  In the study of the conformational behavior of complex systems, such as
proteins, several related statistical measures are commonly used to compare two
different potential energy functions. Among them, the Pearson's correlation
coefficient r has no units and allows only semi-quantitative statements to be
made. Those that do have units of energy and whose value may be compared to a
physically relevant scale, such as the root mean square deviation (RMSD), the
mean error of the energies (ER), the standard deviation of the error (SDER) or
the mean absolute error (AER), overestimate the distance between potentials.
Moreover, their precise statistical meaning is far from clear. In this article,
a new measure of the distance between potential energy functions is defined
which overcomes the aforementioned difficulties. In addition, its precise
physical meaning is discussed, the important issue of its additivity is
investigated and some possible applications are proposed. Finally, two of these
applications are illustrated with practical examples: the study of the van der
Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y)
and the comparison of different levels of the theory in the ab initio study of
the Ramachandran map of the model peptide HCO-L-Ala-NH2.
