Exfoliation Energy of Black Phosphorus Revisited: A Coupled Cluster Benchmark

Black phosphorus (black-P) consists of phosphorene sheets, stacked by van der Waals dispersion. In a recent study based on periodic local second-order Møller-Plesset perturbation theory (LMP2) with higher-order corrections evaluated on finite clusters, we obtained a value of -151 meV/atom for the exfoliation energy. This is almost twice as large as another recent theoretical result (around -80 meV/atom) obtained with quantum Monte Carlo (QMC). Here, we revisit this system on the basis of the recently implemented, periodically embedded ring coupled cluster (rCCD) model instead of LMP2. Higher-order coupled cluster corrections on top of rCCD are obtained from finite clusters by utilizing our new "unit-cell-in-cluster" scheme. Our new value of -92 meV/atom is noticeably lower than that based on LMP2 and in reasonably close agreement with the QMC result. However, in contrast to QMC, no strong effect from the second-neighbor and farther layers in black-P are observed in our calculations.