Computation of the atomic radii through the conjoint action of the effective nuclear charge and the ionization energy

Abstract

A new ansatz for computing the absolute radii (r) of the atoms based upon the conjoint action of two periodic properties namely, ionization energy (I) and effective nuclear charge (Z_eff ) is proposed as r = a(1/I) + b(1/Z_eff ) + c, where a, b and c are constants, determined by regression analysis. The ansatz is invoked to calculate sizes of atoms of 103 elements of the periodic table. In the absence of any benchmark to perform a validity test of any set of atomic size, reliance is upon the ‘sine qua non’ of a set of atomic size. The express periodicity of periods and groups exhibited by the computed size data, d and f block contraction and the manifest relativistic effect in the sizes of lanthanoids and actinoids, etc. speak volumes for the efficacy of the present method. Furthermore, size data have been linked to compute some physical descriptors of the real world, such as equilibrium internuclear distances of a good number of heteronuclear diatomic molecules as validity test. A comparative study of the theoretical vis-à-vis experimental equilibrium inter-nuclear distances reveals that there is close agreement between the theoretical prediction and experimental determination.

Keywords:

• absolute radii
• ionization energy
• effective nuclear charge
• relativistic effect
• internuclear distances of hetero nuclear diatomic molecules