Monopoles, permanent

Weakly polar interactions in proteins and protein-ligand complexes are frequently phenomenologically analyzed and classified in terms of the interacting partners (36). This especially includes interactions with x-sys-tems, such as the NH-T, OH-T, or CH-ir interaction (37, 38), aromatic-aromatic interactions (parallel t-t stacking versus edge-to-face interaction), and the cation-T interaction (39). All of these can mostly be rationalized in terms of electrostatic interactions outlined above that is, they involve interactions between monopoles, dipoles, and quadrupoles (permanent and induced). A more distinct character can be attributed to metal complex-ation, which can play a significant role in individual cases of protein-ligand interactions, as for example in metalloenzymes (2,40, 41). 

Furthermore, the actual Coulomb forces are also important. If the molecules have polar substituents or a permanent dipole moment, or if they are electrically charged in a heteropolar fashion, i.e. the crystals are salts, then the intermolecular interactions are naturally also determined by the static monopole, dipole, and Coulomb forces with their long range. This of course also influences the crystal structures... 

The permanent group monopoles are treated in the same manner with the exception that they need not be zero for the entire group. 

Interactions become shorter-ranged and weaker as higher multipole moments become involved. When a monopole interacts with a monopole. Coulomb s law says u r) oc r But when a monopole interacts with a distant dipole, coulombic interactions lead to u r) oc r (see Equation (21.26)). Continuing up the multipole series, two permanent dipoles that are far apart interact as u(r) oc r Such interactions can be either attractive or repulsive, depending on the orientations of the dipoles. Table 24.2 gives typical energies of some covalent bonds, and Table 24.3 compares covalent to noncovalent bond strengths. 

The electrostatic component is generally the dominant attractive contribution in the case of polar molecules, i.e., systems with nonspherical charge distributions, usually manifested as appreciable permanent dipole and/or quadrupole moments. The classical Coulomb interaction between the respective charge distributions of the interacting molecules is conveniently formulated in terms multipole expansions that consist of dipole/dipole, dipole/quadrupole, quadrupole/quadrupole, etc. type terms, with distance (R) dependences R, R, R, ... (In the case of charged systems the monopole (net charge) terms must of course be also included in the expansion, that give rise to R, ... dependent terms.)... 

The simplest situation is the interaction between particles with a permanent capillary monopole. By Equation 2.10, it means that the particles are under the action of an external vertical force the best-known example is the buoyancy force due to gravity. The potential of mean force between two particles under the action of vertical buoyancy forces and respectively, is asymptotically (i.e.,... 

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