l-Type Doubling in Linear Polyatomic Molecules

The infra-red spectra of ${\mathrm{C}}_2$${\mathrm{H}}_2$, HCN, and C${\mathrm{O}}_2$ give evidence of a splitting of the II vibrational levels (in which a ⊥ vibration is singly excited) into two components which is entirely analogous to the $\Lambda$-type doubling of the electronic states of diatomic molecules and is called here $l$-type doubling. The experimental data show that this $l$-type doubling may be represented by $\Delta \nu =q_{i}J(J+1\mathrm{})\mathrm{}$ and that the constant $q_i$ is of the same order as the constant ${\alpha }_i$ in $B_{\mathrm{}\left[v\right]\mathrm{}}=B_e-\Sigma {\alpha }_i(v_i+\frac{1}{2}{d}_i)$. The existence of the $l$-type doubling also explains the apparent discrepancy that the fundamental bands of HCN and ${\mathrm{C}}_2$${\mathrm{H}}_2$ do not show a convergence of the $P$ and $R$ branches while the $Q$ branch is distinctly shaded to shorter wave-lengths. A preliminary theoretical treatment of the $l$-type doubling is also given. The doubling is due mainly to the fact that in the displaced position of a perpendicular vibration a linear molecule is a slightly asymmetric top, but to some extent also to the Coriolis interaction of different vibrations. The observed values of $q_i$ are all larger than the calculated ones. Taking the $l$-type doubling into account the rotational constants ${\alpha }_i$ of C${\mathrm{O}}_2$ have been newly evaluated and from them and the value $B_{000}={0.3895}_0$ ${\mathrm{cm}}^{-1\mathrm{}}$ the rotational constant $B_e$ in the equilibrium position is found to be 0.3906±0.0002 ${\mathrm{cm}}^{-1\mathrm{}}$ which gives for the moment of inertia $I_e=71.61\mathrm{}·{10}^{-40\mathrm{}}$ g ${\mathrm{cm}}^2$ and for the CO distance $r_e=1.1615\mathrm{}·{10}^{-8\mathrm{}}$ cm.