Dependence between Structural and Electronic Properties of CsPbI3: Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics

Identifying Rare Events in Quantum Molecular Dynamics of Nanomaterials with Outlier Detection Indices

Nanoscale and condensed matter systems evolve on multiple length- and time-scales, and rare events such as local phase transformation, ion segregation, defect migration, interface reconstruction, and grain boundary sliding can have a profound influence on material properties. We demonstrate how outlier detection indices can be used to identify rare events in machine-learning based, high-dimensional molecular dynamics (MD) simulations. Designed to order data-points from typical to untypical, the indices enable one to capture atomic events that are hard to detect otherwise. We demonstrate the approach with a nanosecond MD simulation of a grain boundary in a metal halide perovskite that is extensively studied for solar energy and optoelectronic applications. The method captures the initial grain boundary sliding and a spontaneous fluctuation half a nanosecond later, both events giving rise to persistent deep electronic trap states that impact charge carrier lifetime and transport and material performance. The approach offers a generalizable and simple method for identifying outlier events in complex condensed matter, molecular, and nanoscale systems.

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

Exploring the Global Reaction Coordinate for Retinal Photoisomerization: A Graph Theory-Based Machine Learning Approach

Unraveling the reaction pathway of photoinduced reactions poses a great challenge owing to its complexity. Recently, graph theory-based machine learning combined with nonadiabatic molecular dynamics (NAMD) has been applied to obtain the global reaction coordinate of the photoisomerization of azobenzene. However, NAMD simulations are computationally expensive as they require calculating the nonadiabatic coupling vectors at each time step. Here, we showed that ab initio molecular dynamics (AIMD) can be used as an alternative to NAMD by choosing an appropriate initial condition for the simulation. We applied our methodology to determine a plausible global reaction coordinate of retinal photoisomerization, which is essential for human vision. On rank-ordering the internal coordinates, based on the mutual information (MI) between the internal coordinates and the HOMO energy, NAMD and AIMD give a similar trend. Our results demonstrate that our AIMD-based machine learning protocol for retinal is 1.5 times faster than that of NAMD to study reaction coordinates.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

Nuclear Quantum Effects Accelerate Charge Recombination but Boost the Stability of Inorganic Perovskites in Mild Humidity

Experiments have demonstrated that mild humidity can enhance the stability of the CsPbBr3 perovskite, though the underlying mechanism remains unclear. Utilizing ab initio molecular dynamics, ring polymer molecular dynamics, and non-adiabatic molecular dynamics, our study reveals that nuclear quantum effects (NQEs) play a crucial role in stabilizing the lattice rigidity of the perovskite while simultaneously shortening the charge carrier lifetime. NQEs reduce the extent of geometric disorder and the number of atomic fluctuations, diminish the extent of hole localization, and thereby improve the electron-hole overlap and non-adiabatic coupling. Concurrently, these effects significantly suppress phonon modes and slow decoherence. As a result, these factors collectively accelerate charge recombination by a factor of 1.42 compared to that in scenarios excluding NQEs. The resulting sub-10 ns recombination time scales align remarkably well with experimental findings. This research offers novel insight into how moisture resistance impacts the stability and charge carrier lifetime in all-inorganic perovskites.

Estimating Nonradiative Excited-State Lifetimes in Photoactive Semiconducting Nanostructures

The time evolution of the exciton generated by light adsorption in a photocatalyst is an important feature that can be approached from full nonadiabatic molecular dynamics simulations. Here, a crucial parameter is the nonradiative recombination rate between the hole and the electron that form the exciton. In the present work, we explore the performance of a Fermi's golden rule-based approach on predicting the recombination rate in a set of photoactive titania nanostructures, relying solely on the coupling of the ground and first excited state. In this scheme the analysis of the first excited state is carried out by invoking Kasha's rule thus avoiding computationally expensive nonadiabatic molecular dynamics simulations and resulting in an affordable estimate of the recombination rate. Our results show that, compared to previous ones from nonadiabatic molecular dynamics simulations, semiquantitative recombination rates can be predicted for the smaller titania nanostructures, and qualitative values are obtained from the larger ones. The present scheme is expected to be useful in the field of computational heterogeneous photocatalysis whenever a complex and computationally expensive full nonadiabatic molecular dynamics cannot be carried out.

