Orbital radii and environment-independent transferable atomic length scales

Abstract

The importance of the orbital radii, r_l, obtained from the classical turning point of the valence electron wave function of angular momentum, I, in obtaining interatomic distances for all bonding situations is demonstrated. Single bond interatomic distances may be expressed in terms of a universal multiplicative constant of a core s orbital radius and another universal additive term which is close to the interatomic distance in the hydrogen molecule. These relationships are obtained from the dependence of the radii of positive or negative singly charged ionic species, CR⁺ and CR^-, on r_l. The shortening of the distances in multiple bond systems or in systems involving transition metal d electron elements is described by a simple universal function, F_s, associated with the number of unpaired valence electrons. A principle of maximum mechanical hardness based on minimization of bond distances is proposed to obtain correct distances in heteropolar MX bonds. The application of these rules to a large number of compounds with ionic, covalent, metallic, and nonbonded interactions yield interatomic distances which are within 2% of the observed distances. A brief discussion is made on the physical significance of the transferable length scales CR⁺ and CR^- in the context of discrimination of structure based on radius ratio and the requirement of a universal equilibrium chemical potential for transferability.