High pressure chemistry has enjoyed a long and fruitful tradition dating back to the early 20th century. Through the strong changes that extreme pressure brings to the table, it has been proven to be an invaluable tool to develop new materials, control chemical reactions and fine‑tune properties. Despite this long tradition, the field of chemical reactivity has mainly been devoted to thermodynamics and the effects of volume changes, while electronic effects have enjoyed comparatively less attention. These electronic properties are the focus of this thesis and are computed through the extension of the conceptual density functional theory (CDFT) framework. To model the effects of pressure, the extreme pressure polarizable continuum model (XP‑PCM) is applied at the DFT level of theory. Atomic properties were considered for the elements hydrogen to krypton in the pressure range up to 50 GPa. Starting from the ionization potential and electron affinity, the electronegativity and hardness were found to decrease and increase respectively, with rising pressure. The known relationship between the cube of the softness (S³) and the polarizability (α) was confirmed and the electrophilicity was evaluated, but found to be inappropriate to describe reactivity at high pressure. Next, the electron densities were analysed using radial distribution functions (RDFs), the Carbo Quantum Similarity Index (QSI) and the Kullback‑Leibler information deficiency (∆SKL). A clear shift of electron density from the outer to inner regions was found for atoms, with a maximum decrease at the cavity boundary, which marks the spatial border between the molecule and the medium in the XP‑PCM model. Using the Carbo QSI and ∆SKL, a recurrent decrease in the periodic table was retrieved. Finally, some preliminary data on the compressibility of the H2 bond were obtained.