  Amorphous red phosphorus (a-P) is one of the remaining puzzling cases in the
structural chemistry of the elements. Here, we elucidate the structure,
stability, and chemical bond-ing in a-P from first principles, combining
machine-learning and density-functional theo-ry (DFT) methods. We show that a-P
structures exist with a range of energies slightly higher than those of
phosphorus nanorods, to which they are closely related, and that the stability
of a-P is linked to the degree of structural relaxation and medium-range order.
We thus complete the stability range of phosphorus allotropes [Angew. Chem.
Int. Ed. 2014, 53, 11629] by now including the previously poorly understood
amorphous phase, and we quantify the covalent and van der Waals interactions in
all main phases of phos-phorus. We also study the electronic densities of
states, including those of hydrogenated a-P. Beyond the present study, our
structural models are expected to enable wider-ranging first-principles
investigations - for example, of a-P-based battery materials.
