ABSTRACT
This chapter is dedicated to generalizing the characterization of potential energy surfaces into multidimensional spaces. Finding minima and transition states is something we can do in one or two dimensions with a simple graph. However, the exploration of multidimensional potential models for realistic simulations of clusters and other kinds of condensed matter presents formidable challenges. Not only can we not simply graph the potential energy surface and locate the points of interest, but the number of minima and transition states grows exponentially with size. Given the difficulty associated with the characterization of potential energy surfaces, the field remains a fertile ground for research and innovation.
