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Present address of David J. Finnigan: Dept. of Chemistry, Harvard University, Cambridge, Mass. 02138 $^{1}$ A.P. Cox, A.H. Brittain and M. J. Whittle, J. Mol. Spectr., 35, 49 (1970). $^{2}$ M. L. Grenier-Besson and G. Amat, J. Mol. Spectr., 8, 22 (1962)."" ; Author Institution: School of Chemistry, The University ; An analysis of the microwave spectrum of the $C_{5v}$ molecule $C_{5}H_{5}NiNO$ in the first excited state, $v_{14} = 1$, of the lowest $E_{1}$ vibration has been $reported.^{1}$ A perturbation formula was used, analogous to that derived by Grenier-Besson and $Amat^{2}$ for $C_{3v}$ molecules. The present communication by describes the analysis of higher excited states, $v_{14} = {2,3}$ and 4, where perturbation techniques are inadequate due to strong accidental $\ell$-type resonances. Considering only the $\langle\ell,K|h^{\prime}_{2}|\ell\pm2,K\pm2\rangle$ off-diagonal elements, the energy matrices can be factorized into submatrices of maximum order $(v+1)$. This factorization facilitates the diagonalization of the energy matrices and hence computation of the microwave frequencies. The usual vibration-rotation constants have been determined by a non-linear least squares treatment together with the anharmonic constant, $x_{\ell_{t} \ell_{t}}$ associated with $\ell$-type resonance for$\ v > 1$. For $C_{3v}$ molecules in the absence of r-type resonances involving the $\langle 2,-1 \rangle$ elements the same factorization is proposed. This enables the analytical procedure outlined above to be applied, thus accounting accurately for $\ell$-type resonance where perturbation methods prove inadequate. This treatment facilitates the analysis of higher excited states, but is often required for $v_{t} = 1$ when ${_{q}}[J(J+1)]/2\sim|B-A+A\xi|$. Such is the case for $CF_{3}CN$ and an analysis for $v_{8} = 1$ and 2 will be reported. |