In halide perovskites, photocarriers can have strong polaronic interactions with point defects. For iodide-deficient MAPbI3, we found that the Fermi level can shift significantly by 0.6-0.7 eV upon light illumination. This energy level shift is accompanied by the formation of deep electron traps. These experimental observations are consistent with the formation of a Pb-Pb dimer when photoexcited electrons are trapped at an iodide vacancy. Interestingly, we found that this polaronic interaction is suppressed when a portion of MA+ cations is replaced by smaller Cs+ ions. Density functional theory calculations reveal that Cs-doping can reduce the distance between two Pb atoms across an iodide vacancy, even without electron trapping. The predistortion of the lattice induced by cation replacement resembles the Pb-Pb dimer formed by electron trapping at the defect site, which explains the suppression of light-induced effects observed in the experiment. Our finding unveils a counterintuitive strategy to enhance the photostability of halide perovskites by preintroducing distortions into its lattice.

Metal halide perovskites (MHPs) have attracted strong interest for a variety of applications due to their low cost and excellent performance, attributed largely to favorable defect properties. MHPs exhibit complex dynamics of charges and ions that are coupled in unusual ways. Focusing on a combination of two common MHP defects, i.e., a grain boundary (GB) and a Pb interstitial, we developed a machine learning model of the interaction potential, and studied the structural and electronic dynamics on a nanosecond timescale. We demonstrate that point defects at MHP GBs can create new chemical species, such as Pb-Pb-Pb trimers, that are less likely to occur with point defects in bulk. The formed species create structural instabilities in the GB and prevent it from healing towards the pristine structure. Pb-Pb-Pb trimers produce deep trap states that can persist for hundreds of picoseconds, having a strong negative influence on the charge carrier mobility and lifetime. Such stable chemical defects at MHP GBs can only be broken by chemical means, e.g., the introduction of excess halide, highlighting the importance of proper defect passivation strategies. Long-lived GB structures with both deep and shallow trap states are found, rationalizing the contradictory statements in the literature regarding the influence of MHP GBs on performance.

Ternary I-III-VI2 semiconductors, such as CuInSe2, exhibit diverse polymorphs with unique structural characteristics and optoelectronic properties. This study investigates the pressure-induced phase transitions of metastable wurtzite-like CuInSe2 nanocrystals. Using a combination of synchrotron X-ray diffraction, pair distribution function analysis, and density functional theory calculations, we reveal a transition from cation-ordered wurtzite-like (Pmc21) to cation-disordered NaCl-like (Fm3̅m) structures at 7.7 GPa. The cation-disordered NaCl-like phase persists upon decompression. Bulk modulus calculations highlight size-dependent deviations from bulk material behavior. These findings deepen our understanding of phase stability in colloidal I-III-VI2 semiconductor nanocrystals, with implications for tailoring functional materials under extreme conditions.

Controlling charge transport at the interfaces of nanostructures is crucial for their successful use in optoelectronic and solar energy applications. Mixed-dimensional heterostructures based on single-walled carbon nanotubes (SWCNTs) and transition metal dichalcogenides (TMDCs) have demonstrated exceptionally long-lived charge-separated states. However, the factors that control the charge transport at these interfaces remain unclear. In this study, we directly image charge transport at the interfaces of single- and multilayered MoS2 and (6,5) SWCNT heterostructures using transient absorption microscopy. We find that charge recombination becomes slower as the layer thickness of MoS2 increases. This behavior can be explained by electron delocalization in multilayers and reduced orbital overlap with the SWCNTs, as suggested by nonadiabatic (NA) molecular dynamics (MD) simulations. Dipolar repulsion of interfacial excitons results in rapid density-dependent transport within the first 100 ps. Stronger repulsion and longer-range charge transport are observed in heterostructures with thicker MoS2 layers, driven by electron delocalization and larger interfacial dipole moments. These findings are consistent with the results from NAMD simulations. Our results suggest that heterostructures with multilayer MoS2 can facilitate long-lived charge separation and transport, which is promising for applications in photovoltaics and photocatalysis.

