INFLECTION SPACING SYMMETRY OF DIATOMIC POTENTIAL CURVES

Molecular ground states are found to have an approximate symmetry rela ted to equally spaced inflection points from d(j)V(R)/dR(j) = 0. Morse , Kratzer-Coulomb, Rydberg, (n + l,n), exp-exp, and cubic-anharmonic p otentials turn out to have exact equal spacing of all inflection point s out to dissociation. Equal spacing near equilibrium is consistent wi th the rule (R-0+R-2)/2=R-e, connecting the hard-sphere radius and the point of maximum attractive bonding force to the equilibrium bond len gth. In theoretical and experimental molecular curves, the rule tends to be exact at high reduced force constant k(e), with symmetry breakin g over k(e)=4-81 related to covalent, ionic, and van der Waals bonding character. Scaling preserves spacing symmetry, and maps two-term pote ntials into a universal exp-exp limit, including the (2n,n) potential into the Morse potential. Scaled spacing parameters for different mole cules are nearly constant. Anharmonic shape parameters for ''tilt'' an d ''width'' of the well are linked to empirical correlations of Dunham constants [J. L. Graves and R. G. Parr, Phys. Rev. A 31, 1 (1985)], a nd RKR analysis suggests correlations induced by equal-spacing constra ints. The inflection structure is linked to threshold singularities in the inverse Born-Oppenheimer potential R(V), which predicts the (2n, n) potential as a first approximation. (C) 1998 American Institute of Physics.