Understanding the Uniqueness of 2p Elements in Periodic Tables.

Zhen-Ling Wang,Hermann Stoll,W H Eugen Schwarz,László Von Szentpály,Jun Li,Stephan Fritzsche,Pekka Pyykkö,Han-Shi Hu

doi:10.1002/chem.202003920

Abstract

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r (2s)≈r(2p) leads to pronounced sp‐hybrid bonding of the light p‐block elements, whereas the heavier p elements with n≥3 exhibit r (ns) ≪ r (np) of approximately −20 to −30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear‐attraction and electron‐screening effects. For hydrogen‐like atoms and all inner shells of the heavy atoms, r (2s) ≫ r (2p) by +20 to +30 %, whereas r (3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Highlights

Knowing the trends along a series of related compounds is valuable for every chemist
We here present a comprehensive analysis of the nsp valence atomic orbitals (AOs) of the p-block elements, that is, of the canonical orbitals from Hartree–Fock or Dirac–Fock or Kohn–Sham levels of theory; which simulate the observable spatial and energetic changes in physical ionization and excitation processes
The radii of the valence AOs, the Radial Node Effect, and the screening of the nuclear attraction potential by the electronic core shells were explicated by Shchukarev in great chemical detail, and reviewed in the 1970s.[3,4]

Summary

Introduction

Knowing the trends along a series of related compounds is valuable for every chemist. The radii of the valence AOs, the Radial Node Effect, and the screening of the nuclear attraction potential by the electronic core shells were explicated by Shchukarev in great chemical detail, and reviewed in the 1970s.[3,4] Following Jørgensen, he was the first to rationalize the comprehensive bulk of empirical chemistry of those elements, where an orbital angular momentum number ‘ appears for the first time. For the second period p-block elements with somewhat larger and slightly screened nuclear Coulomb potentials (by the 1s2 core shell), the valence 2s,2p AOs with somewhat different energies e(2s) < e(2p) have similar radial www.chemeurj.org. DQn is the mean reduction of the hydrogenic Qn value. lar trends for rmax , hri, Dainffderpenhrt2ic,ofmorptuhteatwiohnoalleapp-pbrlooacckh.[7e–s9, yield very

F Mean DQ2

Mean DQ5

Conclusion