INVERSE VIRIAL SYMMETRY OF DIATOMIC POTENTIAL CURVES

The virial theorem for potential curves V(R) is recast into a linear s econd-order differential equation in the inverse picture R(V), which p rovides a framework for correlating the inner and outer walls of the p otential well. Leading solutions extended for scaling define a new cla ss of five-parameter potentials in terms of Gauss hypergeometric funct ions. Curves are classified with two labels (p,q) related to Dunham sp ectroscopic constants and long-range threshold behavior. Special limit ing cases include the Morse potential, the harmonic oscillator, and th e 2n:n inverse-power generalization of the Lennard-Jones 12:6 and Krat zer-Coulomb 2:1 potentials. Empirical maps of (p,q) values from experi mental molecular data reveal distinct clustering of points correlated to covalent, van der Waals and ionic bonding. Semiclassical quantizati on gives hypergeometric formulas for energy levels and RKR potentials. Threshold behavior of exact molecular curves is consistent with a lin ear combination of elementary inverse potentials, with the extended hy pergeometric basis as a first approximation. (C) 1998 American Institu te of Physics. [S0021-9606(98)01825-X].