Excitonic Properties of Monolayer Black Phosphorus: Critical Role of Electronic Exchange

Recent interest in monolayer black phosphorus (ML-BP) as a promising 2D material for optoelectronic and solar energy harvesting applications stimulated the state-of-the-art characterization of the static and dynamic properties of excitons this material can support. Computational characterization of the exciton binding energy and nonradiative dynamics of excitons are the two key conundrums. In this work, we investigate the applicability of time-dependent density functional theory (TD-DFT) combined with hybrid density functionals as a methodology to capture strong quantum confinement effects in ML-BP and describe its exciton binding energies and excited state properties. We find remarkable positive correlations between the fraction of exact (Hartree–Fock) exchange in hybrid density functionals and the magnitudes of the optical gap, exciton binding energy, and degree of configurational mixing in the pseudowave functions describing bright excitons. As the fraction of the Hartree–Fock exchange increases, the weight of the leading single-particle configuration generally decreases and the corresponding single-particle transition is more likely to involve energetically more-distant orbitals. It also increases the degree of electron and hole charge density overlap, while it has a minor effect on the localization of the corresponding natural transition orbitals. Our findings establish a conceptual framework for understanding the performance of various hybrid functionals in modeling excitonic effects and nonradiative dynamics of excitons. Pragmatically, our judicious assessment of seven popular hybrid functionals suggests that PBE0 and B3LYP functionals used with the TD-DFT framework are the most suitable for capturing excitonic effects in the ML-BP.