Orientational Disorder and Molecular Correlations in Hybrid Organic-Inorganic Perovskites: From Fundamental Insights to Technological Applications

Abstract

Hybrid organic-inorganic perovskites (HOIP) have emerged in recent years as highly promising semiconducting materials for a wide range of optoelectronic and energy applications. Nevertheless, the rotational dynamics of the organic components and many-molecule interdependencies, which may strongly impact the functional properties of HOIP, are not yet fully understood. In this study, we quantitatively analyze the orientational disorder and molecular correlations in archetypal perovskite CH₃NH₃PbI₃ (MAPI) by performing comprehensive molecular dynamics simulations and entropy calculations. We found that, in addition to the usual vibrational and orientational contributions, rigid molecular rotations around the C-N axis and correlations between neighboring molecules noticeably contribute to the entropy increment associated with the temperature-induced order-disorder phase transition, ΔS_t. Molecular conformational changes are equally infrequent in the low-T ordered and high-T disordered phases and have a null effect on ΔS_t. Conversely, the couplings between the angular and vibrational degrees of freedom are substantially reinforced in the high-T disordered phase and significantly counteract the phase-transition entropy increase resulting from other factors. Furthermore, the tendency for neighboring molecules to be orientationally ordered is markedly local, consequently inhibiting the formation of extensive polar nanodomains at both low and high temperatures. This theoretical investigation not only advances the fundamental knowledge of HOIP but also establishes physically insightful connections with contemporary technological applications like photovoltaics, solid-state cooling, and energy storage.

Keywords: entropy calculations; hybrid organic–inorganic perovskites; molecular correlations; molecular dynamics simulations; molecular rotational dynamics.

Figure 1

MAPI unit cell and MA molecule angular coordinates. (a) Sketch of MAPI in the high-temperature cubic perovskite phase. MA molecules are orientationally disordered. (b) Angles definition for describing the orientation of MA molecules. Angles θ and ϕ describe the orientation of the molecular C–N axis. Angle ψ refers to the rotation of the molecule around its C–N axis. (c) Dihedral angle describing the conformations of a MA molecule. Hydrogen, carbon, and nitrogen atoms are represented with white, green, and blue spheres, respectively.

Figure 2

VDOS and vibrational entropy (S_vib) of MAPI calculated at different temperatures. VDOS results were obtained (a) for the ordered phase at T = 240 K and (b) for the disordered phase at T = 245 K. (c) Vibrational entropy of MAPI expressed as a function of temperature.

Figure 3

VDOS of MAPI in the low-frequency range. (a) Total VDOS for the ordered phase at T = 240 K and disordered phase at T = 245 K. (b) Inorganic contribution to the total VDOS for the ordered phase at T = 240 K and disordered phase at T = 245 K. (c) Organic contribution to the total VDOS for the ordered phase at T = 240 K and disordered phase at T = 245 K. To improve the visualization, a change of scale has been applied on the coordinate axis of this figure.

Figure 4

Bivariate angular probability density function (pdf) for MA molecules in the low-T ordered phase. Results were obtained at T = 240 K in the (a) lab-fixed (“lab”) and (b) molecule-mobile (“rel”) reference systems. For the “rel” case, the six MA cations within the first coordination shell were considered. Red, green, and blue colors represent high-probability, medium-probability, and low-probability configurations, respectively.

Figure 5

Bivariate angular probability density function (pdf) for MA molecules in the high-T disordered phase. Results were obtained at T = 260 K in the (a) lab-fixed (“lab”) and (b) molecule-mobile (“rel”) reference systems. For the “rel” case, the six MA cations within the first coordination shell were considered. Red, green, and blue colors represent high-probability, medium-probability, and low-probability configurations, respectively.

Figure 6

Dynamical description of the MA cation orientation around its C–N axis and molecular conformations for the low-temperature ordered phase. Time evolution of (a) the azimuthal angle ψ_lab describing the MA⁺ rotation around its C–N axis and (b) the dihedral angle ε_dih describing molecular conformation (Figure 1).

Figure 7

Dynamical description of the MA cation orientation around its C–N axis and molecular conformations for the high-temperature disordered phase. Time evolution of (a) the dihedral angle ε_dih describing molecular conformation, and the rest of MA angles (b) ϕ_lab, (c) θ_lab, and (d) ψ_lab describing molecular orientation (Figure 1).

Figure 8

Angular probability density function (pdf) for the molecular dihedral angle ε_dih describing the conformation of MA molecules. Results are represented for the low-T ordered (red circles) and high-T disordered (black squares) phases. Solid lines are guides to the eye.

Figure 9

Probability density function (pdf) for the molecular dipole orientation in the coMobile (“rel”) reference system obtained across successive coordination shells. Results obtained for (a) first, (b) second, (c) third, and (d) fourth coordination shells. Orange and green bars represent results obtained for the low-temperature ordered and high-temperature disordered phases, respectively.

Figure 10

Probability distribution function (pdf) for the number of molecules in the first coordination shell of a MA cation that are parallel and antiparallel to it. Results were obtained by averaging over all molecules and simulation time. Pdf corresponding to (a) parallel and (b) antiparallel relative molecular dipole orientations (black and red boxes). The crosses in the figures represent analogous results obtained for a random distribution of relative molecular dipole orientations.