Electron Localization and the Second Moment of the Exchange Hole

The localization tensor, which is a global measure of the itinerant character of the electrons, has been defined by Resta as the second cumulant moment of the position operator per electron. It seems to be a meaningful parameter not only for solids but also for finite molecular systems. In the independent-particle limit, this quantity can be interpreted as the density-weighted average of the second moment of the exchange hole. After examining several possible local measures based on the moment analysis of the exchange hole, it turns out that the density weighted squared exchange hole dipole moment might be a useful local indicator of electron localization. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109:2340-2347, 2009