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The fast evolution of computers and of their processing speed has allowed to pass from the simulation of simple systems to more complex ones in few years. Recently, given their applied interest, much effort is devoted to the simulation of heterogenous environments such as biological systems, polymers and surfaces. To realistically model this kind of systems, the classical force fields are evolving towards the inclusion of polarization effects. Taking into account these effects is fundamental to reproduce and to understand the behaviour of molecules in non-homogeneus surroundings.

Polarization refers to the redistribution of a particle's (or molecule's) electron density due to an electric field. In terms of molecular interactions, polarization leads to nonadditivity, since a molecule polarized by another molecule will interact differently with a third one than it would if it were not polarized. The change in the electron density can be characterized by changes in the monopole charges, dipole moments and higher order moments.

In Molecular Dynamics simulations the are two ways of including polarization effects: implicitly or explicitly. In implicit models it is considered that a mean polarization can be averaged out and its effect is included in the functional form of the interaction potential. Moreover, in condensed phase simulations, the dipole moment of dipolar molecules is artificially overestimated with respect to gas phase values. The main drawback of implicit models is that they don't take into account the real dipole fluctuations occuring during the dynamic evolution of the systems. Even if they succeed in reproducing many interesting properties quite well, and are not very computationally demanding, it is known that a more detailed description is needed in many cases. In particular, when systems with high polarizabilities and/or highly charged species are studied, both static and dynamic properties are strongly correlated with dipole moments. That's why for the last 15 years a great effort has been done to develop explicit models, i. e. techniques reproducing the many body dipolar interactions which could give a more appropriate description of molecular polarization.

Since the interaction of these substances with ions is of particular interest, we dedicated our attention on the explicit models used to implement polarization in MD simulations. Important quantum effects, such as hyperpolarizability and orbital overlaping at short distances, are usually not taken into account in the most widespread classical algorithms. In liquid state simulations it is not easy to disentangle the effects of all types of interaction, so that obtaining a clear view of the range of validity and limits of these methods is difficult. For this reason we used a minimalist approach to face the problem: we used as benchmark a series of configurations for ion-molecule dimers, the simplest systems where polarization effects are present and their properties can be studied separately; moreover, since the ion-molecule electric interactions are very strong, these systems represent the limiting situation which coud be found in the liquid phase. We calculated the electrostatic properties of the dimers with first principles calculations and compared the results with classical polarizable models. Interesting results came out from our analysis which allowed us to classify the methods according to their efficiency. Furthermore, we observed that a better agreement between quantum and classical calculations could be achieved, if different parameters for the interactions were choosen.