Statistical Methods for Studying Solutions

A correct calculation of solvation thermodynamics and solution structure is conceivable only in terms of the methods of statistical physics, in particular, the computer experiment schemes, including, in the first place, the molecular dynamics (MD) and the Monte-Carlo (MC) methods [10]. By means of the MD method Newton s classic equations of motion are solved numerically with the aid of a computer assuming that the potential energy of molecular interaction is known. In this manner, the motion of molecules of the liquid may be observed , the phase trajectories found and then the values of the necessary functions are averaged over time and determined. This method permits both the equilibrium and the kinetical properties of the system to be calculated. 

A basically different approach is used in the MC method. The states of a system of particles are taken to be stochastic and one has to select the most probable configurations over which various properties are then averaged. Therefore, this method is suitable only for calculating equilibrium quantities since it cannot, in principle, give an answer to the question how the system achieves its equilibrium because, instead of a genuine dynamic evolution of the system, an artificial stochastic process is modelled. A possibility arises of taking into account by statistical methods the effect of the temperature on the properties of a solution. 

The methods of the computer experiment require simplified representation of the potential energy T(/ ), so in most calculations only the two-particle contributions are taken into account  

Moreover, the two-particle contributions Vij are, as a rule, calculated as a sum of the atom-atom interactions  

Unlike the monohydration schemes, the computer experiment methods account in solutions both for interactions of the solute molecule with molecules of the solvent and for those of solvent molecules among each other. In some cases, particularly for aqueous solutions, the latter component is comparable to and may even exceed the water-solute molecule interaction energy. This results in considerable differences in the structure of solvation shells. Below (Fig. 3.1), solvation shells are given of 4-pyridone obtained by calculations using the MC method [8] and the monohydration scheme. The data presented show that for correct determination of localization sites of the point charges and dipoles of solvent molecules, the calculations should be employed based on statistical methods. 

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