On the exfoliation and anisotropic thermal expansion of black phosphorus†
Black phosphorus is a bulk solid allotrope of elemental phosphorus and can be seen as an infinite stack of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [M. Schütz, L. Maschio, A. J. Karttunen and D. Usvyat, J. Phys. Chem. Lett., 2017, 8, 1290–1294] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppresses London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional, we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations, however, do not support the existence of negative thermal expansion in black phosphorus, as reported in some theoretical studies.