A Comprehensive First-Principles Investigation of Bulk and Layered Phosphorus α and β Allotropes: From Ground-State to Excited-State Properties

We present a comparative study of the geometric, electronic, and optical properties of black phosphorus (α-P) and blue phosphorus (β-P) in both multilayer and bulk forms. A combined computational approach was employed, in which structural and electronic properties were obtained from periodic DFT calculations, while excited-state properties were evaluated using time-dependent DFT (TD-DFT) on finite clusters embedded in point-charge arrays to reproduce the periodic electrostatic environment. Our results show that α-P exhibits a relatively low exfoliation energy and a layer-dependent direct band gap, whereas β-P has a very low exfoliation energy, even lower than graphite, and an indirect but more pronounced layer-dependent band gap. In contrast to α-P, β-P presents significantly larger hole masses compared to the electron ones, suggesting lower electron and hole recombination in the latter than in the former. Simulated UV–Vis spectra indicate that while both bulk α-P and β-P show strong absorption in the visible range, more pronounced differences are obtained between the multilayered structures of these two phosphorus phases. Overall, the proposed computational protocol provides and efficient and reliable framework for modeling the structural, electronic and optical properties of phosphorus allotropes both in bulk and multilayer forms. The present results suggest that certain β-P multilayer systems may be of interest for applications where electron-dominated transport or reduced recombination rates are desirable, such as in selected photovoltaic or photocatalytic contexts, while recognizing that charge transport limitations must be carefully considered in practical device implementations.