One-electron relativistic molecules with Coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator {Mathematical expression} with Zj≧0, e^-2=137.04. H is bounded below if and only if e²Zj≦2/π all j. Assuming this condition, the system is unstable when e²∑Zj>2/π in the sense that E0=inf spec(H)→-∞ as the Rj→0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely {Mathematical expression}. We also show that E0 is an increasing function of the internuclear distances |Ri-Rj|. © 1983 Springer-Verlag.

Duke Scholars

Author Ingrid Daubechies Mathematics