Functional form for representing all vibrational eigenenergies of a diatomic molecule state. IV. Application to the Br2 B(3Π+u) state

Publisher Website
Google Scholar
Abstract
A composite expression for diatomic vibrational energy levels is here tested by application to the B state of Br2. The form is Ev=D−(vD−v)m[L/N], where Ev is the energy of vibrational level v, D the dissociation limit, vD the value of v at dissociation, and [L/N] a ratio of polynomials in (vD−v). This functional form with a variety of [L/N] is fitted to experimental data for 79,79Br2. The best fits, both with m variable and with m fixed at the value 10/3 predicted by near‐dissociation theory, have an overall rms error of 0.015 cm−1. The best fits with m≡10/3 all yield realistic estimates of the coefficient C5 (of R−5, with R nuclear separation) in the long‐range potential; moreover, fixing m at 10/3 offers computational and interpretational advantages. Analogous fits to Dunham polynomials in (v+1/2) are found to be distinctly less reliable than these composite ‘‘near‐dissociation expansion’’ (NDE) functions with m fixed or variable. In order to test the interpolation and low‐v extrapolation power of the composite functions, fits are made with 12 of the 56 Ev excluded from the data set; the NDE functions again perform as well as or better than Dunham polynomials. In addition, use of Stwalley’s mass‐reduced quantum numbers in the best of the m=10/3 functions obtained for 79,79Br2 yields predicted vibrational spacings for 81,81Br2 with errors (−1) only slightly larger than the experimental uncertainties.