The wave mechanical evaluation of the absolute radii of atoms

Abstract

Relying upon Slater’s definition that the maximum of the radial density function of the orbital of the valence shell might be considered as a measure of the theoretical atomic radius and using the radial part of the Slater’s one-electron function, the STO’s, the formula for calculation of theoretical radii is derived as R = n ∗/ ξ, where n ∗ is the effective principal quantum number and ξ is the orbital exponent. We have computed the radii of the atoms of 103 elements of periodic table in terms of orbital exponent ( ξ) evaluated following the rules laid down by Slater. Two more sets of atomic radii are evaluated using the same formula but orbital exponents taken from the Hartree–Fock non-relativistic calculation and the set of the orbital exponents computed from the effective nuclear charge determined by Mande Deshmukh and Deshmukh invoking Dirac’s relativistic equation using X-ray spectroscopic data. In order to explore the efficacy of the semi-empirical wave mechanical method of evaluation of atomic radii, a comparative critical study of the relative sizes of atoms evaluated by quantum mechanical semi-empirical, non-empirical Hartree–Fock and relativistic quantum mechanical methods is presented. Analysis of the results reveals that the set of radii computed through semi-empirical wave mechanical method satisfies all the essential criteria of the sizes of the atoms those follow from periodic table. It is observed that (i) the d-block and f-block contractions are nicely reproduced, (ii) the physical behaviour of profiles of the atomic radii against the atomic number is perfectly in accordance with the periodic law, (iii) the relativistic effect is reasonably incorporated in the computed radii of lanthanides and post lanthanide elements, (iv) the peculiar physical and chemical properties of Hg and Au atoms are perfectly justified in terms of their evaluated sizes, and (v) when compared with the results of a more reliable relativistic quantum mechanical calculation, it seems that, in the lanthanide series, the relativistic effect scintillates better in the sizes of the present calculation.