Lattice Distortion and Low-Frequency Anharmonic Phonons Suppress Charge Recombination in Lead Halide Perovskites upon Pseudohalide Doping: Time-Domain Ab Initio Analysis

Perovskite solar cells have witnessed a surge in interest as a promising technology for low-cost, high-efficiency photovoltaics with certified power conversion efficiencies beyond 25%. However, their commercial development is hindered by poor stability and nonradiative losses that restrict their approach to the theoretical efficiency limit. Using ab initio nonadiabatic molecular dynamics, we demonstrate that nonradiative charge recombination is suppressed when the iodide in formamidinium lead iodide (FAPbI3) is partially replaced with pseudohalide anions (SCN-, BF4-, and PF6-). The replacement breaks the symmetry of the system and creates local structural distortion and dynamic disorder, decreasing electron-hole overlap and nonadiabatic electron-vibrational coupling. The charge carrier lifetime is found to increase with increased structural distortion and is the longest for PF6-. This work is fundamentally relevant to the design of high-performance perovskite materials for optoelectronic applications.

Fluctuations at Metal Halide Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis

All-inorganic perovskites are promising candidates for solar energy and optoelectronic applications, despite their polycrystalline nature with a large density of grain boundaries (GBs) due to facile solution-processed fabrication. GBs exhibit complex atomistic structures undergoing slow rearrangements. By studying evolution of the Σ5(210) CsPbBr₃ GB on a nanosecond time scale, comparable to charge carrier lifetimes, we demonstrate that GB deformations appear every ∼100 ps and increase significantly the probability of deep charge traps. However, the deep traps form only transiently for a few hundred femtoseconds. In contrast, shallow traps appear continuously at the GB. Shallow traps are localized in the GB layer, while deep traps are in a sublayer, which is still distorted from the pristine structure and can be jammed in unfavorable conformations. The GB electronic properties correlate with bond angles, with notable exception of the Br-Br distance, which provides a signature of halide migration along GBs. The transient nature of trap states and localization of electrons and holes at different parts of GBs indicate that charge carrier lifetimes should be long. At the same time, charge mobility can be reduced. The complex, multiscale evolution of geometric and electronic structures of GBs rationalize the contradictory statements made in the literature regarding both benign and detrimental roles of GBs in perovskite performance and provide new atomistic insights into perovskite properties.

Structural Disorder in Higher-Temperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites

Solar cells and optoelectronic devices are exposed to heat that degrades performance. Therefore, elucidating temperature-dependent charge carrier dynamics is essential for device optimization. Charge carrier lifetimes decrease with temperature in conventional semiconductors. The opposite, anomalous trend is observed in some experiments performed with MAPbI₃ (MA = CH₃NH₃⁺) and other metal halide perovskites. Using ab initio quantum dynamics simulation, we establish the atomic mechanisms responsible for nonradiative electron-hole recombination in orthorhombic-, tetragonal-, and cubic MAPbI₃. We demonstrate that structural disorder arising from the phase transitions is as important as the disorder due to heating in the same phase. The carrier lifetimes grow both with increasing temperature in the same phase and upon transition to the higher-temperature phases. The increased lifetime is rationalized by structural disorder that induces partial charge localization, decreases nonadiabatic coupling, and shortens quantum coherence. Inelastic and elastic electron-vibrational interactions exhibit opposite dependence on temperature and phase. The partial disorder and localization arise from thermal motions of both the inorganic lattice and the organic cations and depend significantly on the phase. The structural deformations induced by thermal fluctuations and phase transitions are on the same order as deformations induced by defects, and hence, thermal disorder plays a very important role. Since charge localization increases carrier lifetimes but inhibits transport, an optimal regime maximizing carrier diffusion can be designed, depending on phase, temperature, material morphology, and device architecture. The atomistic mechanisms responsible for the enhanced carrier lifetimes at elevated temperatures provide guidelines for the design of improved solar energy and optoelectronic materials.

The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics

The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.

Great Influence of Organic Cation Motion on Charge Carrier Dynamics in Metal Halide Perovskite Unraveled by Unsupervised Machine Learning

Unsupervised machine learning combined with time-dependent density functional theory reveals the significant influence of organic cation on the charge carrier lifetime of FAPbI₃ (FA = HC(NH₂)₂⁺) by analyzing their mutual information (MI) between the geometric features and the nonadiabatic coupling (NAC) and bandgap. Analysis of MI values demonstrates that the NAC and bandgap are dominated by the orientation and shape of the inorganic octahedron because iodine and lead atoms are composed of the band edge states. Counterintuitively, the correlated motion promotes the contribution of the FA cation to the NAC; in particular, one type of FA rotation even supersedes the influence of the velocities of the lead and iodine atoms due to the enhanced hydrogen bond interaction. Our study demonstrates the importance of the correlated motion on the excited-state lifetimes of FAPbI₃, which provides a guidance for optimizing the optoelectronic properties of metal halide perovskites.

