Solvation models are nowadays widespread computational techniques to study solvent effects on energy/geometry/reactivity and properties of very different molecular systems (from small molecules to very large biochemical systems such as proteins and enzymes). Many alternative theoretical models and computational algorithms have been proposed so far; among them, however, two main classes can be identified, namely that using an equivalent description (either quantum-mechanical or classical) for all the components of the system (the solute and the solvent molecules in a dilute solution, the molecules of the different species forming a mixture, etc.), and the other introducing a focused approach, i.e., a hierarchical approach in which the most interesting part of the system is treated at a much more accurate level than the rest. The first class of models include very different approaches going from classical Molecular Dynamics (MD) and Monte Carlo (MC) simulations to quantum mechanical (QM) calculations on small-medium clusters and to ab-initio MD simulations on larger sets of molecules. Also the second class of methods include very different approaches which however present the common characteristic of using a partition of the system into a QM and a classical part, generally coinciding with the solute and the solvent respectively, even if clusters formed by the solute and few solvent molecules (those more strongly interacting) can alternatively be defined as the QM part while the rest of the solvent molecules is the classical part. Among these hybrid methods, it is common to distinguish between two main sub-classes. The first one, generally indicated as QM/MM approach, presents many characteristics which are common to classical simulations belonging to the first class of methods, such as the use of force fields to represent the classical part of the system and the necessity to introduce averages on different solute-solvent configurations in order to get a physically and statistically meaningful picture.
In the second sub-class of focused methods, the classical part of the system is represented by a polarizable continuum dielectric. In such models, the QM solute is assumed to be inside a cavity of proper shape and dimension within an infinite continuum dielectric mimicking the solvent. Contrary to the QM/MM approaches, QM/continuum approaches do not need to introduce any force field neither to average on different configurations. The averaged effects of the solvent are in fact automatically introduced in the QM description of the solute (or of its generalized definition including some solvent molecules) in a self-consistent way once the cavity is defined and the macroscopic dielectric properties of the solvent are known.
This tutorial will focus on presenting some of the fundamental concepts and techniques currently used in those solvation methods that introduce a QM description for at least a part of the system (namely the solute or its generalized definition). The presentation will be divided in three parts, devoted to ab-initio MD, QM/MM and QM/continuum approaches, respectively. The presentation of these various parts will follow a step-by-step scheme in which the physical bases of the models come first followed by an analysis of both mathematical and computational aspects and finally by a review on their applications to different physical-chemical problems. In parallel, possible limitations or incompleteness of each approach will be pointed out with indications of future developments.