Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of compute time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multi-element complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermalisobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

Dielectric constants of MAPbX3 (X = Br, I) in the 1 kHz–1 MHz range show strong temperature dependence near room temperature, in contrast to the nearly temperature-independent dielectric constant of CsPbBr3. This strong temperature dependence for MAPbX3 in the tetragonal phase is attributed to the MA+ dipoles rotating freely within the probing time scale. This interpretation is supported by ab initio molecular dynamics simulations on MAPbI3 that establish these dipoles as randomly oriented with a rotational relaxation time scale of ∼7 ps at 300 K. Further, we probe the intriguing possibility of transient polarization of these dipoles following a photoexcitation process with important consequences on the photovoltaic efficiency, using a photoexcitation pump and second harmonic generation efficiency as a probe with delay times spanning 100 fs–1.8 ns. The absence of a second harmonic signal at any delay time rules out the possibility of any transient ferroelectric state under photoexcitation.

The high efficiency of lead organo-metal-halide perovskite solar cells has raised many questions about the role of the methylammonium (MA) molecules in the Pb-I framework. Experiments indicate that the MA molecules are able to 'freely' spin around at room temperature even though they carry an intrinsic dipole moment. We have performed large supercell (2592 atoms) finite temperature ab-initio molecular dynamics calculations to study the correlation between the molecules in the framework. An underlying long range anti-ferroelectric ordering of the molecular dipoles is observed. The dynamical correlation between neighboring molecules shows a maximum around room temperature in the mid-temperature phase. In this phase, the rotations are slow enough to (partially) couple to neighbors via the Pb-I cage. This results in a collective motion of neighboring molecules in which the cage acts as the mediator. At lower and higher temperatures the motions are less correlated.PACS numbers: 61.50. Ah, The spectacular rise of perovskite photovoltaics 1 has sparked much research effort into the physical mechanisms behind these materials' good photovoltaic performance. From a solid state physics perspective, the answer seems simple: the well suited electronic structure of methylammonium lead-iodide (MAPbI 3 ). With a band gap of ∼1.6 eV 2-6 and a high absorption coefficient 2,5,6 , it is expected to be a high efficiency solar cell material for the solar radiation spectrum observed on earth.7 Density Functional Theory (DFT) calculations have shown that an s-p mixture in the valence band maximum (VBM) and p-states in the conduction band minimum (CBM), combined with a direct band gap lead to an absorption coefficient up to an order of magnitude higher than GaAs.8 However, the crystal structure of MAPbI 3 is completely different from GaAs. It even possesses temperature depended dynamical contributions arising from the organic constituent. The perovskite structure of MAPbI 3 is composed of three iodine atoms (monovalent anions) combined with a lead atom (divalent cation) and a CH 3 NH 3 (MA) molecule (monovalent cation). The Pb-I framework forms the perovskite structure out of PbI 6 octahedra and the molecules are trapped in the cavities. Whether the cubic perovskite structure is stable or becomes orthorhombic or tetragonal is determined by the temperature 6 combined with a balance between the size of the molecule and the Pb-I bond length.9 NMR experiments have indicated that at high temperatures (>300 K) the MA molecule exhibits complete orientational disorder.10,11 This means that the MA molecules have enough kinetic energy to overcome the rotational barriers and can rotate in their 'cage'. Around room temperature this process has a typical relaxation time of ∼ 5 ps.12 These rotations apparently do not effect the charge carriers in the system, since very long electronhole diffusion lengths have been reported. 13,14 From an electronic point of view this is not surprising, because the Pb-I framework is electronically decoupled from the m...

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)-an accurate many body theory-is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI_{3}, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI_{3}, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

The phonon dispersion relations of crystal lattices can often be well described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in the case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with machine-learning force fields of near-first-principles accuracy. Through large-scale molecular dynamics simulations the projected velocity autocorrelation function (PVACF) is obtained. We apply this approach to the inorganic perovskite CsPbBr 3 . Imaginary modes in the harmonic picture of this perovskite are absent in the PVACF, indicating a dynamic stabilization of the crystal. The anharmonic nature of the potential makes a decoupling of the system into a weakly interacting phonon gas impossible. The phonon spectra of CsPbBr 3 show the characteristics of a phonon liquid. Rattling motions of the Cs + cations are studied by self-correlation functions and are shown to be nearly dispersionless motions of the cations with a frequency of ∼0.8 THz within the lead-bromide framework.