A new general-purpose reactivity indicator is derived. Unlike existing indicators, this indicator can describe the reactivity of molecules that lie between the electrostatic (or charge) control and electron-transfer (or frontier-orbital) control paradigms. Depending on the parameters in the indicator, it describes electrostatic control (where the electrostatic potential is the appropriate indicator), electron-transfer control (where the Fukui function's potential is the appropriate indicator), and intermediate cases (where linear combinations of the electrostatic potential and the Fukui function's potential are appropriate indicators). Our analysis gives some insight into the origins of the local hard/soft-acid/base principle. The "minimum Fukui function" rule for hard reagents also emerges naturally from our analysis: if (1) a reaction is strongly electrostatically controlled and (2) there are two sites that are equally favorable from an electrostatic standpoint, then the most reactive of the electrostatically equivalent sites is the site with the smallest Fukui function. An analogous electrostatic potential rule for soft reagents is also introduced: if (1) a reaction is strongly electron-transfer-controlled and (2) there are two sites where the Fukui function's potential are equivalent, then the most reactive of the Fukui-equivalent sites will be the one with greatest electrostatic potential (for electrophilic attack on a nucleophile) or smallest electrostatic potential (for nucleophilic attack on an electrophile).
To verify whether the maximum or the minimum Fukui function site is better for protonation reactions or an
altogether different local reactivity descriptor, viz., the charge is necessary, we calculate the Fukui functions
(using a finite-difference approximation as well as a frozen-core approximation) and charges (Mulliken,
Hirshfeld, and natural population analysis schemes) of several hydroxylamine derivatives, their sulfur-containing
variants, and amino acids using B3LYP/6-311G(d,p) technique. While the Fukui functions provide the wrong
selectivity criterion for hard−hard interactions, the charges are found to be more reliable, vindicating Klopman's
idea. It is transparent from the present results that the hard−hard interactions are better explained in terms of
charges, whereas the Fukui functions can properly account for soft−soft interactions known to be frontier-controlled.
This paper examines cases where frontier molecular orbital theory is known to fail, specifically electrophilic aromatic substitution reactions on isoquinoline and borazarophenanthrenes. While we are able to explain the experimental regioselectivity preferences for isoquinoline without too much difficulty, describing the regioselectivity of the borazarophenanthrenes is much more challenging. This is attributed to the fact that these molecules lie between the electrostatic (or charge) control and electron-transfer (or frontier-orbital) control paradigms. These molecules can, however, be described using the general-purpose reactivity indicator introduced in the first paper of this series. The variation of the general-purpose reactivity indicator with respect to the parameters is readily summed up using what we term "reactivity transition tables", which provide a compact summary of which products form under different reaction conditions. For the otherwise problematic molecules considered here, the new reactivity indicator performs better than either the Fukui function or the electrostatic potential alone.
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