Knowledge Bank

Using the spectroscopic constants $\omega ,\omega eXe$, and $\omega eYe$, the equilibrium internuclear distance $re$, the bond energy $WDo$, and the reduced mass $\mu$, one can calculate for a diatomic molecule the band origin $\sigma$ of the 1-0 band, the force constants $fe=4\pi 2C2\omega e2\mu$ and $f\sigma =4\pi 2C2\sigma 2\mu$ the constant $Ct=fe/f\sigma =(\omega e/\sigma )2$ the zero-point energy $W00$, the equilibrium dissociation energy $WDe$, the constant $Cw=WDe/WD0$, the bond strength S, and the constant $\alpha$ in the Morse function for the potential energy U. For different molecules of the same bond type, the values of $Ct$ and $Cw$ are nearly constant, and one can therefore establish average values $C¯r$ and $C¯w$ for each bond type. Such calculations were made for 49 diatomic molecules having the bond types B-A, B-B, B-C, B-D, and B-E. When $\omega e,\omega eXe$ and $\omega eYe$ are not known, these values of $C¯f$ and $C¯w$ can be used with $\sigma$ and $WD0$ to calculate good approximate values of $fe,\omega e,\omega eXe,W00,WDe$ and S. This was done for all the 49 diatomic molecules to determined values was remarkably good. Similar calculations were made for the bonds C-H, C-F, C-Cl, C-Br, and C-I (which include the same bond types) in 24 substituted methanes, using $C¯t,C¯w,WD0$, and $\sigma$ or $f\sigma$ for the stretching vibration. For $CH3X(X=H,F,Cl,Br,andI)$, there was good agreement between our values of $\omega e$ and the corresponding w values reported by Dennison; by King, Mills, and Crawford; and by Aldous and Mills.