Atomic charges, dielectric constant electrostatic energies

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

Predicted ionic radii r, experimental ionic radii n, central charge Q and RF potential Ok in atomic units. Electrostatic free energies of solvation, 8pel, in kcal/mol. Experimental values from reference [16]. Electrostatic potential for anions from reference [19]. For all calculations done, the effective dielectric constant reported in [16] was used. 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

The work done in placing a charged sphere in a medium of dielectric constant s was addressed by Bom (1920) with respect to the hydration energies of ions in solution. In the case of crystals, similar treatments can be applied when explicit provision is made for the electrostatic forces exerted by atoms adjacent to the defect (Mott and Littleton, 1938). For illustration and to gain a qualitative... 

The simplest continuum solvent model simply adju.sts the dielectric constant to equal the medium dielectric. An approximation widely used in MD simulations is known as the distance-dependent dielectric constant. In this approach, the dielectric con.stant is set equal to the distance r,/. as shown in Equation 28-38. The electrostatic energy is now proportional to Mr rather than l/r. When this was first proposed, the idea was to help reduce CPU lime. The rationalization is that the chtirges on two nonbonded atoms in a macromolecule are separated hy the protein, which should reduce the interaction terms. Thus, the interaction energy should fall off faster than l/r because the charges arc masked. 

Here the first term equals the electrostatic interaction (q and are the net atomic charges of the interacting atoms of the receptor r and the substrate s, respectively, D is the interatomic distance between them, and e is the conventional dielectric constant of the medium). The second term stands for covalent contribution and ,, are the MO energies of occupied and unoccupied MO, respectively. c and are AO coefficients of the atoms r and s in the appropriate MO, P, is the resonance integral. 

The strength of any electrostatic interaction can be calculated from equation (4), where and qj are two charges separated by a distance Vjj in a medium of dielectric constant D. This equation applies equally to ionic interactions, where the charges qi and qj are integer values, or to polar interactions, in which the totd energy is sununed over the contributions calculated from the partial charges on all the individual atoms. 

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