Knowledge Bank

The method of laser-induced reaction} {\bf 127} (2007) Art. No. 154317.} has been used for the first time to detect rotational transitions. The astronomically important $101-000$ and $111-000$ transitions of H$2$D$+$ and HD$\mathrm{2+}$, respectively, have been recorded by observing the enhancement of their D/H isotope exchange reactions with $p$-H$2$ upon rotational excitation in a cryogenic multipole ion trap. While the frequency for HD$\mathrm{2+}$ is in good agreement with a previous, unpublished result,} {\bf 233} (2005) 7.} but more accurate, the frequency for H$2$D$+$ is some 60,MHz lower than the value from the same unpublished source ($b$). The present H$2$D$+$ frequency has been fit together with previously published pure rotational transitions and with infrared ground state combination differences (GSCDs).} {\bf 364} (2006) 2943.} Starting values for spectroscopic parameters were derived from energies up to $J=Ka=7$ calculated ab initio} {\bf 157} (1993) 237; J. Ramanlal and J. Tennyson, {\it Mon. Not. R. Astron. Soc.} {\bf 354} (2004) 161.} because of the smallness of the data set. Since the molecular ion is fairly floppy, the Hamiltonian has been expanded in Euler functions} {\bf 233} (2005) 174.} up to 6th order. Omitting one GSCD because of a large residual, the remaining GSCDs were reproduced to almost 0.002,cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ releasing only 7 parameters. Thus, for the first time this IR spectroscopic data has been reproduced within experimental uncertainties. The pure rotational transitions were fit overall within the reported experimental uncertainties. In Ref.~$c$ the wrong $101-000$ transition frequency required 11 parameters to fit the pure rotational transitions within experimental uncertainties, albeit with somewhat larger residuals for the GSCDs than in the present work.