Relativistic effects in bonding and dipole moments for the diatomic hydrides of the sixth-row heavy elements

Ab initio Dirac-Fock (DF) and nonrelativistic-limit (NRL) wave functions and dipole moments are calculated to investigate the bonding characteristics and the relativistic effects in the systems ${\mathrm{HgH}}^{+}$, TlH, ${\mathrm{PbH}}^{+}$, and BiH. The dipole moment of AuH is evaluated using the DF self-consistent field and relativistic configuration-interaction wave functions obtained by G. L. Malli and N. C. Pyper [Proc. R. Soc. London, Ser. A 407, 377 (1986)]. Contour plots of relativistic molecular orbital densities and difference density maps are presented to illustrate the arrangement of electronic charge in these systems. It is found that the 5d orbitals are involved in the bonding of ${\mathrm{HgH}}^{+}$, whereas they do not play a significant role in TlH and ${\mathrm{PbH}}^{+}$. The relativistic calculations predict ${\mathrm{HgH}}^{+}$, TlH, and ${\mathrm{PbH}}^{+}$ to be bound. The nonrelativistic-limit wave functions predict ${\mathrm{HgH}}^{+}$ and BiH to be unbound but TlH and ${\mathrm{PbH}}^{+}$ to be bound. It is also found that the calculated dipole moments using the DF and the NRL wave functions for these heavy systems differ significantly in magnitude, and in some cases even in the sign.