Averaging, solvent motions

The SCRF models assume that solvent response to the solute is dominated by motions that are slow on the solute electronic motion time scales, i.e., Xp Telec. Thus, as explained in Section 2.1, the solvent sees the solute electrons only in an averaged way. If, in addition to the SCRF approximation, we make the usual Bom-Oppenheimer approximation for the solute, then we have xs Xelect-In this case the solute electronic motion is treated as adjusting adiabatically both to the solvent motion and to the solute nuclear motion. 

It is clear that the function U ( qint ) tmy be approximated by an expression of the form of eqn. (6). Whether a potential of Ais form, involving no explicit description of the solvent, is appropriate depends on the relative relaxation rates of the solvent motions and the macromolecular intramolecular coordinates. For the slow, conformationally most significant, glycosidic and exocyclic bond rotations of the carbohydrate it is apparent Aat averaging of solvent motions can occur easily on the time scale of these torsions. It is more ficult, however, to know how much important conformational detail is submerged by the averaging process. 

Solvent separated ion pairs will also be overall uncharged and will execute Brownian motion. They will also be enclosed in a cage of solvent molecules, but since the interactions between the ions will be considerably smaller than those between ions in contact, they will separate and escape from the cage much sooner than the contact ion pairs. On the time scale of colUsions they can be considered as separating and thus not moving as a single entity. The translational Brownian motion could then be perturbed by an external field, so that, on average, the motion of a cation could be in the direction of the external field and so be able to conduct the current, and if the ion is an anion it will move in the opposite direction. 

Structure determination in the context of this chapter means the determination of the atomic arrangements in materials in the crystalline state. There are a number of aspects to structural analyses. They may be used to identify substances since they can be performed without previous knowledge of chemical composition. It is possible to determine from structural analyses the connectedness, conformation, configuration (or absolute configuration under special experimental circumstances), packing, solvent interactions, and average thermal motion associated with the substances of interest. With careful experimentation in properly chosen cases, electron density distributions can also be evaluated. 

As it was mentioned in Section 9.4.1, 3D structures generated by DG have to be optimized. For this purpose, MD is a well-suited tool. In addition, MD structure calculations can also be performed if no coarse structural model exists. In both cases, pairwise atom distances obtained from NMR measurements are directly used in the MD computations in order to restrain the degrees of motional freedom of defined atoms (rMD Section 9.4.2.4). To make sure that a calculated molecular conformation is rehable, the time-averaged 3D structure must be stable in a free MD run (fMD Sechon 9.4.2.5J where the distance restraints are removed and the molecule is surrounded by expMcit solvent which was also used in the NMR measurement Before both procedures are described in detail the general preparation of an MD run (Section 9.4.2.1), simulations in vacuo (Section 9.4.2.2) and the handling of distance restraints in a MD calculation (Section 9.4.2.3) are treated. Finally, a short overview of the SA technique as a special M D method is given in Sechon 9.4.2.6. 

The equations of motion (75) can also be solved for polymers in good solvents. Averaging the Oseen tensor over the equilibrium segment distribution then gives = l/ n — m Y t 1 = p3v/rz and Dz kBT/r sNY are obtained for the relaxation times and the diffusion constant. The same relations as (80) and (82) follow as a function of the end-to-end distance with slightly altered numerical factors. In the same way, a solution of equations of motion (75), without any orientational averaging of the hydrodynamic field, merely leads to slightly modified numerical factors [35], In conclusion, Table 4 summarizes the essential assertions for the Zimm and Rouse model and compares them. 

When an ionic compound is dissolved in a solvent, the crystal lattice is broken apart. As the ions separate, they become strongly attached to solvent molecules by ion-dipole forces. The number of water molecules surrounding an ion is known as its hydration number. However, the water molecules clustered around an ion constitute a shell that is referred to as the primary solvation sphere. The water molecules are in motion and are also attracted to the bulk solvent that surrounds the cluster. Because of this, solvent molecules move into and out of the solvation sphere, giving a hydration number that does not always have a fixed value. Therefore, it is customary to speak of the average hydration number for an ion. 

For gas-phase molecules the assumption of electronic adiabaticity leads to the usual Bom-Oppenheimer approximation, in which the electronic wave function is optimized for fixed nuclei. For solutes, the situation is more complicated because there are two types of heavy-body motion, the solute nuclear coordinates, which are treated mechanically, and the solvent, which is treated statistically. The SCRF procedures correspond to optimizing the electronic wave function in the presence of fixed solute nuclei and for a statistical distribution of solvent coordinates, which in turn are in equilibrium with the average electronic structure. The treatment of the solvent as a dielectric material by the laws of classical electrostatics and the treatment of the electronic charge distribution of the solute by the square of its wave function correctly embodies the result of... 

---