There are two main advantages of using a combined quantum mechanical and molecular mechanical (QM/MM) potential in molecular dynamics and Monte Carlo simulations. First, since only a small portion of the condensed phase system is treated by an explicit electronic structure method, combined QM/MM methods can be applied to large molecular systems along with extensive configurational sampling. Secondly, the accuracy of the QM model representing the solute molecule can be systematically improved by using larger basis sets and by including better treatment of electron correlation. Parallel to the QM treatment, the quality of the MM approximation for the solvent system can also be improved by including polarization terms to account for the mutual solute (QM) and solvent (MM) charge polarization. In this talk, I will summarize early studies and highlight some recent developments including the use of mixed molecular orbital and valence bond (MOVB) models and the incorporation of solvent polarization in combined QM/MM simulations.

In this tutorial, I will present a few specific applications in which the need for an explicit treatment of the electronic structure of the solute is particularly important and cannot be conveniently circumvented by developing a problem-specific force field. The examples include the computation of the pKa of organic acid in the electronically excited state, the solvatochormic shifts of an organic chromophore from steam vapor to ambient water, the vibrational energy relaxation of a ligand in the enzyme active site, and the kinetic isotope effects in a proton transfer reaction in water using Feynman path integrals.

Continuum solvation models have a quite long history which goes back to the first versions by Onsager (1936) and Kirkwood (1934), however only recently (starting since the 90’s) they have become one of the most used computational techniques in the field of molecular modelling. This has been made possible by two factors which will be presented and discussed in the present talk, namely the increase in the realism of the model on the one hand, and the coupling with quantum-mechanical approaches on the other hand. In particular, the talk will focus on a specific class of continuum solvation models, namely those using as a descriptor for the solvent polarization an apparent surface charge (ASC) spreading on the molecular cavity which contains the solute.

Examples of application of QM continuum models to the study of solvent effects on molecular properties and spectroscopies are presented and discussed together with their generalizations to hybrid continuum/discrete approaches in which the presence of specific interactions (e.g. solute-solvents H-bonds) is explicitly taken into account by including some solvent molecules strongly interacting with the solute.

In an ab initio molecular dynamics calculation, the finite-temperature dynamics of a system is generated using forces obtained directly from electronic structure calculations performed ``on the fly'' as the simulation proceeds. Within this approach, manybody forces, electronic polarization, and chemical bond-breaking and forming evnets are treated explicitly, thereby allowing chemical processes in condensed phases to be studied efficiently and with reasonable accuracy. The method of Car and Parrinello, first introduced in 1985, allows such calculations to be performed within the elegant framework of an extended Lagrangian and has become an immensely popular approach for performing ab initio molecular dynamics simulations. The aim of this tutorial is to develop the basic theory of ab initio molecular dynamics and its implementation via the Car-Parrinello method. Questions of how ab initio molecular dynamics is derived from the Schroedinger equation, adiabatic dynamics and the justification of the Car-Parrinello approach, and several algorithmic issues including basis sets and pseudopotentials will be addressed.

In this tutorial, we will show how to incorporate nuclear quantum effects into an ab initio molecular dynamics calculation via the Feynman path-integral formulation of quantum statistical mechanics. Important algorithmic advances needed to accelerate the convergence of the calculations will be discussed as well as approximation dynamical path-integral schemes. Finally, an application of the ab initio molecular dynamics and ab initio path-integral approaches to the problem of the solvation and transport of topological charged defects in water will be discussed.