A NEW FUNCTIONAL FORM FOR REPRESENTING VIBRATIONAL EIGENERGIES OF DIATOMIC MOLECULES APPLICATION TO THE $Br_{2}$ B $STATE^{*}$

$^{*}$Supported by Grant No. AFOSR-77-3132 $^{1}$R. F. Barrow, et al., J. Mol. Spectrosc. 51, 428 (1974).Author Institution:An expression previously applied to the ground electronic states of $H2^{+}$ and $H_{2}$ is here applied to the B state of $Br_{2}$. 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 $\Delta E(\nu + \frac{1}{2})$ of Barrow et $al.^{1}$ for $^{79}Br_{2}$. Our best fits each have an overall rms error of $0.012 cm^{-1}$ in the $\Delta $E. Apparently erroneous experimental results are exposed through consistently large errors in the same $\Delta E’s$ among different fits. Twelve of the $56 E_{\nu}$ are excluded as data to test the interpolation and extrapolation power of the proposed formula. The rms error in the interpolated $\Delta E’s$ is essentially the same whether these $\Delta E’s$ 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 $D-E_{55}$ is $1.00 cm^{-1}$. Finally, using the best $^{79}Br_{2}$ fits and mass reduced quantum numbers as suggested by Stwalley, we fit to $^{81}Br_{2}$ and find an rms error of $