Vibrational Spectroscopy Of H₂he⁺ And D₂he⁺

Vibrational modes of the relatively strongly bound H$_2$He$^+$ molecular ion and its deuterated congener D$_2$He$^+$ are investigated by low-resolution multi-photon photodissociation spectroscopy, using a combination of a 4~K cryogenic ion-trap machine and the free electron laser FELIX. The band origins obtained are fully explained by accurate variational calculations of the rovibrational states based on the three-dimensional potential energy surface of Koner \textit{et al.} [Phys.\ Chem.\ Chem.\ Phys.\ {\bf 21} (2019) 24976]. Results from second-order vibrational perturbation theory, based on a linear H--H--He equilibrium structure, agree well with those of the variational calculations for energy levels up to about 1300~cm$^{-1}$. The low-resolution experiments corroborate the linear structure of the ions and identify the bright IR-active HH-stretch fundamental in H$_2$He$^+$ at about 1840~cm$^{-1}$ and the DD-stretch fundamental in H$_2$He$^+$ at about 1309~cm$^{-1}$. The calculations also reveal the H$_2^+$--He bend and stretch fundamentals to be at 640 and 732~cm$^{-1}$ and the D$_2^+$--He bend and stretch fundamentals at 478 and 641~cm$^{-1}$, respectively. A short outlook is given on future high-resolution experiments