Conceptual density-functional theory for general chemical reactions, including those that are neither charge- nor frontier-orbital-controlled. 1. Theory and derivation of a general-purpose reactivity indicator

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).