Solvation/solvents Monte Carlo simulation

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

Quantitative models of solute-solvent systems are often divided into two broad classes, depending upon whether the solvent is treated as being composed of discrete molecules or as a continuum. Molecular dynamics and Monte Carlo simulations are examples of the former 8"11 the interaction of a solute molecule with each of hundreds or sometimes even thousands of solvent molecules is explicitly taken into account, over a lengthy series of steps. This clearly puts a considerable demand upon computer resources. The different continuum models,11"16 which have evolved from the work of Bom,17 Bell,18 Kirkwood,19 and Onsager20 in the pre-computer era, view the solvent as a continuous, polarizable isotropic medium in which the solute molecule is contained within a cavity. The division into discrete and continuum models is of course not a rigorous one there are many variants that combine elements of both. For example, the solute molecule might be surrounded by a first solvation shell with the constituents of which it interacts explicitly, while beyond this is the continuum solvent.16... 

X-ray and neutron diffraction methods and EXAFS spectroscopy are very useful in getting structural information of solvated ions. These methods, combined with molecular dynamics and Monte Carlo simulations, have been used extensively to study the structures of hydrated ions in water. Detailed results can be found in the review by Ohtaki and Radnai [17]. The structural study of solvated ions in lion-aqueous solvents has not been as extensive, partly because the low solubility of electrolytes in 11011-aqueous solvents limits the use of X-ray and neutron diffraction methods that need electrolyte of -1 M. However, this situation has been improved by EXAFS (applicable at -0.1 M), at least for ions of the elements with large atomic numbers, and the amount of data on ion-coordinating atom distances and solvation numbers for ions in non-aqueous solvents are growing [15 a, 18]. For example, according to the X-ray diffraction method, the lithium ion in for-mamide (FA) has, on average, 5.4 FA molecules as nearest neighbors with an... 

As a second example, we have determined the influence of solvation on the steric retardation of SN2 reactions of chloride with ethyl and neopentyl chlorides in water, which has recently been studied by Vayner and coworkers [91]. In their study solvent effects were examined by means of QM-MM Monte Carlo simulations as well as with the CPCM model. Solvation causes a large increase in the activation energies of these reactions, but has a very small differential effect on the ethyl and neopentyl substrates. Nevertheless, a quantitative difference was found between the stability of the transition states determined using discrete and continuum treatments of solvation, since the activation free energies for ethyl chloride and neopentyl chloride amount to 23.9 and 30.4kcalmoF1 according to MC-FEP simulations, but to 38.4 and 47.6 kcal moF1 from CPCM computations. 

The explicit modeling approach surrounds a solute molecule with solvent molecules and then examines each molecule in that solvated environment. Quantum chemical methods, both semiempiricaP and ab initio" have been used to do this however, molecular dynamics and Monte Carlo simulations using force fields are used most often.Calculations on ensembles of molecules are more complex than those on individual molecules. Dykstra et al. discuss calculations on ensembles of molecules in a chapter in this book series. Because of the many conformations accessible to both solute and solvent molecules, in addition to the great number of possible solute molecule-solvent molecule orientations, such direct QM calculations are very computer intensive. However, the information resulting from this type of calculation is comprehensive because it provides molecular structures of the solute and solvent, and takes into account the effect of the solvent on the solute. This is the method of choice for assessing specific bonding information. 

The best strategy to be followed in order to get accurate sets of A values has not been defined, so at present more or less complex statistical elaborations of some data are used. Among the numerical data that have been used we mention solvation and solvent transfer energies, intrinsic solute properties (electron isodensity surfaces, isopotential electronic surfaces, multipole expansions of local charge distribution), isoenergy surfaces for the interaction with selected probes (water, helium atoms), Monte Carlo simulations with solutes of various nature. All these sets of data deserve comments, that are here severely limited not to unduly extend this Section. 

The Monte Carlo method can also be used to study the effect of solvent on the position of tautomeric equilibrium (Metropolis et al., 1953). This method models a dilute solution as N solvent molecules (N — 102) and 1 solute molecule. The fundamental requirement for a Monte Carlo simulation of tautomer solvation is a set of pair potentials for the solvent-solvent and solvent-solute interactions because approximately 106 config-... 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

An obvious way to combine Monte Carlo with molecular d)mamics is to use each technique for the most appropriate part of a simulation. For example, when simulating a solvated macromolecule, the equilibration phase is usually performed in a series of stages. In the first stage, the solute is kept fixed while the solvent molecules (and any ions, if present) are allowed to move under the influence of the solute s electrostatic field. This solvent equilibration may often be performed more effectively using a Monte Carlo simulation as the solvent and ions do not have any appreciable conformational flexibility. To simulate the whole system, molecular d)maimcs is then the most appropriate method. Such a protocol has been used to perform long simulations of DNA molecules [Swaminathan et al. 1991]. 

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