THE MOLECULAR QUADRUPOLE MOMENT AND THE SIGN OF THE ELECTRIC DIPOLE MOMENT OF WATER.

$^{\ast}$ H. Bluyssen, A. Dymanus and J. Verhoeven, Phys, Letters 24A, 482 (1967); H. Bluyssen, J. Verhoeven and A. Dymanus, ibid, 25A, 214 (1967): J. Verhoeven, H. Bluyssen and A. Dymanus, ibid, 26A, 424 (1968).Author Institution: Physical Laboratory University of Nijmegen, Nijmegen, The NetherlandsZeeman effect of the $2_{2}\rightarrow 2_{1}$ rotational transition of HDO at 10278 MHz, of the $3_{-2}\rightarrow 2_{2}$ and $4_{+3}\rightarrow 5_{1}$ transitions of $D_{2}O$ at 10919 and 10947 MHz, respectively, and of the $6_{-5}\rightarrow 5_{-1}$ transition of $H_{2}O$ at 22235 MHz was investigated with a beam-maser Zeeman spectrometer. The observed Zeeman splittings were up to 5 MHz at the maximum available field of 12 KGauss. The half-width of the lines was about 2 KHz. The interpretation of the hyperfine spectra is based on a Hamiltonian comprising both hyperfine and magnetics effects. The hyperfine Hamiltonian includes the electric quadrupole interaction of the deuteron, the direct nuclear spin-spin interaction, and the spin rotation interaction. The Zeeman Hamiltonian includes interactions of the external magnetic field with the molecular magnetic moment, with the magnetic susceptibility and with the nuclear moment including magnetic shielding. The hyperfine coupling constants were obtained from the zero-field experiments,$^{1}$ the molecular magnetic moment $gj_{r} ^{\mu}N$ and the anisotropy in the magnetic susceptibility $Xj^{2}_{r}$ were determined from the measured transitions in an external magnetic field. The isotopic part of the magnetic suceptibility and of the nuclear magnetic shielding could not be measured in this experiment while the anisotropic part of the nuclear magnetic shielding was below the present resolution. The absolute value and the sign of the electric dipole moment were obtained from the experimental values of $gj_{r}$ of $H_{2}O, D_{2}O$ and HDO and the relation between the components of the G-tensor and the electric dipole moment in the three isotopic molecules. The absolute value agrees within 15% with the value obtained from measurements on the Stark effect of several microwave transitions. This deviation may be explained by the isotopic dependence of the paramagnetic part of the molecular magnetic moment. The measurements show that the electric dipole moment is directed from the oxygen nucleons to the middle of the proton-proton bar, as can be accepted on theoretical grounds. The molecular quadrupole moment tensor can be expressed in terms of the elements of the G-tensor and the anisotropics in the magnetic susceptibility. The results for $D_{2}O$ are: $\begin{array}{l} \theta_{aa} = \quad(2.75\pm0.006) 10^{-26} esu\\ \theta_{bb} = -(0.37\pm0.11) 10^{-26} esu\\ \theta_{cc} = -(2.38\pm0.05) 10^{-26} esu \end{array}$ Details of the experiment will be given and a comparison of the results with recent ab initio calculations