Atom-centered monopoles

CM Breneman, KB Wiberg. Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density m formamide conformational analysis. J Comput Chem 11 361-373, 1990. 

Breneman, C. M. and K. B. Wiberg. 1990. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Computational Analysis. J. Comp. Chem. 11, 361. 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

The atom-centered monopole charges have been determined by fitting the quantum mechanically derived electrostatic potential in the region... 

As mentioned after Equation [24], atom-centered monopoles in principle generate the higher multipoles required to describe the electronic distribution (although, of course, a finite number n of charges can give at most n nonvanishing multipole moments), and as noted by Dillet et al., the distributed monopole term provides the vast majority of the polarization effect (albeit not all). We note this only for comparative purposes, though, since calculation of the ENP terms does not actually involve the multipole moments explicitly. 

Figure 3.12. Different approaches to localization of chaigeused in electrostatic models, (a) Atom-centered monopole (b) atom-centered dipole and (c) atom-centered quadrapole.

Although we shall not discuss the technique, it should be noted that Williams has developed a program to fit an expansion of atomic-centered monopoles, dipoles, and quadrupoles to the electrostatic potential.- ... 

The belief that electrostatic (Coulomb) interactions exhibit little directionality (i.e., that their energy hardly depends on the bond angle) is widespread. This is because the concept of net atomic charges (atom-centered monopoles) has become ingrained in chemists thinking, so that Coulomb interactions with a polar atom are believed to be necessarily isotropic and directionahty of Coulomb interactions only to be the result of secondary interactions with more distant atoms. Neither of these assumptions is correct and the reasons have been known for decades. Nonetheless, directionality in noncovalent interactions is still often attributed to covalent contributions or donor-acceptor interactions because the Coulomb interaction is believed not to be able to give rise to significant directionality. The purpose of this chapter is to discuss Coulomb interactions with special emphasis on directionality and anisotropy of the molecular electrostatic potential (MEP) [1] around atoms. 

Breneman CM, Wibeig KB (1990) Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis. J Comput Chem ll(3) 361-373. doi 10.1002/jcc.540110311 Stephan DW (2015) Frustrated Lewis pairs from concept to catdysis. Acc Chem Res 48(2) 306-316. doi 10.1021/ar500375j Uzarewicz A (1964) Rocz Chem 38 599... 

The electrostatic potential energy is computed as the sum of pairwise interactions between atom-centered monopole partial charges ... 

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