*Phys Rev Lett ; 124(20): 206001, 2020 May 22.*

##### RESUMO

We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian, and subsequently, the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian, and the conductivity increases with applied field. This nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady states.

*J Chem Phys ; 152(23): 230901, 2020 Jun 21.*

##### RESUMO

We present a perspective on recent observations of the photoinduced phase separation of halides in multi-component lead-halide perovskites. The spontaneous phase separation of an initial homogeneous solid solution under steady-state illumination conditions is found experimentally to be reversible, stochastic, weakly dependent on morphology, yet strongly dependent on composition and thermodynamic state. Regions enriched in a specific halide species that form upon phase separation are self-limiting in size, pinned to specific compositions, and grow in number in proportion to the steady-state carrier concentration until saturation. These empirical observations of robustness rule out explanations based on specific defect structures and point to the local modulation of an existing miscibility phase transition in the presence of excess charge carriers. A model for rationalizing existing observations based on the coupling between composition, strain, and charge density fluctuations through the formation of polarons is reviewed.

*Phys Chem Chem Phys ; 22(19): 10480-10489, 2020 May 20.*

##### RESUMO

We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the constraint of fixed electrostatic potential for each configuration of the electrolyte. The present work clarifies the role of the overall electroneutrality constraint, as well as the link between the averages computed within the Born-Oppenheimer approximation and that of the full constant-potential ensemble. This allows us in particular to derive a complete fluctuation-dissipation relation for the differential capacitance, that includes a contribution from the charge fluctuations (around the charges satisfying the constant-potential and electroneutrality constraints) also present in the absence of an electrolyte. We provide a simple expression for this contribution from the elements of the inverse of the matrix defining the quadratic form of the fluctuating charges in the energy. We then illustrate numerically the validity of our results, and recover the expected continuum result for an empty capacitor with structureless electrodes at large inter-electrode distances. By considering a variety of liquids between graphite electrodes, we confirm that this contribution to the total differential capacitance is small compared to that induced by the thermal fluctuations of the electrolyte.

*J Chem Phys ; 151(1): 014101, 2019 Jul 07.*

##### RESUMO

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here, we introduce a way to compute arbitrarily high order transport coefficients of stochastic systems, using the framework of large deviation theory. Leveraging time reversibility in the microscopic dynamics, we relate nonlinear response to equilibrium multitime correlation functions among both time reversal symmetric and asymmetric observables, which can be evaluated from derivatives of large deviation functions. This connection establishes a thermodynamiclike relation for nonequilibrium response and provides a practical route to its evaluation, as large deviation functions are amenable to importance sampling. We demonstrate the generality and efficiency of this method in predicting transport coefficients in single particle systems and an interacting system exhibiting thermal rectification.

*J Chem Phys ; 151(1): 014106, 2019 Jul 07.*

##### RESUMO

We present a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation and treated as sources of static disorder. In this way, we adopt the recently developed frozen-mode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic time scale of the bath in a two-mode model of photoisomerization. We find that the yield is monotonically increasing with reorganization energy for a Markovian bath but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase.

*J Chem Phys ; 150(23): 234112, 2019 Jun 21.*

##### RESUMO

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. The numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.

*J Chem Phys ; 150(19): 191102, 2019 May 21.*

##### RESUMO

We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogeneous systems. Using the relationship between rate constants and path space partition functions, we illustrate that the relative change in the rate of a rare event through space is isomorphic to the calculation of a free energy difference, albeit in a trajectory ensemble. Like equilibrium free energies, relative rate constants can be estimated by importance sampling. An extension to transition path sampling is proposed that combines biased path ensembles and weighted histogram analysis to accomplish this estimate. We show that rate constants can also be decomposed into different contributions, including relative changes in stability, barrier height, and flux. This decomposition provides a means of interpretation and insight into rare processes in complex environments. We verify these ideas with a simple model of diffusion with spatially varying diffusivity and illustrate their utility in a model of ion pair dissociation near an electrochemical interface.

