First-principles theory of tetrahedral bonding and crystal structure of lead

Abstract

From linear muffin-tin-orbital calculations using suitable basis sets we derive, from first principles, $s{p}^{3}$ bonding characteristics for group-IV elements. Particular attention is paid to lead, for which the importance of relativistic effects in determining the most stable structure is examined. The mass-velocity shift of the $\mathrm{Pb} 6s$ state is so large that the $s\ensuremath{-}p$ hybridization in a hypothetical diamond structure is too weak to allow the formation of sufficiently strong $s{p}^{3}$ bonding. Omission of relativistic effects would make the diamond structure of Pb more stable than the observed (fcc).