The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.

The metadynamics or hills method is a relatively new molecular dynamics technique aimed to enhance the sampling of separated regions in phase space and map out the underlying free energy landscape as a function of a small number of order parameters or collective variables. The high efficiency allows for the application of metadynamics in combination with first principles dynamics methods, in particular with Car-Parrinello molecular dynamics, to study processes in which changes in the electronic structure play a dominant role, such as chemical reactions. The option to choose several independent collective variables is important to tackle complex and concerted transformations that lack an obvious a priori choice for a single reaction coordinate. In this Account, we discuss the role of metadynamics in the search of transition states, local minima, reaction paths, free energy profiles, and reaction coordinates among a growing list of alternative methods.

We present an accurate adaptive multiscale molecular dynamics method that will enable the detailed study of large molecular systems that mimic experiment. The method treats the reactive regions at the quantum mechanical level and the inactive environment regions at lower levels of accuracy, while at the same time molecules are allowed to flow across the border between active and environment regions. Among many other things, this scheme affords accurate investigation of chemical reactions in solution. A scheme like this ideally fulfills the key criteria applicable to all molecular dynamics simulations: energy conservation and computational efficiency. Approaches that fulfill both criteria can, however, result in complicated potential energy surfaces, creating rapid energy changes when the border between regions is crossed. With the difference-based adaptive solvation potential, a simple approach is introduced that meets the above requirements and reduces fast fluctuations in the potential to a minimum. In cases where none of the current adaptive QM/MM potentials are able to properly describe the system under investigation, we use a continuous force scheme instead, which, while no longer energy conserving, still retains a related conserved quantity along the trajectory. We show that this scheme does not introduce a significant temperature drift on time scales feasible for QM/MM simulations.