Global Potential Energy Contour Plots for Chemical Reactions. Stepwise vs Concerted 2 + 2 Cycloaddition

A global contour plot is described for reactions involving stepwise or concerted addition of two ethylenes to form cyclobutane. The relevant isomers of the various species and of the reaction paths, with plains or valleys, minima, saddle points, and domes or conical intersections, are described. Two collective asymmetric coordinates are introduced as axes for the plot, which presents an overview of the system and which complements the usual 2-dimensional cuts of the many-dimensional potential energy surface. Other global coordinates are also introduced. The plot involves a pointwise minimization of the potential energy with respect to the coordinates not used as axes. A permutation symmetry can be used to derive the various coordinates. Free energy and entropy (or number of states) curves versus a reaction coordinate are discussed