Hamiltonians and order parameters for crystals of orientable molecules

Abstract

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 CH 3 NH 3 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 parameterization 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 CH 3 NH 3 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.

Stability of Prismatic and Octahedral Coordination in Layered Oxides and Sulfides Intercalated with Alkali and Alkaline-Earth Metals

“…Because some configurations are mechanically unstable, the intercalant ordering and host type (O1, O3, and P3) of each relaxed structure was determined using a mapping score that accounts for lattice deformation and atomic displacements. 42 Also, calculations that failed to meet electronic or ionic convergence criteria were discarded.…”

Mapping skyrmion stability in uniaxial lacunar spinel magnets from first principles

“…We construct the magnetic cluster expansion following a methodology similar to that described by Thomas and Van der Ven [23,25,26]. Our cluster expansion of the internal energy only includes magnetic degrees of freedom, where the moment on each M 4 tetrahedron is represented by a 3-dimensional unit vector.…”

Long-range order imposed by short-range interactions in methylammonium lead iodide: Comparing point-dipole models to machine-learning force fields

“…The presence of the reorienting molecules makes it difficult to apply models used for other perovskites, like BaTiO 3 25 . Therefore point-dipole (pd) based model Hamiltonians 24,[26][27][28][29][30][31][32][33] , a rigid rotor cluster expansion 34 and classical force fields 35,36 have been designed. Often pd-models have been constructed in such a way that the heat capacity as function of temperature and/or phase transitions resemble experimental data.…”