Observations and analysis of molecular emission have long provided valuable insights into the interstellar medium (ISM). Hot (highly excited) molecules are commonly observed in intense UV-irradiated regions, e.g., photodissociation regions (PDRs), circumstellar envelopes (CSEs), and surface layers of protoplanetary disks (PPDs). The excitation properties of molecules directly reveal the physical conditions of the gas and thus are unique probes of these energetic environments. Particularly, low-density environments with intense UV radiation may be in non-local thermal equilibrium (NLTE), in which high excitation molecular analysis is especially of interest. For such studies, a quantitative understanding of micro-processes (e.g., collisional rate coefficients of molecular excitation, radiative transfer, etc.) is needed, while being previously limited. In this thesis, I discuss NLTE simulations of high excitation molecular emission in UV-pumped gas with state-of-the-art theoretical calculations and simulation techniques. Furthermore, a few applications of this simulation approach in realistic astrophysical environments, e.g., PDRs and circumstellar envelopes, are highlighted. This work is essential to the interpretation of highly (rotationally and vibrationally) excited molecular emission from high-resolution observational data (e.g., Spitzer, Herschel, SOFIA, ALMA, and soon from JWST), as well as opening up the near- to mid-infrared window for NLTE molecular analysis.