Metal halide perovskites (MHP) have attracted great attention in the photovoltaic industry due to their high and rapidly rising power conversion efficiencies, currently over 25%. However, hybrid organic-inorganic MHPs are inherently chemically unstable, limiting their application. All-inorganic MHPs perovskites, such as CsPbI3, have many merits, but their stable conversion efficiency is lower, around 18%, due to a larger band gap causing a mismatch with the solar spectrum. Choosing α-CsPbI3 as a prototypical system, we demonstrate a new general concept of dynamic defects that fluctuate between deep and shallow states, and increase the range of absorbed solar photons, without accelerating the nonradiative electron-hole recombination. In their deeper energy state, the defects narrow the band gap and allow the harvesting of light with longer wavelengths. Fluctuating to shallower energies, the defects allow the escape of photogenerated charges into bands, enabling charge transport and resulting in the defect-mediated upconversion of thermal energy into electricity. Defect covalency and participation of low-frequency anharmonic vibrations decouple trapped charges from free charge carriers, minimizing nonradiative charge carrier losses. Our findings demonstrate that defect covalency and defect dynamics are unique and important properties of MHPs, and can be used to optimize MHPs for efficient solar energy harvesting and optoelectronic applications.

The polycrystalline nature of perovskites, stemming from their facile solution-based fabrication, leads to a high density of grain boundaries (GBs) and point defects. However, the impact of GBs on perovskite performance remains uncertain, with contradictory statements found in the literature. We developed a machine learning force field, sampled GB structures on a nanosecond time scale, and performed nonadiabatic (NA) molecular dynamics simulations of charge carrier trapping and recombination in stoichiometric and doped GBs. The simulations reveal long, microsecond carrier lifetimes, approaching experimental data, stemming from charge separation at the GBs and small NA coupling, 0.01-0.1 meV. Stoichiometric GBs exhibit transient trap states, which, however, are not particularly detrimental to the carrier lifetime. Halide dopants form interstitial defects in the bulk, but have a stabilizing influence on the GB structure by passivating undersaturated Pb atoms and reducing the transient trap state formation. On the contrary, excess Pb destabilizes GBs, allowing formation of persistent midgap states that trap charges. Still, the charge carrier lifetime reduces relatively little, because the midgap states decouple from the bands, and charges are more likely to escape back into bands upon a GB structural fluctuation. The atomistic study into the structural dynamics of perovskite GBs and its influence on charge carrier trapping and recombination provides valuable insights into the complex properties of perovskites and the intricate role of GBs in the material performance.

Metal halide perovskites (MHPs) exhibit unusual properties and complex dynamics. By combining ab initio time-dependent density functional theory, nonadiabatic molecular dynamics and machine learning, we advance quantum dynamics simulation to nanosecond timescale and demonstrate that large fluctuations of MHP defect energy levels extend light absorption to longer wavelengths and enable trapped charges to escape into bands. This allows low energy photons to contribute to photocurrent through energy up-conversion. Deep defect levels can become shallow transiently and vice versa, altering the traditional defect classification into shallow and deep. While defect levels fluctuate more in MHPs than traditional semiconductors, some levels, e.g., Pb interstitials, remain far from band edges, acting as charge recombination centers. Still, many defects deemed detrimental based on static structures, are in fact benign and can contribute to energy up-conversion. The extended light harvesting and energy up-conversion provide strategies for design of novel solar, optoelectronic, and quantum information devices.

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.