*J Chem Phys ; 151(24): 244123, 2019 Dec 28.*

##### RESUMO

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions and find that in many cases, the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. We then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.

*J Chem Phys ; 149(21): 214109, 2018 Dec 07.*

##### RESUMO

We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely on prior knowledge of transition states or reactive pathways and thus can provide mechanistic insight into ultrafast relaxation processes in addition to their associated rates. In particular, we formulate a quantum path ensemble using the stochastic realizations of an unravelled quantum master equation, which results in trajectories that can be conditioned on starting and ending in particular quantum states. Because the dynamics rigorously obeys detailed balance, rate constants can be evaluated from reversible work calculations in this conditioned ensemble, allowing for branching ratios and yields to be computed in an unbiased manner. We illustrate the utility of this method with three examples: energy transfer in a donor-bridge-acceptor model, and models of photo-induced proton-coupled electron transfer and thermally activated electron transfer. These examples demonstrate the efficacy of path ensemble methods and pave the way for their use in studying complex reactive quantum dynamics.

*Proc Natl Acad Sci U S A ; 115(47): 11929-11934, 2018 11 20.*

##### RESUMO

Facile ionic transport in lead halide perovskites plays a critical role in device performance. Understanding the microscopic origins of high ionic conductivities has been complicated by indirect measurements and sample microstructural heterogeneities. Here, we report the direct visualization of halide anion interdiffusion in CsPbCl3-CsPbBr3 single crystalline perovskite nanowire heterojunctions using wide-field and confocal photoluminescence measurements. The combination of nanoscale imaging techniques with these single crystalline materials allows us to measure intrinsic anionic lattice diffusivities, free from complications of microscale inhomogeneity. Halide diffusivities were found to be between 10-13 and â¼10-12 cm2/second at about 100 °C, which are several orders of magnitudes lower than those reported in polycrystalline thin films. Spatially resolved photoluminescence lifetimes and surface potential measurements provide evidence of the central role of halide vacancies in facilitating ionic diffusion. Vacancy formation free energies computed from molecular simulation are small due to the easily deformable perovskite lattice, accounting for the high equilibrium vacancy concentration. Furthermore, molecular simulations suggest that ionic motion is facilitated by low-frequency lattice modes, resulting in low activation barriers for vacancy-mediated transport. This work elucidates the intrinsic solid-state ion diffusion mechanisms in this class of semisoft materials and offers guidelines for engineering materials with long-term stability in functional devices.

*J Phys Chem Lett ; 9(14): 3998-4005, 2018 Jul 19.*

##### RESUMO

Photoinduced phase separation in mixed halide perovskites emerges from their electro-mechanical properties and high ionic conductivities, resulting in photoinduced I--rich charge carrier traps that diminish photovoltaic performance. Whether photoinduced phase separation stems from the polycrystalline microstructure or is an intrinsic material property has been an open question. We investigate the nanoscale photoinduced behavior of single-crystal mixed Br-/I- methylammonium (MA+) lead halide perovskite (MAPb(Br xI1- x)3) nanoplates, eliminating effects from extended structural defects. Even in these nanoplates, we find that phase separation occurs, resulting in I--rich clusters that are nucleated stochastically and stabilized by polarons. Upon lowering the electron-phonon coupling strength by partially exchanging MA+ for Cs+, a phase-separated steady state is not reached, nevertheless transient I- clustering still occurs. Our results, supported by multiscale modeling, demonstrate that photoinduced phase separation is an intrinsic property of mixed halide perovskites, the extent and dynamics of which depends on the electron-phonon coupling strength.

*Phys Rev Lett ; 120(21): 210602, 2018 May 25.*

##### RESUMO

We describe a framework to reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into trajectory based Monte Carlo calculations, through a transformation of the system's propagator using an approximate guiding function. This procedure importance samples the trajectories that most contribute to the large deviation function, mitigating the exponential complexity of such calculations. We illustrate the method by studying driven diffusion and interacting lattice models in one and two spatial dimensions. Our work offers an avenue to calculate large deviation functions for high dimensional systems driven far from equilibrium.

