Many modern functional materials exhibit microscopic degrees of freedom that are difficult to describe mathematically or do not conform to conventional models in solid state physics. In this paper, we consider crystals containing orientable molecular species, which encompass the class of promising photovoltaic materials ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbX}}_3$. Abstracting these materials as crystals of orientable rigid rotors, we develop an effective Hamiltonian that expresses the crystal potential energy in terms of collective orientations of interacting rigid rotors. The approach is motivated by the cluster expansion framework from alloy theory and is appropriate for describing both chiral and achiral molecules. This framework utilizes a quaternion parametrization of molecular orientation and makes full use of the symmetry both of the rotors and of the crystal in order to constrain the functional form of the final Hamiltonian expression. The resulting Hamiltonian is compact, systematically improvable, and is suitable for Monte Carlo or molecular dynamics simulation. We apply this formalism to ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ and report symmetry-adapted basis functions that can be used to construct order parameters or Hamiltonians that describe orientational correlation of methylammonium ions in hybrid organic-inorganic halide perovskite materials.

• Received 18 April 2018

DOI:https://doi.org/10.1103/PhysRevB.98.094105