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The chemical characterisation of exoplanet atmospheres plays a crucial role in profoundly enriching our comprehension of exoplanets. By deciphering the array of molecular species shaping the chemical composition of a given exoplanet atmosphere, we unlock invaluable insights into its chemical evolution, climate, physical dynamics, and even its potential for harbouring life. High-resolution molecular spectroscopy provides the fundamental data needed for robustly identifying molecules in exoplanet atmospheric spectra, as recorded from ground- and/or space-based telescopes. However, the availability of high-resolution molecular spectroscopic data is limited, given its intensive and time-consuming generation process, involving costly quantum chemistry calculations and exhaustive experimental measurements. By the time this thesis was submitted, the repository of high-resolution infrared molecular spectroscopic data encompasses around 100 molecular species. This constrain considerably hinders the scope of new molecular detections in exoplanet atmospheres; if there is no spectroscopic data for a given molecule, we simply cannot find it. To address this challenge, this thesis introduces a pioneering approach that complements the traditional method for generating high-resolution molecular spectroscopic data. By leveraging routine quantum chemistry calculations, specifically harmonic frequency calculations, this research provides a high-throughput method to rapidly generate approximate vibrational spectral data for thousands of potential biosignature molecules. This thesis is organised into two main themes. Firstly, it focuses on refining harmonic frequency calculations for large-scale spectral data generation. Previous research lacked comprehensive benchmarking, making it difficult for users to choose appropriate levels of theory and basis set pairs (aka model chemistries) for these calculations. This work addresses such limitation by performing an extensive evaluation of over 600 model chemistries using a newly developed vibrational frequency benchmark data set. The findings from this work highlight the B97-1/def2-TZVPD model chemistry for its exceptional balance between accuracy and computational cost. Indeed, a median error of 10 cm-1 is expected in the calculated harmonic frequencies after scaling, along with good transition intensity predictions due to its accurate dipole moment calculations. With the optimised harmonic frequency calculations in place, the second theme of the thesis focuses on generating approximate spectral data for thousands of astrochemistry-relevant molecules, specifically potential biosignatures. Employing an automated high-throughput approach, this thesis produces approximate vibrational spectra for 2743 molecules, most of which had limited, or completely absent, spectroscopic data available in the literature. While these approximate spectral data are not accurate enough to enable definitive molecular detections in exoplanet atmospheres, and cannot replace the generation of high-resolution spectroscopic data, they have powerful applications in identifying potential molecular candidates responsible for unknown spectral features. This application is firstly explored using the SO2 detection in the atmospheric spectrum of WASP-39b as a proof-of-concept, and then applied to shortlist potential molecular candidates to the 4.25 microns (2352 cm-1) spectral feature in the same spectrum, which by the time this thesis was submitted had not been assigned to any molecular species yet. Beyond screening potential molecular candidates to unknown spectral features, this large-scale approximate spectral data generation offers broader applications, such as identifying molecules with strong absorption features that may be detectable at low abundances, and serving as a training set for machine learning predictions of vibrational frequencies. The approximate spectral data generated in this thesis will play a crucial role in supporting our understanding of the chemical composition of exoplanet atmospheres. By highlighting potential candidates to unknown spectral features, this approach seeks to complement the generation of high-resolution molecular spectroscopic data, directing attention towards prioritised molecules warranting meticulous data acquisition. This synergy between approximate and high-resolution spectroscopic data will certainly amplify our potential to unveil the chemical composition of exoplanet atmospheres, providing directions into possible initial identifications of the more unusual molecules to emerge.