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

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 (<0.03 cm−1) only slightly larger than the experimental uncertainties.