where E(G) is the ground-state energy at geometry G, G 0 the exact geometry and G an approximate geometry. The theoretically exact geometry is defined here as the exact minimum of the exact ground-state potential energy surface, and the Born-Oppenheimer approximation is assumed throughout this work. Defined this way, GEO represents an energetic distance between the exact and approximate geometries, and thus provides a single number measure for the quality of geometries. At minima, GEO vanishes only if G = G 0 , and otherwise it is always a positive number given in energy units.