VIBRATION-ROTATION EFFECTS ON THE INTENSITIES OF WATER: APPLICATION TO $\nu_{2}$

$^{1}$S. A. Clough, Y. Beers, G. Klein, and L, S. Rothman, J. Chem. Phys. 59, 2254 (1973).Author Institution: Air Force Cambridge Research LaboratoriesThe expansion of the dipole moment projection operator as a function of the rotational operators for a type B band using the notation of clough et al.,$^{1}$ is given through third order as \begin{array}{ll}\underline{M}&={C}_{b}\Phi_{b}+{C}_{ca}\{\Phi_{c}, {P}_{a}\}+{C}_{ca}\{\Phi_{a}, {P}_{c}\}+{C}_{bbb}\{\Phi_{b}, {P}^2_{b}\}\\ &+{C}_{bbc}\{\Phi_{b}, {P}^2_{c}\}+{C}_{baa}\{\Phi_{b}, {P}^2_{a}\}+{C}_{cab}\{\Phi_{c}, \{{P}^2_{a}{P}^2_{b}\}\}\\&+{C}_{abc}\{\Phi_{c}, \{{P}_{b}{P}_{c}\}\}\end{array} for a C$_{2{v}}$ molecule. The rigid rotor line strength is obtained from [T$_{RR}(\chi)\underline{{M}} {T}_{RR}(\chi)$ where T$_{RR}$ ($\chi$)are the eigenvectors for the chosen value of In this work the correct eigenvectors of the upper and Lower states have been used for $\nu_{2}$ giving the result $\langle{T}_{010} |{M}| {T}_{000}\rangle$. Since the constants C$_{\alpha\ldots}$ appear linearly in this calculation, they may be readily obtained using a least squares method on the square root of the experimental line strengths. This procedure requires the assumption of the phase of the transition moment of the given transition. The effect of using rigid rotor and ground state eigenvectors will be discussed and A comparison of the experimentally obtained constants with theoretical values will be made