Knowledge Bank

A new approach to the determination of the dipole moment of asymmetric top molecules will be discussed. The contribution to the energy of a molecule in a given vibration-rotation state due to the presence of an electric field, $ϵ$, in the z direction may be written as $E=2Ea+4E8$ where the superscripts indicate the order of magnitude of the contribution. The second order Stark energy, $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}Es$, is given by \begin{equation}^{2}{E}=\Sigma_{g}{g}{\mu{e}}^{2}{C}_{\pi{g}}\epsilon^{2}\end{equation} where $g\mu e$ is the dipole moment in the $molecularg$ direction which is independent of isotopic substitution and vib-rotational state and $Czg$ is determined from the direction cosine operator evaluated in the energy representation. The fourth order contribution, $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}E8$, is a result of three considerations: (1) the variation of the effective dipole moment with vib-rotational state; (2) the polarizability of the molecule; and (3) the fourth order correction to the second order calculation for $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}E8$. The fourth order contribution is subtracted from the observed frequencies and the resultant quantities are fitted to Eq. (1) using the method of least squares to obtain $g\mu e$. This approach has been applied to water molecule using two transitions in $H2O$ and three transitions in $HDO2$.