  The rigorous two-center approach based on the dual-kinetically balanced
finite-basis-set expansion is applied to one-electron, heteronuclear diatomic
Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained $1\sigma$ ground-state
energies are compared with previous calculations, when possible. Upon analysis
of three different placements of the coordinate system's origin in the monopole
approximation of the two-center potential: (1) in the middle, between the
nuclei, (2) in the center of the heavy nucleus, and (3) in the center of the
light nucleus, a substantial difference between the results is found. The
leading contributions of one-electron quantum electrodynamics (self-energy and
vacuum polarization) are evaluated within the monopole approximation as well.
