Phosphine is now well-established as a biosignature, which has risen to prominence with its recent tentative detection on Venus. To follow up this discovery and related future exoplanet biosignature detections, it is important to spectroscopically detect the presence of phosphorus-bearing atmospheric molecules that could be involved in the chemical networks producing, destroying or reacting with phosphine. We start by enumerating phosphorus-bearing molecules (P-molecules) that could potentially be detected spectroscopically in planetary atmospheres and collecting all available spectral data. Gaseous P-molecules are rare, with speciation information scarce. Very few molecules have high accuracy spectral data from experiment or theory; instead, the best current spectral data was obtained using a high-throughput computational algorithm, RASCALL, relying on functional group theory to efficiently produce approximate spectral data for arbitrary molecules based on their component functional groups. Here, we present a high-throughput approach utilizing established computational quantum chemistry methods (CQC) to produce a database of approximate infrared spectra for 958 P-molecules. These data are of interest for astronomy and astrochemistry (importantly identifying potential ambiguities in molecular assignments), improving RASCALL's underlying data, big data spectral analysis and future machine learning applications. However, this data will probably not be sufficiently accurate for secure experimental detections of specific molecules within complex gaseous mixtures in laboratory or astronomy settings. We chose the strongly performing harmonic ωB97X-D/def2-SVPD model chemistry for all molecules and test the more sophisticated and time-consuming GVPT2 anharmonic model chemistry for 250 smaller molecules. Limitations to our automated approach, particularly for the less robust GVPT2 method, are considered along with pathways to future improvements. Our CQC calculations significantly improve on existing RASCALL data by providing quantitative intensities, new data in the fingerprint region (crucial for molecular identification) and higher frequency regions (overtones, combination bands), and improved data for fundamental transitions based on the specific chemical environment. As the spectroscopy of most P-molecules have never been studied outside RASCALL and this approach, the new data in this paper is the most accurate spectral data available for most P-molecules and represent a significant advance in the understanding of the spectroscopic behavior of these molecules.