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

Nonadiabatic molecular dynamics (NA-MD) is a powerful tool to model far-from-equilibrium processes, such as photochemical reactions and charge transport. NA-MD application to condensed phase has drawn tremendous attention recently for development of next-generation energy and optoelectronic materials. Studies of condensed matter allow one to employ efficient computational tools, such as density functional theory (DFT) and classical path approximation (CPA). Still, system size and simulation timescale are strongly limited by costly ab initio calculations of electronic energies, forces, and NA couplings. We resolve the limitations by developing a fully machine learning (ML) approach in which all the above properties are obtained using neural networks based on local descriptors. The ML models correlate the target properties for NA-MD, implemented with DFT and CPA, directly to the system structure. Trained on small systems, the neural networks are applied to large systems and long timescales, extending NA-MD capabilities by orders of magnitude. We demonstrate the approach with dependence of charge trapping and recombination on defect concentration in MoS 2 . Defects provide the main mechanism of charge losses, resulting in performance degradation. Charge trapping slows with decreasing defect concentration; however, recombination exhibits complex dependence, conditional on whether it occurs between free or trapped charges, and relative concentrations of carriers and defects. Delocalized shallow traps can become localized with increasing temperature, changing trapping and recombination behavior. Completely based on ML, the approach bridges the gap between theoretical models and realistic experimental conditions and enables NA-MD on thousand-atom systems and many nanoseconds.

Hematite (alpha-Fe2O3) is a typical semiconducting transition metal oxide that exhibits attractive properties for photoelectrochemical (PEC) water splitting and other applications. However, it has been widely reported that charge recombination in alpha-Fe2O3 photoanodes is a serious problem, hindering further improvement in the efficiency of PEC water splitting. We used ab initio nonadiabatic molecular dynamics (NAMD) to investigate the charge recombination in bulk and surface phases of alpha-Fe2O3. The NAMD simulations employ the decoherence-induced surface hopping (DISH) method implemented within time-dependent density functional theory. We test and demonstrate the need to incorporate both the phase-consistency correction and the all-electron calculation of the NA coupling, the latter needed for transition metals with d-shell electrons. The NAMD simulations show that the time scale of intrinsic charge recombination in bulk alpha-Fe2O3 can reach microseconds, in accordance with the existence of long-lived photogenerated charge carriers observed in transient absorption measurements on alpha-Fe2O3 electrodes. However, the hydroxylated iron-termination of the alpha-Fe2O3(0001) surface, one of the most stable alpha-Fe2O3 surfaces in aqueous solution, exhibits a much faster charge recombination, about 1 order of magnitude faster compared to bulk alpha-Fe2O3. The key factor for the fast charge recombination in the surface can mainly be assigned to the strong fluctuations in the NAC and the energy gap between the conduction band minimum (CBM) and valence band maximum (VBM) and the quantum anti-Zeno effect. This work extends the charge recombination dynamics from bulk phase to aqueous interfacial phase of alpha-Fe2O3, approaching the PEC reaction conditions, and thus assists in understanding of the charge dynamics underlying the oxygen evolution reaction (OER) at the Fe2O3-water interface and design of new efficient Fe2O3-based photoanode materials.

Two-dimensional graphitic carbon nitride (GCN) is a popular metal-free polymer for sustainable energy applications due to its unique structure and semiconductor properties. Dopants and defects are used to tune GCN, and dual defect modified GCN exhibits superior properties and enhanced photocatalytic efficiency in comparison to pristine or single defect GCN. We employ a multistep approach combining time-dependent density functional theory and nonadiabatic molecular dynamics (NAMD) with machine learning (ML) to investigate coupled structural and electronic dynamics in GCN over a nanosecond timescale, comparable to and exceeding the lifetimes of photo-generated charge carriers and photocatalytic events. Although frequent hydrogen hopping transitions occur among four tautomeric structures, the electron-hole separation and recombination processes are only weakly sensitive to the tautomerism. The charge separated state survives for about 10 ps, sufficiently long to enable photocatalysis. The employed ML-NAMD methodology provides insights into rare events that can influence excited state dynamics in the condensed phase and nanoscale materials and extends NAMD simulations from pico- to nanoseconds. The ab initio quantum dynamics simulation provides a detailed atomistic mechanism of photoinduced evolution of charge carriers in GCN and rationalizes how GCN remains photo-catalytically active despite its multiple isomeric and tautomeric forms.

