Classical Force-Field Parameters for CsPbBr3 Perovskite Nanocrystals

Abstract

Understanding the chemico-physical properties of colloidal semiconductor nanocrystals (NCs) requires exploration of the dynamic processes occurring at the NC surfaces, in particular at the ligand-NC interface. Classical molecular dynamics (MD) simulations under realistic conditions are a powerful tool to acquire this knowledge because they have good accuracy and are computationally cheap, provided that a set of force-field (FF) parameters is available. In this work, we employed a stochastic algorithm, the adaptive rate Monte Carlo method, to optimize FF parameters of cesium lead halide perovskite (CsPbBr₃) NCs passivated with typical organic molecules used in the synthesis of these materials: oleates, phosphonates, sulfonates, and primary and quaternary ammonium ligands. The optimized FF parameters have been obtained against MD reference trajectories computed at the density functional theory level on small NC model systems. We validated our parameters through a comparison of a wide range of nonfitted properties to experimentally available values. With the exception of the NC-phosphonate case, the transferability of the FF model has been successfully tested on realistically sized systems (>5 nm) comprising thousands of passivating organic ligands and solvent molecules, just as those used in experiments.

Scheme 1. (a) Different Force-Field Components (Interactions) and Respective Descriptions in an Oleate-Capped CsPbBr₃ NC Solvated in Octadecene and (b) Adaptive Rate Monte Carlo Parametrization Workflow

Figure 1

Snapshots of the NC models parametrized in this work: (a) inorganic CsPbBr₃ core and nanocrystal models capped with (b) acetate, (c) methylphosphonate, (d) methylsulfonate, (e) methylammonium (a primary amine), and (f) trimethyl propylammonium (a quaternary amine).

Figure 2

(a) Relative errors obtained for the accepted MD iterations during the ARMC fitting, over a maximum of 1500 iterations. (b) Example of the comparison between ab initio computed RDFs (QM-MD, orange line) and classical RDFs (MM-MD, blue line), computed using the ARMC-optimized FF parameters, for the phosphonate-capped NC model at the first iteration and at the best iteration. (c) Comparison between the QM (orange line) and MM (blue line) potential of mean force computed using eq 2 from the provided RDFs. Altogether, the following ligand charges have been taken into account (in parentheses are the name types according to CHARMM FFs): for carboxylate-based acetate, the carboxylic C (C2O3) and the two oxygens (O2D2); for phosphonate, P (PG1), the two O atoms connected by a single bond (O2P1) and the oxygen connected by a double bond (O311); the charges of the sulfur atom (S3O1) and of the negatively charged oxygen atoms bound to it (O2S1) for sulfonate; the nitrogen atom (N3P3) and the hydrogens (HGP2) in the primary amine and nitrogen (N3P0) and hydrogen (HGP5) charges, as well as those of the adjacent carbon atoms C334 for the methyl and C324 for the methylene bound to the propyl group for the quaternary ammonium cation, trimethyl propylammonium.

Figure 3

Comparison between ab initio computed ADFs (QM-MD, orange line) and classical ADFs (MM-MD, blue line) for the Pb–Br–Pb angle (between two nearby octahedra), predicted using the best ARMC-optimized FF parameters, for the inorganic core and the ligand-capped NC models.

Figure 4

RMSD and RMSF plots: comparison between ab initio computed (QM-MD) and classically predicted properties using the best set of parameters fitted with the ARMC procedure (MM-MD), for the inorganic core and the ligand-capped NC models.

Figure 5

Comparison between the ADFs of the Pb–Br–Pb angle obtained for the downscaled 2.3 nm NC model capped by oleate ligands (blue plot), for the upscaled 5.0 nm NC model capped by oleate ligands (red plot) in vacuum, and for the bulk structure (green plot), plotted from MM-MD simulations obtained using the best ARMC-optimized FF parameters.