Knowledge Bank

Recent increases in accuracy of triatomic molecular energy level calculations for high rotational quantum numbers J is reviewed. Variational calculations which use exact kinetic energy operators can treat all vibrational states simultaneously. These calculations can use high quality ab initio and fitted potential energy surfaces. For spectroscopic accuracy on hydrogen containing molecules, it is necessary to include adiabatic and nonadiabatic corrections to the Born-Oppenheimer approximation. Relativistic corrections can also be important. Application of the resulting calculations of energy levels and spectra to the analysis of seemingly unassignable spectra of water and $H3+$ is described. Spectra of water in sunspot $(T\sim 3200K)$, laboratory $(T\sim 1600K)$ and even room temperature contain hundreds or thousands of lines which remained unassigned for more than a decade (see for example Polyansky et al., Science, v. 277, N5324, pp. 346-348 (1997)). We present here the results of the assignments of these water lines. $H3-$ line assignment is also considered as well as progress on $H2S,NO2,O3$ and the analysis of the spectra of other triatomic molecules.