A Note Concerning the Coriolis Contribution to the Energy of a Symmetric Polyatomic Molecule

Abstract

By a third-order perturbation calculation it is shown that the degenerate Coriolis interaction term in the vibration-rotation energy of a symmetric polyatomic molecule should be written $\mp 2\Sigma t^{}{\zeta }_t{l}_{t}K{C}_v$ rather than $\mp 2\Sigma t^{}{\zeta }_t{l}_{t}K{C}_e$, $C_e$ being equal to ($\frac{h}{8{\pi }^{2}I_{\mathrm{zz}}^{}{}_{}{}^{\mathrm{}\left(e\right)\mathrm{}}c}$) and $C_v=C_e-\Sigma t^{}\left(\frac{v_t+g_t}{2}\right){\Gamma }_t$, ${\Gamma }_t$ being a constant ${\gamma }_t+\Sigma {t^{\prime }{\sigma }^{\prime }}^{}\frac{\zeta _{t\sigma ,t^{\prime }{\sigma }^{\prime }}^{}{}_{}{}^2(3\mathrm{}{\omega }_t+{\omega }_{t^{\prime }})}{(\omega _t^{}{}_{}{}^2-\omega _{t^{\prime }}^{}{}_{}{}^2)}$ where ${\gamma }_t$ is the usual correction term of the effective reciprocal of inertia.