electrophilicity” (s k +/s k -) and “relative nucleophilicity” (s k -/s k +), which will help to locate the preferable reactive sites. Our results show that local hardness can be used as a guiding parameter when constructing intermolecular reactivity sequences.

In this paper we have analyzed the factors which cause Fukui function (FF) indices to be negative, when evaluated in condensed form through crude finite difference approximation. Inability to take care of the relaxation effect and improper charge partitioning techniques have been cited to be the probable reasons. For the first time, we have shown that the “stockholders” charge partitioning technique (i.e., Hirshfeld’s analysis) produces non-negative FF values which, when evaluated through other kinds of charge partitioning techniques, become negative in some cases. Advantages of “stockholders” charge partitioning over other kinds of partitioning techniques are also discussed, particularly in case of evaluation of condensed FF.

Two recent papers [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000); 123, 2007 (2001)] have shown how variational principles for the energy may be used to derive and elucidate the significance of the chemical reactivity indices of density-functional theory. Here, similar ideas are applied, yielding a systematic, mathematically rigorous, and physically sound approach to condensed reactivity indices. First, we use the variational principle for the energy to derive an expression for the condensed Fukui function index in terms of the condensed hardness kernel. Next, we address an important open problem pertaining to condensed reactivity indices: when (if ever) is the condensed Fukui function for an atom in a molecule negative? In particular, our analysis confirms the observation, hitherto based only on computational evidence, that the Hirshfeld partitioning is optimal for obtaining non-negative Fukui functions. We also hypothesize that the strong diagonal dominance of the condensed hardness kernel is sufficient for the non-negativity of the Fukui function. Errors in the partitioning of molecules into atoms and inadequate treatment of correlation are pinpointed as the most likely causes of negative condensed Fukui functions. We conclude by noting that the condensed Fukui functions are, in some respects, more appropriate indicators of a molecular site’s reactivity than the Fukui function itself.

In this paper we address the long standing problem regarding the site for gas-phase protonation in aniline and substituted anilines. Our study reveals that DFT-based reactivity descriptors can reproduce the experimentally observed preferable protonation sites. However, it is found that the quantity / , termed “relative nucleophilicity” and a measure of “local polarizability”, produces more reliable results than the local softness, . The problem which sometimes arises in taking / as the reactivity descriptor is also discussed.