Atom-centered charges

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. 

The fiuid-phase simulation approach with the longest tradition is the simulation of large numbers of the molecules in boxes with artificial periodic boundary conditions. Since quantum chemical calculations typically are unable to treat systems of the required size, the interactions of the molecules have to be represented by classical force fields as a prerequisite for such simulations. Such force fields have analytical expressions for all forces and energies, which depend on the distances, partial charges and types of atoms. Due to the overwhelming importance of the solvent water, an enormous amount of research effort has been spent in the development of good force field representations for water. Many of these water representations have additional interaction sites on the bonds, because the representation by atom-centered charges turned out to be insufficient. Unfortunately it is impossible to spend comparable parameterization work for every other solvent and... 

To make an accurate FEP calculation, a good description of the system is required. This means that the parameters for the chosen force field must reproduce the dynamic behaviour of both species correctly. A realistic description of the environment, e.g. size of water box, and the treatment of the solute-solvent interaction energy is also required. The majority of the parameters can usually be taken from the standard atom types of a force field. The electrostatic description of the species at both ends of the perturbation is, however, the key to a good simulation of many systems. This is also the part that usually requires tailoring to the system of interest. Most force fields require atom centered charges obtained by fitting to the molecular electrostatic potential (MEP), usually over the van der Waals surface. Most authors in the studies discussed above used RHF/6-31G or higher methods to obtain the MEP. 

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). 

What are the most important weaknesses in the above-described parameterizational approach and the use of Equation (4.1) In our opinion, the main ones are the use of an effective two-body potential and the use of only atom-centered charges. 

Bayly Cl, Cieplak P, Cornell WD, Kollman PA. A well-behaved electrostatic potential based method using charge restraints for determining atom-centered charges the RESP model. J Phys Chem 1993 97 10269-10280. 

We mention the following for nonbonding terms. We assume that, even in the H-ras complexes, we can use the values of L-J parameters of the Mg + in water. For Coulomb terms, we use atom-centered charges calculated in the subsystem. 

However, perhaps surprisingly, the quantum mechanical electrostatic energy at this same configuration is attractive (by a few kcal mor ). While this is impossible to rationalize using any picture based on atom-centered charges, it is a natural consequence of the... 

The most fundamental level of modeling of any chemical system employs quantum mechanics. Quantum mechanical (QM) treatments are required to understand many important chemical and biological properties of nucleic acids. Moreover, empirical force-field methods, employed to study the conformations of polynucleotides, rely on quantum calculations to obtain crucial parameters that are difficult to measure experimentally, such as atom-centered charges for calculating electrostatic interactions. The obtain a description of a chemical system using QM one solves the time-independent Schrodinger equation with or without the use of empirical parameters. 

The electrostatic contribution (G/aq)) is modeled by the generalized Bom approximation [49] with atom-centered charges and with the effects of dielectric descreening by other parts of the solute calculated from a conformationally sensitive solute shape molecular model [50-53] based on overlapping atomic spheres. It leads to the following equation ... 

Thus, when evaluating the effective electrostatic term between a pair of atoms across the docking interface, a constant value of 1.5 A is added to the distance separating both nuclei. This modified Coulombic term is evaluated for every pair of atom-centered charges (a 10 A cutoff is used through this work) across the molecular interface. 

A routine way to obtain atom-centered charge distributions is provided by the Mulliken population analysis, available in most ab initio and semiempirical quantum chemistry packages. In this approach, the net charge borne by atom i, of a given molecule, takes the form ... 

The q are atomic-centered charges that are computed in some reasonable manner, such as from a Mulliken population analysis [8-10,28], Stockholder analysis [30], fitting the electrostatic potential [30], or numerical integration [24,25], The term q(N) refers to the atomic charges computed for the original, iV-electron system q(N + 1) to charges computed for the system with an additional electron and q(N- 1) to an electron deficient system. 

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