Theoretical calculations of the nuclear quadrupole coupling in the spectra of D 3+, H 2D +, and HD 2+

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The present paper reports a purely theoretical calculation of the quadrupole hyperfine structure in the rotation-vibration spectra of D 3 +, H 2D +, and HD 2 +. As the initial step in the calculation we have computed ab initio extensive sets of electric field gradient values for these molecules. These ab initio values are used, together with rotation-vibration wavefunctions obtained using the rotation-vibration theory developed previously for X 3 and Y 2 X equilateral triangular molecules [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan, J. Mol. Spectrosc. 112, 183–202 (1985); P. Jensen, V. Špirko, and P. R. Bunker, J. Mol. Spectrosc. 115, 269–293 (1986)] to obtain the quadrupole splitting parameters for the individual rotation-vibration states of the molecules in question. We have calculated actual quadrupole splittings for selected transitions of H 2D + and HD 2 + and find these to be less than 100 kHz. Laboratory measurements of these small splittings would require sub-Doppler resolution and do not seem feasible at the present time. Even in cold interstellar clouds H 2D + lines certainly have widths larger than the calculated splittings so that interstellar detection of the splittings is impossible. Clearly in the present study theory is very far ahead of experiment. One might hope that in a not-too-distant future experimental techniques will be developed which allow the observation of the small splittings.