Equilibrium-bond-length predictions of very heavy heteronuclear molecules

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 Å. 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 $Z_2$→∞. A linear relationship is found between $Z_2$/$R_e$ and $Z_2$.