  The structural relaxation of multilayer graphene is essential in describing
the interesting electronic properties induced by intentional misalignment of
successive layers, including the recently reported superconductivity in twisted
bilayer graphene. This is difficult to accomplish without an accurate
interatomic potential. Here, we present a new, registry-dependent
Kolmogorov-Crespi type interatomic potential to model interlayer interactions
in multilayer graphene structures. It consists of two parts representing
attractive interaction due to dispersion, and repulsive interaction due to
anisotropic overlap of electronic orbitals. An important new feature is a
dihedral-angle-dependent term that is added to the repulsive part in order to
describe correctly several distinct stacking states that the original
Kolmogorov-Crespi potential cannot distinguish. We refer to the new model as
the Dihedral-angle-corrected Registry-dependent Interlayer Potential (DRIP).
Computations for several test problems show that DRIP correctly reproduces the
binding, sliding, and twisting energies and forces obtained from ab initio
total-energy calculations based on density functional theory. We use the new
potential to study the structural properties of a twisted graphene bilayer and
the exfoliation of graphene from graphite. Our potential is available through
the OpenKIM interatomic potential repository at https://openkim.org.
