Solute-solvent radial distribution function

Note that the binary HMSA [60] scheme gives the solute-solvent radial distribution function only in a limited range of solute-solvent size ratio. It fails to provide a proper description for such a large variation in size. Thus, here the solute-solvent radial distribution function has been calculated by employing the well-known Weeks-Chandler-Anderson (WCA) perturbation scheme [118], which requires the solution of the Percus-Yevick equation for the binary mixtures [119]. 

It is found that as the solute size is increased, keeping all other parameters fixed, the peak in the solute-solvent radial distribution function slowly disappears and approaches the value 1. This implies that the probability of a solvent particle, provided that there is a solute at the origin, is same everywhere. The solute-solvent static structure factor Si2(q), which can be obtained from g 12(f), will also have no structure and will have a uniform value that is, Si2(q) = 1 for all wavenumbers. 

We should hasten to note that these fundamental difficulties do not mean that this theory does not often work. The most common application of IBC theory points to its particularly simple prediction for the dependence of relaxation rates on the thermodynamic state of the solvent with the Enskog estimate of collision rates, the ratio of vibrational relaxation rates at two different liquid densities p and p2 is just the ratio of the local solvent densities [pigi(R)//02g2(R)], where g(r) is the solute-solvent radial distribution function and R defines the solute-solvent distance at... 

Figure 48. Solute-solvent radial distribution functions and running coordination numbers. The radial distribution (the solid line using the left scale) and the running coordination number (the dashed line using the right scale) are plotted versus distance in angstroms for the distribution of water oxygens around apolar atoms (o) Asp-48 Cs (b) Ser-72 O3 (c) Asn-46 C 3 and ((i) Gly-71 C .

Figure 2. Computed solute-solvent radial distribution function g(r) in hard disc system. Unit distance is solvent diameter a. Data points were tabulated over 100 intervals, equally spaced in r. ...

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

Yes (Shimizu 2004) (i) Equation 11.2 has been derived rigorously from FST (Chitra and Smith 2001b Shimizu 2004) and (ii) FST shows that N21 and A23 (for each of the conformations) are defined microscopically through the solute-solvent and solute-cosolvent radial distribution function g2i(r),... 

The results of BOSS calculations can be analyzed In ChemEdit. Some plots from a BOSS calculation are shown in Figure 6. Information extracted from a BOSS output includes (a) geometries of the solutes (b) radial distribution functions (c) energy and energy pair distributions (d) average thermodynamic properties (e) components of the solvent-solute energy and (f) AH, AS, and AG for perturbations. 

One important class of integral equation theories is based on the reference interaction site model (RISM) proposed by Chandler [77]. These RISM theories have been used to smdy the confonnation of small peptides in liquid water [78-80]. However, the approach is not appropriate for large molecular solutes such as proteins and nucleic acids. Because RISM is based on a reduction to site-site, solute-solvent radially symmetrical distribution functions, there is a loss of infonnation about the tliree-dimensional spatial organization of the solvent density around a macromolecular solute of irregular shape. To circumvent this limitation, extensions of RISM-like theories for tliree-dimensional space (3d-RISM) have been proposed [81,82],... 

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

The probability of cavity formation in bulk water, able to accommodate a solute molecule, by exclusion of a given number of solvent molecules, was inferred from easily available information about the solvent, such as the density of bulk water and the oxygen-oxygen radial distribution function [65,79]. 

The reason for the early crossover can be understood from the following discussion. When the interaction energy between the solute and the solvent is increased, the peak of the radial distribution function does not disappear. Thus c 2(q) 0 for all wavenumbers. Hence the density mode contribution does not become zero as happens in the case where the size of the solute is only increased. Hence Dmicroi along with the binary term, also contains the contribution from the density mode. This results in faster decrease of Dmjcro > leading to an early crossover. 

In short, our S-MC/QM methodology uses structures generated by MC simulation to perform QM supermolecular calculations of the solute and all the solvent molecules up to a certain solvation shell. As the wave-function is properly anti-symmetrized over the entire system, CIS calculations include the dispersive interaction[35]. The solvation shells are obtained from the MC simulation using the radial distribution function. This has been used to treat solvatochromic shifts of several systems, such as benzene in CCI4, cyclohexane, water and liquid benzene[29, 37] formaldehyde in water(28, 38] pyrimidine in water and in CCl4(31] acetone in water[39] methyl-acetamide in water[40] etc. 

Figure 10. Solvation of twelve 18C6 crowns "diluted" in dry versus humid [BMI][PF6] solutions. Typical snapshots of die "first shell" solvent molecules and radial distribution functions "RDFs" around the center of the crown 18C6 BMI (bold), 18C6 F (dotted), 18C6 P (plain) and Sr OH2 (inversed ordinate).

A different approach to mention here because it has some similarity to QM/MM is called RISM-SCF [5], It is based on a QM description of the solute, and makes use of some expressions of the integral equation of liquids (a physical approach that for reasons of space we cannot present here) to obtain in a simpler way the information encoded in the solvent distribution function used by MM and QM/MM methods. Both RISM-SCF and QM/MM use this information to define an effective Hamiltonian for the solute and both proceed step by step in improving the description of the solute electronic distribution and solvent distribution function, which in both methods are two coupled quantities. There is in this book a contribution by Sato dedicated to RISM-SCF to which the reader is referred. Sato also includes a mention of the 3D-RISM approach [6] which introduces important features in the physics of the model. In fact the simulation-based methods we have thus far mentioned use a spherically averaged radial distribution function, p(r) instead of a full position dependent function p(r) expression. For molecules of irregular shape and with groups of different polarity on the molecular periphery the examination of the averaged p(r) may lead to erroneous conclusions which have to be corrected in some way [7], The 3D version we have mentioned partly eliminates these artifacts. 

Fig. 26. Comparison between radial distribution functions for 3 M silver(I) nitrate in aqueous and in DMSO solutions. Intramolecular interactions of the solvent molecules have been removed. The derived structures for the solvated silver(I) ion in the two solvents are shown.

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