Simulation in the Theory of Ionic Solutions

All parts of the physical sciences are now served by calculation techniques that would not have been possible without the speed of electronic computers. Such approaches are creative in the sense that, given the law of the energy of interaction between the particles, the software allows one to predict experimental quantities. If agreement with experiment is obtained, it tells us that the energy of interaction law assumed is correct. Sometimes this approach can be used to calculate properties that are difficult to determine experimentally. Such calculations may allow increased insight into what is really happening in the system concerned or they may be used simply as rapid methods of obtaining the numerical value of a quantity. There are two main computational approaches and these will be discussed next. 

The Monte Carlo approach was invented hy Metropolis (Metropolis, 1953). The system concerned is considered in terms of a small number of particles—a few hundred. The basic decision that has to be made is What law are the particles i and going to follow in expressing the interaction energy between them as a function of their distance apart For example, a useful law might be the well-known Lennard-Jones equation  

Such a calculation is then carried out successively on each particle many times. Since each can move to any point within the allotted space, a large enough number of moves allows one to reach the equilibrium state of the system while calculating a targeted quantity, e.g., the pressure of an imperfect gas. The result is compared with that known experimentally, thus confirming or denying the force law assumed (and other assumptions implicit in the calculation). 

Card and Valleau (1970) were the first to apply the Metropolis Monte Carlo method to an electrolytic solution. Their basic assumption was that if 

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