Weaker than ionic and covalent bonding, van der Waals (vdW) interactions can have a significant impact on structure and function of molecules and materials, including stabilities of conformers and phases, chemical reaction pathways, electro-optical response, electron-vibrational dynamics, etc. Metal halide perovskites (MHPs) are widely investigated for their excellent optoelectronic properties, stemming largely from high defect tolerance. Although MHPs are primarily ionic compounds, we demonstrate that vdW interactions contribute ∼5% to the total energy, and that static, dynamics, electronic and optical properties of point defects in MHPs depend significantly on the vdW interaction model used. Focusing on widely studied CsPbBr3 with the common Br vacancy and interstitial defects, we compare the PBE, PBE+D3, PBE+TS, PBE+TS/HI and PBE+MBD-NL models and show that vdW interactions strongly alter the global and local geometric structure, and change the fundamental bandgap, midgap state energies and electron-vibrational coupling. The vdW interaction sensitivity stems from involvement of heavy and highly polarizable chemical elements and the soft MHP structure.

Metal halide perovskites (MHPs) have attracted attention because of their high optoelectronic performance that is fundamentally rooted in the unusual properties of MHP defects. By developing an ab initio-based machine-learning force field, we sample the structural dynamics of MHPs on a nanosecond time scale and show that halide vacancies create midgap trap states in the MHP bulk but not on a surface. Deep traps result from Pb-Pb dimers that can form across the vacancy in only the bulk. The required shortening of the Pb-Pb distance by nearly 3 Å is facilitated by either charge trapping or 50 ps thermal fluctuations. The large-scale structural deformations are possible because MHPs are soft. Halide vacancies on the MHP surface create no deep traps but separate electrons from holes, keeping the charges mobile. This is particularly favorable for MHP quantum dots, which do not require sophisticated surface passivation to emit light and blink less than quantum dots formed from traditional inorganic semiconductors.

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

Essential for understandingfar-from-equilibrium processes,nonadiabatic(NA) molecular dynamics (MD) requires expensive calculations of theexcitation energies and NA couplings. Machine learning (ML) can simplify computation; however, the NA Hamiltonian requires complex ML modelsdue to its intricate relationship to atomic geometry. Working directlyin the time domain, we employ bidirectional long short-term memorynetworks (Bi-LSTM) to interpolate the Hamiltonian. Applying this multiscaleapproach to three metal-halide perovskite systems, we achieve twoorders of magnitude computational savings compared to direct ab initiocalculation. Reasonable charge trapping and recombination times areobtained with NA Hamiltonian sampling every half a picosecond. TheBi-LSTM-NAMD method outperforms earlier models and captures both slowand fast time scales. In combination with ML force fields, the methodologyextends NAMD simulation times from picoseconds to nanoseconds, comparableto charge carrier lifetimes in many materials. Nanosecond samplingis particularly important in systems containing defects, boundaries,interfaces, etc. that can undergo slow rearrangements.

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.

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.

Supervised machine learning (ML) and unsupervised ML have been performed on descriptors generated from nonadiabatic (NA) molecular dynamics (MD) trajectories representing non-radiative charge recombination in CsPbI3, a promising solar cell and optoelectronic material. Descriptors generated from every third atom of the iodine sublattice alone are sufficient for a satisfactory prediction of the bandgap and NA coupling for the use in the NA-MD simulation of nonradiative charge recombination, which has a strong influence on material performance. Surprisingly, descriptors based on the cesium sublattice perform better than those of the lead sublattice, even though Cs does not contribute to the relevant wavefunctions, while Pb forms the conduction band and contributes to the valence band. Simplification of the ML models of the NA-MD Hamiltonian achieved by the present analysis helps to overcome the high computational cost of NA-MD through ML and increase the applicability of NA-MD simulations.

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.