New high precision linelist of H3+

As the simplest polyatomic molecule, H$_3^+$ serves as an ideal benchmark for theoretical predictions of rovibrational energy levels. By strictly \textit{ab initio} methods, the current accuracy of theoretical predictions is limited to an impressive one hundredth of a wavenumber,\footnote{O.~L. Polyansky, \textit{et al.} \emph{Phil. Trans. R. Soc. A} (2012), \textbf{370}, 5014--5027.} which has been accomplished by consideration of relativistic, adiabatic, and non-adiabatic corrections to the Born-Oppenheimer PES. More accurate predictions rely on a treatment of quantum electrodynamic effects, which have improved the accuracies of vibrational transitions in molecular hydrogen to a few MHz.\footnote{J. Komasa, \emph{et al.} \emph{J. Chem. Theor. Comp.} (2011), \textbf{7}, 3105--3115.} High precision spectroscopy is of the utmost importance for extending the frontiers of \textit{ab initio} calculations, as improved precision and accuracy enable more rigorous testing of calculations. Additionally, measuring rovibrational transitions of H$_3^+$ can be used to predict its forbidden rotational spectrum. Though the existing data can be used to determine rotational transition frequencies, the uncertainties are prohibitively large.\footnote{C.~M. Lindsay, B.~J. McCall, \emph{J. Mol. Spectrosc.} (2001), \textbf{210}, 66--83.} Acquisition of rovibrational spectra with smaller experimental uncertainty would enable a spectroscopic search for the rotational transitions. The technique Noise Immune Cavity Enhanced Optical Heterodyne Velocity Modulation Spectroscopy, or NICE-OHVMS has been previously used to precisely and accurately measure transitions of H$_3^+$, CH$_5^+$, and HCO$^+$ to sub-MHz uncertainty.\footnote{J.~N. Hodges, \textit{et al.} \emph{J. Chem. Phys.} (2013), \textbf{139}, 164201.} A second module for our optical parametric oscillator has extended our instrument's frequency coverage from 3.2-3.9 $\mu$m to 2.5-3.9 $\mu$m. With extended coverage, we have improved our previous linelist by measuring additional transitions