Capacitance scaling law for diatomic molecules and prediction of their electron detachment energies

Abstract

The variation or ``scaling'' of the quantum capacitances is explored for 45 diatomic molecules as a function of their dimensions. Scaling trends in the capacitances of these diatomic molecules dictate an ``atoms-in-molecules'' view of their valence energetics. That is, experimentally derived quantum capacitances for both homonuclear and heteronuclear diatomic molecules scale linearly with the average of the mean radii for the outermost orbitals of their component atoms. This is in accord with Maxwell's law for classical capacitors formed from two conducting atom-sized spheres in tangential contact. However, the scaling behavior for the molecules has some nonclassical features. Notably, the quantum capacitances extrapolate to nonzero values at zero dimensions. Radius-capacitance points of the homonuclear diatomics lie primarily along five scaling lines, with each determined by points for molecules composed of atoms with the same atomic symmetry (i.e., atoms from the same column in the periodic table). Five scaling lines for heteronuclear diatomics each are determined by points for molecules of the same or similar molecular symmetries. The molecules' quantum capacitances are calculated from their ionization potentials (IPs) and electron affinities (EAs). Thus, equations or laws for the scaling lines impose mutual consistency conditions among these electron detachment energies for different diatomics of similar symmetries. By taking advantage of this, the linear quantum capacitance scaling laws and ab initio atomic mean radii are used to predict IPs for two diatomics with known EAs (Ga${}_{2}$ and SeO), but for which there is no standard value of the IP. Similarly, the laws are used to predict EAs that were unknown or uncertain for several diatomics (Li${}_{2}$, LiF, CSe, PN, BF, BCl, SiO, GeO, NCl, CaO, SrO, and BaO) with known IPs.