Atom-centered point charges

Atom-Centered Point Charges. In the Mulliken population analysis, all the one-center charge on an atom is assigned to that atom, whereas the two-center charge is divided equally between the two atoms in the... 

Kollman suggested that the electron density could be partitioned into a set of monopole charges based on the electrostatic potential. At the same time, Momany showed that a set of monopole charges could be fit to the electrostatic potential. Atom-centered point charges that best fit the overall MEP were determined by iterative minimization of the following function ... 

In molecular mechanics, the calculation of electrostatic interactions most often is based on the Coulomb potential energy function (Eq. [15]) using atom-centered point charges q. A few force fields use bond dipoles (jl and the electrostatic interactions are then calculated using the Jeans formula (Eq. [16]).i... 

The solute charge distribution can be represented by atom centered point charges or as multipole expansions. Of course, if the solute is treated quantum mechanically the charge distribution can be obtained directly from its wave function. Depending on the solvation model, the electrostatic potential derived from the wave function is fitted to atomic charges or multipoles that are then used to construct the solvent reaction field. 

A molecule s electronic distribution is perhaps the most fundamental property that must be reproduced by an electronic structure method. An overview of how to compute molecular electrostatic potentials and their influence on chemical reactivity has been presented by Politzer and Murray. Without an accurate electronic structure, no other property is likely to be accurately described by a quantum mechanical model. It is sometimes unclear just how to determine the accuracy of a theoretical method, but one way is to compare calculated and experimental dipole moments. From good electronic distributions, one can extract atom-centered point charges for use in molecular mechanical applications. 

The reaUstic character of simulations and the accuracy of the results depend largely upon the potential energy model used. Here, the carbon dioxide molecule is modeled as Lennard-Jones interaction sites on the atoms plus point charges to account for the quadrupole (three center LJ model). The interactions are cut (but not shifted) at 2.0 nm. Because of this relatively large cutoff and the confinement of the molecules in the micropores, no long range corrections have been employed. 

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

An important difference between the BO and non-BO internal Hamiltonians is that the former describes only the motion of electrons in the stationary field of nuclei positioned in fixed points in space (represented by point charges) while the latter describes the coupled motion of both nuclei and electrons. In the conventional molecular BO calculations, one typically uses atom-centered basis functions (in most calculations one-electron atomic orbitals) to expand the electronic wave function. The fermionic nature of the electrons dictates that such a function has to be antisymmetric with respect to the permutation of the labels of the electrons. In some high-precision BO calculations the wave function is expanded in terms of basis functions that explicitly depend on the interelectronic distances (so-called explicitly correlated functions). Such... 

Alkane carbon atoms satisfy the charge-NMR shift correlation [Eq. (6.8)]. With the alkylamines, things could be different because of a possible extra effect due to the presence of the nitrogen atom a-carbons should perhaps be compared only among themselves, and so should the /3- and y-carbons. The S-carbons, in contrast, which are sufficiently separated from the nitrogen center, could probably be treated as if they were part of an alkane. This point has been examined as follows for the —C 2—H2—NH2 motif, focusing on the dissociation and intrinsic bond energies, Dc Cp and sc Cp, respectively. 

Another approach to providing atomic charges is to fit the value of some property which has been calculated based on the exact wavefunction with that obtained from representation of the electronic charge distribution in terms of a collection of atom-centered charges. In practice, the property that has received the most attention is the electrostatic potential, 8p. This represents the energy of interaction of a unit positive charge at some point in space, p, with the nuclei and the electrons of a molecule (see Chapter 4). 

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