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\par {\em Ortho-para} mixing interaction due to the coupling of nuclear and electron spins was detected for the first time by millimeter-wave spectroscopy of deuterated vinyl radicals, H$2$CCD and D$2$CCD, of which the ground states are split by the tunneling motion of the $\alpha$ deuteron into two components $0+$ and $0-$, whose separations have been determined to be $\Delta E0=$ 1186.644(16) and 771.978(18) MHz, respectively. The observed tunneling-rotation spectra are significantly perturbed by the {\em othro-para} mixing interaction expressed by $\langle 0^\pm |H'|0^\mp\rangle = (\delta a_{\rm F}^{(\beta)}/2)\mbox{\boldmath $S$} \cdot(\mbox{\boldmath $I$}{\beta 1}-\mbox{\boldmath $I$}{\beta 2})$, where $\mbox{\boldmath $I$}{\beta 1}$ and $\mbox{\boldmath $I$}{\beta 2}$ are spins of the two hydrogen nuclei in the $\beta$ position and {\boldmath $S$} is the electron spin, which connects rotational levels in the $0+$ and $0-$ states, one being an {\em ortho} level and the other a {\em para} level. The $\delta aF(\beta )$ constants for H$2$CCD and D$2$CCD have been determined to be 68.06(53) and 10.63(94) MHz, respectively, consistent each other within the isotopic mass relation. The {\em othro} and {\em para} states are mixed by about 0.097% and 0.0123% due to this interaction. nderline{\textbf{131,}}~111101 (2009).} The $\delta aF$ constant for H$2$CCH should be similar to that for H$2$CCD because of the same probability density of the unpaired electron at the $\beta$ protons, but could not be determined independently in our previous study. It is because the mixing of {\em para}- and {\em ortho}-levels of about 0.00044% is much smaller than that for H$2$CCD due to the large tunneling splitting of $\Delta E0=16271.8429(59)$ MHz. nderline{\textbf{120,}}~3604 (2004).} \par The rate constant of {\em para} to {\em ortho} ($I\beta$ = 0 $\to$ 1) conversion is predicted as $1.2\times 105$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ torr$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ for H$2$CCD, suggesting extremely rapid mutual conversion between {\em ortho} and {\em para} nuclear spin isomers of H$2$CCD, which is more than 10$\mathrm{<mrow\; data-mjx-texclass="ORD">6</mrow>}$ times faster compared with that in closed shell molecules such as H$2$CO and H$2$CCH$2$.