Quantum machine learning for chemistry and physics

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

Electron-Volt Fluctuation of Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale

Metal halide perovskites (MHPs) have gained considerable attention due to their excellent optoelectronic performance, which is often attributed to unusual defect properties. We demonstrate that midgap defect levels can exhibit very large and slow energy fluctuations associated with anharmonic acoustic motions. Therefore, care should be taken classifying MHP defects as deep or shallow, since shallow defects may become deep and vice versa. As a consequence, charges from deep levels can escape into bands, and light absorption can be extended to longer wavelengths, improving material performance. The phenomenon, demonstrated with iodine vacancy in CH₃NH₃PbI₃ using a machine learning force field, can be expected for a variety of defects and dopants in many MHPs and other soft inorganic semiconductors. Since large-scale anharmonic motions can be precursors to chemical decomposition, a known problem with MHPs, we propose that materials that are stiffer than MHPs but softer than traditional inorganic semiconductors, such as Si and TiO₂, may simultaneously exhibit excellent performance and stability.

Point Defects in Two-Dimensional Ruddlesden-Popper Perovskites Explored with Ab Initio Calculations

Two-dimensional Ruddlesden-Popper (RP) halide perovskites stand out as excellent layered materials with favorable optoelectronic properties for efficient light-emitting, spintronic, and other spin-related applications. However, properties often determined by defects are not well understood in these perovskite systems. This work investigates the ground state electronic structure of commonly formed defects in a typical RP perovskite structure by density functional theory. Our study reveals that these 2D perovskites generally retain their defect tolerance with limited perturbation of the electronic structure in the case of neutral-type point defects. In contrast, donor/acceptor defects induce deep midgap states, potentially causing harm to the material's electronic performance. To retain positive intrinsic properties, the halide vacancies and interstitial defects should be avoided. The observed strong electron localization results in trap states and consequently leads to reduced device performance. This understanding can guide experimental efforts that aim for improved 2D halide perovskite-based device performance.

Ag-Bi Charge Redistribution Creates Deep Traps in Defective Cs2AgBiBr6: Machine Learning Analysis of Density Functional Theory

Lead-free double perovskites hold promise for stable and environmentally benign solar cells; however, they exhibit low efficiencies because defects act as charge recombination centers. Identifying trap-assisted loss mechanisms and developing defect passivation strategies constitute an urgent goal. Applying unsupervised machine learning to density functional theory and nonadiabatic molecular dynamics, we demonstrate that negatively charged Br vacancies in Cs₂AgBiBr₆ create deep hole traps through charge redistribution between the adjacent Ag and Bi atoms. Vacancy electrons are first accepted by Bi and then shared with Ag, as the trap transforms from shallow to deep. Subsequent charge losses are promoted by Ag and Bi motions perpendicular to rather than along the Ag-Bi axis, as can be expected. In contrast, charge recombination in pristine Cs₂AgBiBr₆ correlates most with displacements of Cs atoms and Br-Br-Br angles. Doping with In to replace Ag at the vacancy maintains the electrons at Bi and keeps the trap shallow.

Collective Motion Improves the Stability and Charge Carrier Lifetime of Metal Halide Perovskites: A Phonon-Resolved Nonadiabatic Molecular Dynamics Study

By implementing a novel algorithm that realizes the constraints of certain normal modes of interest and using nonadiabatic molecular dynamics for the CsPbBr₃, we explicitly demonstrate for the first time that the collective motion between the Cs atom and inorganic octahedra facilitates to delay the nonradiative recombination of negative and positive charges. The Cs atoms can instantaneously respond to the motion of Pb and Br atoms during normal molecular dynamics, maintain the perovskite structure, and homogenize the structural distortion caused by thermal fluctuations, thus decreasing nonadiabatic coupling and charge recombination. In contrast, the perovskite becomes unstable because geometry distortion is strongly localized when the normal modes of Cs atoms are constrained, which increases the nonadiabatic coupling and accelerates charge recombination. The study emphasizes the important role of correlated motion on the stability and charge-phonon dynamics in metal halide perovskites.

