Effects of exchange on equilibrium bond lengths of heavy, almost spherical, tetrahedral molecules XH4

Abstract

The simplest nonrelativistic density functional theory, namely, that of Thomas, Fermi, and Dirac, is used to study the effect of exchange on the equilibrium bond lengths of heavy tetrahedral molecules XH4. In particular, the limiting bond length as the central atom X becomes infinitely heavy is shown to be reduced by exchange by some 0.34 Å. Comparison with experiment shows that the main features of the bond-length variation through the series CH4PbH4 are reflected by the Thomas–Fermi–Dirac predictions, though the bond lengths remain too large for finite atomic number Z of the central atom. Therefore, a semiempirical correction is proposed, which, however, tends to zero as Z tends to infinity.