The quadrupole moment of the carbon dioxide molecule

A direct measurement of the magnitude and sign of the quadrupole moment of the carbon dioxide molecule has been made by determining the birefringence induced in gaseous CO$_2$ by an inhomogeneous electric field. The method of measurement and the experimental details are described. The observable is the product of the molecular quadrupole moment $\Theta$ and the difference between parallel and perpendicular components of the optical polarizability tensor, $\Theta$($\alpha_{\|}$ -$\alpha_\bot$). For CO$_2$, this quantity was found to have the value -(9.1 $\pm$ 0.5) x 10$^{-50}$ e.s.u. $\alpha_{\|}$ -$\alpha_\bot$ can be determined by other methods, but unfortunately the present uncertainty in this quantity is greater than that of the product $\Theta$($\alpha_{\|}$ - $\alpha_\bot$). The most satisfactory value of $\alpha_{\|}$ - $\alpha_\bot$ is taken to be 2.2 x 10$^{-24}$ cm$^3$, giving for the molecular quadrupole moment of CO$_2$ -4.1 x 10$^{-26}$ e.s.u., the sign indicating that the oxygen atoms are negative with respect to the carbon atom. The role of the `quadrupole polarizability' of the molecule in complicating the interpretation of the experimental results is discussed, and experiments on argon and sulphur hexafluoride used to provide an estimate of its effect in the case of CO$_2$.