03-101 Ph. Briet, H. Hogreve

Two-centre Dirac-Coulomb operators: Regularity and bonding properties (394K, postscript) Mar 9, 03

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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$_2^+$.

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