Correlated organic-inorganic motion enhances stability and charge carrier lifetime in mixed halide perovskites

Organic cations are believed to have little influence on the charge carrier lifetime in hybrid organic-inorganic perovskites. Experiments defy this expectation. We consider formamidinium lead iodide (FAPbI₃) doping with and without Br as two prototypical systems, and perform ab initio time-domain nonadiabatic (NA) molecular dynamics simulations to investigate nonradiative electron-hole recombination. The simulations demonstrate that correlated organic-inorganic motion stabilizes the lattice and inhibits nonradiative charge recombination in FAPbI₃ upon Br doping. Br doping suppresses the rotation of FA and the vibrations of both organic and inorganic components, and leads to hole localization and the extent of localization is enhanced upon thermal impact, notably reducing the NA coupling by decreasing the overlap between the electron and hole wave functions. Doping also slightly increases the bandgap for further decreasing NA coupling and enhances the open-circuit voltage of perovskite solar cells. The small NA coupling and large bandgap beat the slow coherence loss, delaying electron-hole recombination and extending the charge carrier lifetime to 1.5 ns in Br-doped FAPbI₃, which is on the order of 1.1 ns in pristine FAPbI₃. The obtained time scales are in good agreement with experiments. Multiple phonon modes, including those of both the inorganic and organic components, couple to the electronic subsystem and accommodate the excess electronic energy lost during nonradiative charge recombination. The study reveals the unexpected atomistic mechanisms for the reduction of electron-hole recombination upon Br doping, rationalizes the experiments, and advances our understanding of the excited-state dynamics of perovskite solar cells.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Inverse Fast Fourier Transform

Nonadiabatic (NA) molecular dynamics (MD) allows one to investigate far-from-equilibrium processes in nanoscale and molecular materials at the atomistic level and in the time domain, mimicking time-resolved spectroscopic experiments. Ab initio NAMD is limited to about 100 atoms and a few picoseconds, due to computational cost of excitation energies and NA couplings. We develop a straightforward methodology that can extend ab initio quality NAMD to nanoseconds and thousands of atoms. The ab initio NAMD Hamiltonian is sampled and interpolated along a trajectory using a Fourier transform, and then, it is used to perform NAMD with known algorithms. The methodology relies on the classical path approximation, which holds for many materials and processes. To achieve a complete ab initio quality description, the trajectory can be obtained using an ab initio trained machine learning force field. The method is demonstrated with charge carrier trapping and relaxation in hybrid organic-inorganic and all-inorganic metal halide perovskites that exhibit complex dynamics and are actively studied for optoelectronic applications.

Extending the Time Scales of Nonadiabatic Molecular Dynamics via Machine Learning in the Time Domain

A novel methodology for direct modeling of long-time scale nonadiabatic dynamics in extended nanoscale and solid-state systems is developed. The presented approach enables forecasting the vibronic Hamiltonians as a direct function of time via machine-learning models trained directly in the time domain. The use of periodic and aperiodic functions that transform time into effective input modes of the artificial neural network is demonstrated to be essential for such an approach to work for both abstract and atomistic models. The best strategies and possible limitations pertaining to the new methodology are explored and discussed. An exemplary direct simulation of unprecedentedly long 20 picosecond trajectories is conducted for a divacancy-containing monolayer black phosphorus system, and the importance of conducting such extended simulations is demonstrated. New insights into the excited states photophysics in this system are presented, including the role of decoherence and model definition.

Significance of the Chemical Environment of an Element in Nonadiabatic Molecular Dynamics: Feature Selection and Dimensionality Reduction with Machine Learning

Using supervised and unsupervised machine learning (ML) on features generated from nonadiabatic (NA) molecular dynamics (MD) trajectories under the classical path approximation, we demonstrate that mutual information with the NA Hamiltonian can be used for feature selection and model simplification. Focusing on CsPbI₃, a popular metal halide perovskite, we observe that the chemical environment of a single element is sufficient for predicting the NA Hamiltonian. The conclusion applies even to Cs, although Cs does not contribute to the relevant wave functions. Interatomic distances between Cs and I or Pb and the octahedral tilt angle are the most important features. We reduce a typical 360-parameter ML force-field model to just a 12-parameter NA Hamiltonian model, while maintaining a high NA-MD simulation quality. Because NA-MD is a valuable tool for studying excited state processes, overcoming its high computational cost through simple ML models will streamline NA-MD simulations and expand the ranges of accessible system size and simulation time.