Knowledge Bank

``The fourth--order vibration-rotation interaction constants $\rho$ which specify the variation of the quartic centrifugal distortion constants with vibrational state appear in the vibration-rotation Hamiltonian in terms of the form $$ {1/4\tau_{\alpha\alpha\alpha\alpha} +\sum\limits_{k} \rho^{(k)}{\alpha\alpha\alpha\alpha}(v{k}+1/2)}\ \ {J}^{4}{\alpha},\quad\quad\quad \alpha=x,y,z,\ \leftline{and}\$$ $${1/4\tau{\alpha\alpha\beta\beta} +\sum\limits_{k} \rho^{(k)}{\alpha\alpha\beta\beta}(v{k}+1/2)}\ \ ({J}^{2}{\alpha} {J}^{2}{\beta}+{J}^{2}{\beta}{J}^{2}{\alpha})\quad\quad\quad\alpha,\beta=x,y \ or \ y,z \ or \ z,x, $$ where the $\tau \prime s$ are the well-know second order equilibrium centrifugal distortion constants, k enumerates normal modes, and $J\alpha$ and $J\beta$ are angular momentum operators, We have determined algebraic expressions for the complete set of the above $\rho$ constants in terms of fundamental molecular parameters on the basis of the Darling-Dennison model Hamiltonian and with the aid of a recently described $algorithm.1$ the results can be readily specified to the $C2v$ triatomic case which will be emphasized in our presentation. Modifications necessitated by accidental Coriolis resonance, especially between $\nu 1$ and $\nu 3$ in triatomics, remain to be studied. We hope to eventually be able to calculate $\rho$ constants for selected triatomic molecules and compare these to the corresponding empirical values.