Distance dependence charge-dipole interactions

The distance dependence of the charge-dipole interaction is given by 1/r2 and is spatially anisotropic. 

Dipole-dipole interactions are still weaker and of shorter range than the charge-dipole interaction. The strength of the interaction depends on the distance (r) between the centers of the two dipoles, their dipole moments Hi and h2. and the angles i and 2 between each electronic dipole moment and the vector r, and is given by... 

The key differences between ionic and dipolar interactions relate to their dependence on distance and orientation. For charge-dipole interactions, the strength of the interaction depends inversely on the square of the distance, while for dipole-dipole interactions it reduces with the cube of the distance separating the dipoles. 

In Eq. (8-7), which is Coulomb s law, the charges are to be aeeompanied with their signs. Because of the high-order reciprocal dependence on distance in Eqs. (8-11) and (8-12), these quadrupolar interactions are usually negligible. For uncharged polar molecules the dipole-dipole interaction of Eq. (8-10), which has the dependence, is the most important contributor to the electrostatie potential energy. 

From Table 2.5 it is clearly seen that becomes small (less than 0.001 kcal/ mol) beyond a distance of 10 A. The electrostatic interaction reaches the same level of importance at a distance of 30 A. The Table also shows that the interaction between point charges behaves much like a dipole-dipole interaction, i.e. an R dependence. However, the interaction between net charges is very long range even at 100 A separation, there is a 0.34kcal/mol energy contribution. The cut-off distance corresponding to a contribution of 0.001 kcal/mol is of the order of 3000 A ... 

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... 

One of the more profound manifestations of quantum mechanics is that this curve does not accurately describe reality. Instead, because the motions of electrons are correlated (more properly, the electronic wave functions are correlated), the two atoms simultaneously develop electrical moments that are oriented so as to be mutually attractive. The force associated with tills interaction is referred to variously as dispersion , the London force, or the attractive van der Waals force. In the absence of a permanent charge, the strongest such interaction is a dipole-dipole interaction, usually referred to as an induced dipole-induced dipole interaction, since the moments in question are not permanent. Such an interaction has an inverse sixtli power dependence on the distance between the two atoms. Thus, the potential energy becomes increasingly negative as the two noble gas atoms approach one another from infinity. 

Dipole-dipole interaction — refers to intermolecular or intramolecular interaction between molecules or groups having a permanent - dipole moment, ft. The potential energy of the interaction, V, is directly proportional to dipole moments of both dipoles and depends on relative orientation of the - dipoles. For instance, this energy is inversely proportional to the third power of the distance, r, for linearly arranged stationary dipoles of the negative-to-positive directed charges. 

Another derivation of the reiative permittivity dependence of in k has been made by Amis [12, 21, 244] using a Coulomb energy approach for the ion-dipole interaction. Considering the mutual potential energy between an ion A of charge za e and a dipole B of dipole moment at a distance tab leads eventually to Eq. (5-95) ... 

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