A relative energy gradient (REG) study of the planar and perpendicular torsional energy barriers in biphenyl

Biphenyl is a prototype molecule, the study of which is important for a proper understanding of stereo-electronic effects. In the gas phase it has an equilibrium central torsion angle of ~ 45° and shows both a planar (0°) and a perpendicular (90°) torsional energy barrier. The latter is analysed for the first time. We use the newly proposed REG method, which is an exhaustive procedure that automatically ranks atomic energy contributions according to their importance in explaining the energy profile of a total system. Here, the REG method operates on energy contributions computed by the interacting quantum atoms method. This method is minimal in architecture and provides a crisp picture of well-defined and well-separated electrostatic, steric and exchange (covalent) energies at atomistic level. It is shown that the bond critical point occurring between the ortho-hydrogens in the planar geometry has been wrongly interpreted as a sign of repulsive interaction. A convenient metaphor of analysing football matches is introduced to clarify the role of a REG analysis.