Polarization corrections to the interaction energy

The electrostatic potential V(r) is the first order contribution to the interaction energy. The second order contribution P(r), which is commonly referred to as a polarization correction to the electrostatic potential, is defined within the imcoupled Hartree-Fock perturbation theory by [41] 

The i are the orbital energies and the c i are the molecular orbital expansion coefficients in terms of the atomic orbital basis set Xp- Contributions from terms greater than second order are generally small and can for most chemical applications be neglected [41, 42]. Only a limited number of applications of P(r) for analysis of intermolecular interactions have appeared in the literature. The most common approach of analysis has been to calculate a total interaction index, a polarization-corrected electrostatic potential , defined by 

6 Charge Transfer and the Average Local Ionization Energy 

A number of studies have shown thatl(r) calculated on molecular surfaces defined by contours of constant electron density provide an effective tool for analysis of reactivity towards electrophiles [44-49]. The positions on a molecular surface where I(r) has its lowest values, the local surface minima (Is.min), are viewed as the locations of the least tightly bound electrons, and thus as the sites most likely to interact with an electrophile. However, in contrast to the electrostatic potential, I(r) reflects a molecule s ability to undergo charge transfer rather than its electrostatic interaction tendencies. The Is,min are therefore better suited than the Vmin for analyses of strong interactions that lead to the formation of covalent bonds. For example, it has been shown that the Is,min of aromatic systems can be used to identify and rank the sites most likely to undergo electrophilic attack that leads to electrophilic aromatic substitution [44]. The Vmin are not as successful in the same type of analysis. On the other hand, Vmin are much better suited than Is,min for characterization of hydrogen-bond-accepting sites [21]. 

The average local ionization energy is the topic of another chapter in this book, and the interested reader is referred to that chapter for further information about this property. In this chapter we will focus on how I(r) can complement V(r) in quantitative analyses of intermolecular interactions. 

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