Electrostatic potential, molecular interactive reactivity

In the next chapters, one or several of those formalisms are used to describe some aspects of molecular behavior toward other molecules in terms of properties such as electrostatic potential, nonbonded interactions, behavior in solvents, reactivity and behavior during interaction with other molecules, and finally similarity on the basis of nonquantum and quantum properties. 

The symbol V is often associated with the electrical potential in the literature, but U is employed here so as not to conflict with the volume descriptor. Another aspect of chemical reactivity involves the molecular electrostatic potential (MEP). The MEP is the interaction energy between a unit point charge and the molecular charge distribution produced by the electrons and nuclei. The electrostatic potential, U r), at a point, r, is defined by Eq. [13]. 

Note added in proofs. It should be clear that this paper was not designed to offer a review of the applications of the electrostatic approximations to the chemical reactivity or molecular interaction problems. However, it may be of some interest to add a few quotations of further developments and direct applications of the electrostatic molecular potential method performed or noticed by the authors after the completion of the present paper. 

Applications of molecular electrostatic potentials to a variety of areas - chemical reactivity and biological interactions [97-105], solvation [98,106], covalent and ionic radii [107], prediction of condensed-phase physical properties [108-110], atomic and molecular energies [89,92,111] -have been reviewed elsewhere, as indicated. Our purpose here is to relate V(r) to sensitivity. 

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]. 

VB(ri) is the electrostatic potential of molecule B (often called MEP or MESP, according to the authors ). This a true molecular quantity, not depending on interactions, and it is often used to look at local details of the electrostatic interactions between molecules as required, for example, in chemical reactivity and molecular docking problems. 

Rolitzer, R Murray, J. S. 2009. The electrostatic potential as a guide to molecular interactive behavior. In Chemical Reactivity Theory A Density Functional View, edited by R. K. Chattaraj, 243-254. Boca Raton, FL CRC Riess. 

The first term in the decomposition of the supermolecular interaction energy E s has the same formal expression as the corresponding term in the perturbation theory (Eq. 5). The basic expression for the use of the electrostatic potential as an index of chemical reactivity does not depend upon the theory adopted in describing molecular interactions. 

This expression no longer depends on the total number of electrons of A and B but is only determined by the shape of the electron cloud. Carbo already proposed to replace p(r) in (30) by a function more directly representing reactivity, in casu the Molecular Electrostatic Potential [51]. As it turns out that (parts of) the MEP essentially account for the hard-hard interactions (see 3.2.2), and local softness essentially account for soft-soft interactions the substitution p(r) s(r) in (30) and (31) seems promising. The resulting index can then be written as... 

In recent years, the topological analysis of the three-dimensional scalar fields [87-95], such as electron density [55, 67, 92, 95-97], the Laplacian of the electron density [68, 92], the electron localization function (ELF) [94, 98], and molecular electrostatic potential, have been widely used to discern chemical structure and reactivity. This procedure, named quanmm chemical topology (QCT) [99] has been utilized for the study of chemical stmcture and reactivity [100-106]. Since its origins, the well-known approach of the atoms in molecules quantum theory (QTAIM), has evolved to be an invaluable tool for the chemical interpretation of quantum mechanical data, which relies on the properties of the electron density p(r) when atoms interact. Excellent reviews on QTAIM methods have been published elsewhere [69, 96, 107-109]. 

---