Gaussian solvent model

Since the development of the Onsager model, there have been a number of elaborations on the model [4,5]. For example, the spherical cavity has been replaced by molecularly-shaped cavities. The state of the art within the field of solvent effects described by continuum solvent models is now implemented in, e.g., the Gaussian program package. 

Experiments [6,11,12] and simulations [6,16] have recently established that a large part of the relaxation of the nonequilibrium solvation around a solute immediately after its photoexcitation is due to the shortest timescale motions of the first shell solvent molecules. This result is in accord with the theoretical notions we have been developing since 1979 [20a], which after refinement [22] has led to our use of the Gaussian friction model as the basis of our molecular friction methods [19,24],... 

Fig. 4.11 Gas-liquid coexistence curves for hard spheres plus interacting polymers in a good solvent (Gaussian core model) from Monte Carlo simulation [52] data for q = 0.67 (te/t) and q = 1.05 (right) versus GFVT predictions (curves). The GFVT critical point is marked by a filled...

Zimm Model in the Theta Solvent For a polymer chain in the theta solvent, the Gaussian chain model conveniently gives ns an analytical expression of Eq. 3.163. With Eq. 3.56,... 

Finally, analytic predictions for the osmotic pressure of polymers in good and theta solvents can be derived based on the Gaussian thread model, PRISM theory, and the compressibility route. The qualitative form of the prediction for large N is " pP °c (po- ), which scales as p for theta solvents and p " for good solvents. Remarkably, these power laws are in complete agreement with the predictions of scaling and field-theoretic approaches and also agree with experimental measurements in semidilute polymer solutions. ""... 

The solvation term, soiv, is based on the Gaussian solvent exclusion model, which takes the general form [165]... 

For large z, this relationship implies that the root-mean-square end-to-end distance is proportional to 1, which agrees with observations. As in the case of the Flory concept, implicit in this model is the assumption that the end-to-end distance in a good solvent is Gaussian. However, the Gaussian chain model for a polymer molecule is increasingly inaccurate as the solvent power increases. This is taken into account by a mean field theory that has been proposed to describe the excluded volume effect [17]. 

Polymer chains at low concentrations in good solvents adopt more expanded confonnations tlian ideal Gaussian chains because of tire excluded-volume effects. A suitable description of expanded chains in a good solvent is provided by tire self-avoiding random walk model. Flory 1151 showed, using a mean field approximation, that tire root mean square of tire end-to-end distance of an expanded chain scales as... 

It is important to verify that the simulation describes the chemical system correctly. Any given property of the system should show a normal (Gaussian) distribution around the average value. If a normal distribution is not obtained, then a systematic error in the calculation is indicated. Comparing computed values to the experimental results will indicate the reasonableness of the force field, number of solvent molecules, and other aspects of the model system. 

Here,. Ai(X) is the partial SASA of atom i (which depends on the solute configuration X), and Yi is an atomic free energy per unit area associated with atom i. We refer to those models as full SASA. Because it is so simple, this approach is widely used in computations on biomolecules [96-98]. Variations of the solvent-exposed area models are the shell model of Scheraga [99,100], the excluded-volume model of Colonna-Cesari and Sander [101,102], and the Gaussian model of Lazaridis and Karplus [103]. Full SASA models have been used for investigating the thermal denaturation of proteins [103] and to examine protein-protein association [104]. 

Figure 4 Sample spatial restraint m Modeller. A restraint on a given C -C , distance, d, is expressed as a conditional probability density function that depends on two other equivalent distances (d = 17.0 and d" = 23.5) p(dld, d"). The restraint (continuous line) is obtained by least-squares fitting a sum of two Gaussian functions to the histogram, which in turn is derived from many triple alignments of protein structures. In practice, more complicated restraints are used that depend on additional information such as similarity between the proteins, solvent accessibility, and distance from a gap m the alignment.

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