Equilibrium-bond-length predictions of very heavy heteronuclear molecules.

Abstract

The predictions of a central-field molecular model, designed to represent a series such as ${\mathrm{CH}}_{4}$,${\mathrm{SiH}}_{4}$,...,${\mathrm{PbH}}_{4}$, are first derived, within a nonrelativistic framework, in the limit in which the nuclear charge ${Z}_{2}$e of the heavier atom is allowed to tend to infinity. It is shown that in this model, in which the four outer protons in ${\mathrm{PbH}}_{4}$, say, are smeared uniformly over the surface of a sphere of radius R equal to the Pb--H bond length, the equilibrium bond length ${R}_{e}$ can be calculated analytically in the limit as ${Z}_{2}$e tends to infinity. In the series of tetrahedral molecules ${\mathrm{CH}}_{4}$,${\mathrm{SiH}}_{4}$,...,${\mathrm{PbH}}_{4}$, ${R}_{e}$ tends in fact to a finite value equal to 2.68 A\r{}. This prediction of a finite asymptotic bond length is then confronted with the experimental facts not only for the series ${\mathrm{CH}}_{4}$,${\mathrm{SiH}}_{4}$,...,${\mathrm{PbH}}_{4}$ but also for tetrahedral fluorides, chlorides, and bromides, and also for octahedral molecules. The empirical results are entirely consistent with the model prediction of a finite asymptotic limit of the bond length ${R}_{e}$ as ${Z}_{2}$\ensuremath{\rightarrow}\ensuremath{\infty}. A linear relationship is found between ${Z}_{2}$/${R}_{e}$ and ${Z}_{2}$.