On-Top Ratio for Atoms and Molecules

The on-top ratio, <i>R</i>, is the ratio of the on-top pair density to the square of half the total density. Here, we explore the on-top ratio as a tool to understand different types of bonds, including covalent, polar covalent, ionic, and dispersion-dominated weak interactions. We show for several diatomic molecules and for ethylene that the partial derivative of <i>R</i> is a useful indicator of covalent-bond breaking. <i>R</i> also presents a local maximum for each electron shell when all electrons are correlated.