Behavior of molecular potential energy curves for large nuclear separations

✍ Scribed by John D. Morgan III; Barry Simon

• Publisher: John Wiley and Sons
• Year: 1980
• Tongue: English
• Weight: 1006 KB
• Volume: 17
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560170609

✦ Synopsis

Abstract

We prove by elementary geometric methods and within the Born–Oppenheimer approximation that as the nuclei of a molecule are dissociated into spatially separated clusters, the discrete molecular energies approach sums of the energies of isolated subsystems. Our methods also show that the spectral projections associated with the discrete molecular spectrum asymptotically approach direct sums of suitable spectral projections for the isolated subsystems. These results apply to any system of particles interacting by asymptotically vanishing pair potentials. We prove that the 1/R expansion for discrete molecular potential curves is asymptotic as R → ∞, and we discuss the behavior of the coefficients of the 1/R expansion for the ground state of H~2~^+^.