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Amino acids are essential to all life. However, our understanding of some aspects of their intrinsic structure, molecular chemistry, and electronic structure is still limited. In particular the nature of amino acids in their crystalline form, often essential to biological and medical processes, faces a lack of knowledge both from experimental and theoretical approaches. An important experimental technique that has provided a multitude of crucial insights into the chemistry and electronic structure of materials is X-ray photoelectron spectroscopy. Whilst the interpretation of spectra of simple bulk inorganic materials is often routine, interpreting core level spectra of complex molecular systems is complicated to impossible without the help of theory. We have previously demonstrated the ability of density functional theory to calculate binding energies of simple amino acids, using $Δ$SCF implemented in a systematic basis set for both gas phase (multiwavelets) and solid state (plane waves) calculations. In this study, we use the same approach to successfully predict and rationalise the experimental core level spectra of phenylalanine (Phe), tyrosine (Tyr), tryptophan (Trp), and histidine (His) and gain an in-depth understanding of their chemistry and electronic structure within the broader context of more than 20 related molecular systems. The insights gained from this study provide significant information on the nature of the aromatic amino acids and their conjugated side chains.