Ph. Briet, H. Hogreve
Two-centre Dirac-Coulomb operators:
Regularity and bonding properties
(394K, postscript)
ABSTRACT. Assuming the Born-Oppenheimer (clamped nuclei) approximation,
basic properties of the Dirac operator for homonuclear
two-centre one-electron systems are studied. This includes
a rigorous analysis of the regularity of the potential
energy curves as a function of the internuclear distance;
in particular, for all values of the nuclear charge parameter
that guarantee existence of a physically reasonable
self-adjoint extension of the corresponding atomic
Dirac-Coulomb operator, the continuity and differentiability
of the electronic contribution to the potential energy
curves are shown also to hold in the united atom limit.
Furthermore, for nuclear charges not too large,
the ground state united atom energy is
demonstrated to provide a universal lower bound to all
molecular energies within the discrete spectrum. Together
with a generalization of the virial theorem to diatomic
Dirac-Coulomb operators, this leads to a lower bound on
the equilibrium separation between the nuclei. In addition,
by employing appropriate variational arguments, the possibility
of molecular bonding (for sufficiently large nuclear mass)
is proved for all systems with charges up to those of the
hydrogen molecular ion H$_2^+$.