Knowledge Bank

An expression previously applied to the ground electronic states of $H2+$ and $H2$ is here applied to the B state of $Br2$. The form is $E\nu =D–(\nu D–\nu )m[L/N]$, where $E\nu$; is the vibrational eigenenergy, v the quantum number, D the dissociation limit energy, $\nu D$ and m are parameters, and [L/N] is a rational fraction in $(\nu D–\nu )$. We fit this functional form with a variety of [L/N] to the fifty-five experimental first differences $\Delta E(\nu +12)$ of Barrow et $al.1$ for $\mathrm{<mrow\; data-mjx-texclass="ORD">79</mrow>}Br2$. Our best fits each have an overall rms error of $0.012cm-1$ in the $\Delta $E. Apparently erroneous experimental results are exposed through consistently large errors in the same $\Delta E\prime s$ among different fits. Twelve of the $56E\nu$ are excluded as data to test the interpolation and extrapolation power of the proposed formula. The rms error in the interpolated $\Delta E\prime s$ is essentially the same whether these $\Delta E\prime s$ are included or excluded as fitting data; the rms error in the extrapolated $\Delta E$ at the three lowest v increases significantly, however. Our best extrapolation for $D-E55$ is $1.00cm-1$. Finally, using the best $\mathrm{<mrow\; data-mjx-texclass="ORD">79</mrow>}Br2$ fits and mass reduced quantum numbers as suggested by Stwalley, we fit to $\mathrm{<mrow\; data-mjx-texclass="ORD">81</mrow>}Br2$ and find an rms error of $cm-1$ in the $\Delta $E.