Solvation potential theories

VIII. Solvation Potentials and Self-Consistent PRISM 1. Solvation Potential Theories... 

Presently, only the molecular dynamics approach suffers from a computational bottleneck [58-60]. This stems from the inclusion of thousands of solvent molecules in simulation. By using implicit solvation potentials, in which solvent degrees of freedom are averaged out, the computational problem is eliminated. It is presently an open question whether a potential without explicit solvent can approximate the true potential sufficiently well to qualify as a sound protein folding theory [61]. A toy model study claims that it cannot [62], but like many other negative results, it is of relatively little use as it is based on numerous assumptions, none of which are true in all-atom representations. 

On the other hand, the quality of the solvent or the solubility of the polymer in a solvent is determined by the solubility parameter ( ) and the Flory-Huggins polymer-solvent interaction parameter (j). Solvating potential of a solvent can be written by using Hildebrand theory [34, 63, 64]. 

It is here important to reeall that such improvements are not limited to BE solvation methods for example, Rivail and the Nancy group have recently extended their multipole-expansion formalism to permit the analytic computation of first and second derivatives of the solvation free energy for arbitrary cavity shapes, thereby facilitating the assignment of stationary points on a solvated potential energy surface. Analytic gradients for SMx models at ab initio theory have been recently described (even if they have been available longer at the semiempirical level ), and they have been presented also for finite difference solutions of the Poisson equation and for finite element solutions. 

The best test of self-consistent PRISM theory and the different solvation potential approximations is via comparison of its predictions against exact computer simulation studies of the same model. The drawback is that present computer power limits such comparisons to short and intermediate length chains (/V less than roughly 200). Many detailed comparisons have been carried out at all levels of approximation discussed in Section VIII.B. Here we give a few examples along with summarizing remarks. The reader is referred to the original studies for details and a complete discussion. 

Since the solvation potential requires knowledge of Cay (r) and hay (r) obtained from PRISM theory and a>ay (k) is used as input to the PRISM equation, a self-consistent approach must be utilized. Initially, a guess is made for the matrix elements of the solvation potential, Way (r), and single chain simulations are performed to obtain Say (k) for each ay pair. The PRISM equation and closure are solved for Cay (r) and hay (r) and a new estimate of the solvation potential is obtained. This sequence is repeated until Way (r) converges onto a solution. 

In Fig. 4 we also compare the radial distribution functions for two values of ksT/e ksT/e = 1.0 often employed in bead-spring MD studies [76, 49], and ksT le = 10.0 that is more typical of polyolefin melts, as seen in Table 1 [109]. At ksTl = 10.0, SC/PRISM predicts that intermolecular sites have a tendency to be closer together than found in the MD simulation. This result shows that, as expected, SC/PRISM theory for bead-spring melts works better when the repulsive barrier is strong and the potential is closest to a hard core. In previous studies [59] PRISM theory was solved using the exact Q (k) obtained from MD simulation rather than from a self-consistent solution as in Fig. 4. This leads to an intermolecular g(r) in better agreement with MD than seen in Fig. 4. This demonstrates the approximate form of the solvation potential used. 

As discussed above, our implementation of SC/PRISM theory makes use of a single chain simulation and hence is nearly exact for a given solvation potential for the intramolecular part of the problem. An alternative to SC/PRISM theory, exact at zero density, is the two-chain equation for g(r) [95, 143]. This equation was originally suggested by Laria, Wu, and Chandler (LWC) [95] and later derived by Donley, Curro, and McCoy (DCM) [143] using density functional techniques. For a single site model, they showed that g(r) can be written in the form... 

The surface potential of a solution can be calculated, according to Eq. (10.18), from the dilference between the experimental real energy of solvation of one of the ions and the chemical energy of solvation of the same ion calculated from the theory of ion-dipole interaction. Such calculations lead to a value of -1-0.13 V for the surface potential of water. The positive sign indicates that in the surface layer, the water molecules are oriented with their negative ends away from the bulk. 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

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