MD simulation methods

We conducted MD simulations to simulate the layer-controlled CQWs of hybrid organic-inorganic PbBr₂ perovskites with the formula [CH₃(CH₂)₇NH₃]₂[CH₃NH₃PbBr₃]_nPbBr₄, where n is the layer number of perovskite unit cells. Because the layer-controlled CQWs were constructed by 2D CH₃NH₃PbBr₃ perovskite with capping ligand octylammonium [CH₃(CH₂)₇NH₃⁺] layers, a recently developed classical interatomic potential (force field) (52) for bulk CH₃NH₃PbBr₃ perovskite was used to describe the interatomic interactions in the layer structures. This potential has been demonstrated to reasonably reproduce the dynamic [that is, relaxation time of organic cation CH₃NH₃⁺ (MA)] and structural (that is, lattice constants and phase transition) properties of bulk CH₃NH₃PbBr₃ perovskite. Following the assisted model building with energy refinement (AMBER) force field (53) used to describe interactions within MA cations, we used AMBER to model the intermolecular and intramolecular interactions within the CH₃(CH₂)₇NH₃⁺ ligands in these 2D CH₃NH₃PbBr₃ perovskites, as well as to model the organic solvent toluene. The atomic partial charges within these ligands and toluene molecules were determined from quantum chemistry calculations and Mulliken population analysis with the B3LYP/6-31G* basis set using the Gaussian 09 software package (54).

Using the above force field, all the MD simulations of these CH₃NH₃PbBr₃-based CQWs were carried out using the massively parallelized LAMMPS (Large-Scale Atomic/Molecular Massively Parallel Simulator) package (55) at 300 K. The molecular models of individual CQW dispersed in toluene (colloidal solutions) and aggregated CQWs (lamellar solids) were built with n = 3. Periodic boundary conditions were applied along all the directions. Two different surface coverages (50 and 75%) of ligands for CQWs were taken into account as well to explore their impacts on the orientational distribution of surface organic MA cations. A simulation time step of 1 fs was chosen for all the MD simulations here. The particle-particle particle-mesh (PPPM) method (56) was used here to treat long-range Coulombic interactions via the reciprocal space because the PPPM method is significantly faster than the regular particle Ewald summation method (57). To obtain the initial equilibrium state, these molecular models were first relaxed for 500 ps under the NVT ensemble after energy minimization. Only aggregated CQWs were equilibrated for another 400 ps under the NPT ensemble (58) with a high pressure of 2000 bar along the stacking direction, to obtain the fully packed aggregated CQW structures. All the molecular models were then equilibrated further for 2000 ps under the NPT ensemble with a pressure of 1 bar along all the directions to reach full equilibrium states.

After structural equilibration, the atomistic trajectories of surface MA cations were extracted every 20 fs during a period of 100 ps to explore their collective motions. The molecular orientation of MA cation, n^, is defined by the vector connecting the N-C backbone. A spherical coordinate system is used, with the polar axis along the z direction, as well as in-plane azimuthal (φ) and polar (θ) angles (see Fig. 3B). The instantaneous molecular orientation n^ can be determined from the above two angles via n^=(sinθcosφ,sinθsinφ,cosθ) (59), which corresponds to a single point in the (φ, z = cosθ) plane. Therefore, the molecular orientations of MA cations can be represented by the orientational distribution contour map (φ, θ) of MA cations from the collected trajectories. Note that we corrected the solid-angle biasing effect on the orientational distribution with respect to the polar angle θ by dividing the probability distribution by sin θ. Because only pseudocubic-phase CH₃NH₃PbBr₃ perovskites are stable at 300 K, the following crystallographic directions are identical to each other: [100] ≡ [010] ≡ [001] and [110] ≡ [101] ≡ [011].