Precision Measurements and Computations of Transition Energies in Rotationally Cold Triatomic Hydrogen Ions up to the Midvisible Spectral Range

First-principles computations and experimental measurements of transition energies are carried out for vibrational overtone lines of the triatomic hydrogen ion ${\mathrm{H}}_3^{+}$ corresponding to floppy vibrations high above the barrier to linearity. Action spectroscopy is improved to detect extremely weak visible-light spectral lines on cold trapped ${\mathrm{H}}_3^{+}$ ions. A highly accurate potential surface is obtained from variational calculations using explicitly correlated Gaussian wave function expansions. After nonadiabatic corrections, the floppy ${\mathrm{H}}_3^{+}$ vibrational spectrum is reproduced at the $0.1{\mathrm{cm}}^{-1}$ level up to $16600{\mathrm{cm}}^{-1}$.

Figure 1

Visible-light spectroscopy of cold trapped ${\mathrm{H}}_3^{+}$ ions for some of the measured lines detailed in Table . Top marks (full lines): present theoretical results. Orange (gray) symbols and fitted curves: fine scans (right-hand vertical scales) with Doppler-broadened line profiles (effective ion temperature $\sim 85\mathrm{K}$). Dashed marks: earlier predictions by NMT [11] and SAH03 [16] as labeled (arrows and shading indicate scale offsets). Black symbols: search scans (see the text) with breaks marked by thin vertical lines (left-hand vertical scales).

Figure 2

Differences between experimental transition energies $E_{\exp }$ and the present calculation ($E_{\mathrm{calc}}$) for the $\mathrm{BO}+\mathrm{DA}$ PES (diamonds) and for the $\mathrm{BO}+\mathrm{DA}+\mathrm{REL}$ PES plus NA corrections (asterisks). Small red asterisks and light gray diamonds: using experimental data from Refs. 12, 28, 30, 32 ($J\le 3$ initial levels); large orange asterisks and dark gray diamonds: present data with ${00}^0$ $(1,0)$ and $(1,1)$ initial levels.