*J Chem Phys ; 148(12): 124120, 2018 Mar 28.*

##### RESUMO

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

*Nat Mater ; 17(3): 261-267, 2018 03.*

##### RESUMO

Smart photovoltaic windows represent a promising green technology featuring tunable transparency and electrical power generation under external stimuli to control the light transmission and manage the solar energy. Here, we demonstrate a thermochromic solar cell for smart photovoltaic window applications utilizing the structural phase transitions in inorganic halide perovskite caesium lead iodide/bromide. The solar cells undergo thermally-driven, moisture-mediated reversible transitions between a transparent non-perovskite phase (81.7% visible transparency) with low power output and a deeply coloured perovskite phase (35.4% visible transparency) with high power output. The inorganic perovskites exhibit tunable colours and transparencies, a peak device efficiency above 7%, and a phase transition temperature as low as 105 °C. We demonstrate excellent device stability over repeated phase transition cycles without colour fade or performance degradation. The photovoltaic windows showing both photoactivity and thermochromic features represent key stepping-stones for integration with buildings, automobiles, information displays, and potentially many other technologies.

*Proc Natl Acad Sci U S A ; 114(51): 13374-13379, 2017 12 19.*

##### RESUMO

We have used molecular simulation and methods of importance sampling to study the thermodynamics and kinetics of ionic charge separation at a liquid water-metal interface. We have considered this process using canonical examples of two different classes of ions: a simple alkali-halide pair, Na+I-, or classical ions, and the products of water autoionization, H3O+OH-, or water ions. We find that for both ion classes, the microscopic mechanism of charge separation, including water's collective role in the process, is conserved between the bulk liquid and the electrode interface. However, the thermodynamic and kinetic details of the process differ between these two environments in a way that depends on ion type. In the case of the classical ion pairs, a higher free-energy barrier to charge separation and a smaller flux over that barrier at the interface result in a rate of dissociation that is 40 times slower relative to the bulk. For water ions, a slightly higher free-energy barrier is offset by a higher flux over the barrier from longer lived hydrogen-bonding patterns at the interface, resulting in a rate of association that is similar both at and away from the interface. We find that these differences in rates and stabilities of charge separation are due to the altered ability of water to solvate and reorganize in the vicinity of the metal interface.

*Nano Lett ; 17(2): 1028-1033, 2017 02 08.*

##### RESUMO

The distinct physical properties of hybrid organic-inorganic materials can lead to unexpected nonequilibrium phenomena that are difficult to characterize due to the broad range of length and time scales involved. For instance, mixed halide hybrid perovskites are promising materials for optoelectronics, yet bulk measurements suggest the halides reversibly phase separate upon photoexcitation. By combining nanoscale imaging and multiscale modeling, we find that the nature of halide demixing in these materials is distinct from macroscopic phase separation. We propose that the localized strain induced by a single photoexcited charge interacting with the soft, ionic lattice is sufficient to promote halide phase separation and nucleate a light-stabilized, low-bandgap, â¼8 nm iodide-rich cluster. The limited extent of this polaron is essential to promote demixing because by contrast bulk strain would simply be relaxed. Photoinduced phase separation is therefore a consequence of the unique electromechanical properties of this hybrid class of materials. Exploiting photoinduced phase separation and other nonequilibrium phenomena in hybrid materials more generally could expand applications in sensing, switching, memory, and energy storage.

*Proc Natl Acad Sci U S A ; 113(44): 12347-12349, 2016 11 01.*

*J Phys Chem Lett ; 7(13): 2333-8, 2016 Jul 07.*

##### RESUMO

We use molecular dynamics simulations in a constant potential ensemble to study the effects of solution composition on the electrochemical response of a double layer capacitor. We find that the capacitance first increases with ion concentration following its expected ideal solution behavior but decreases upon approaching a pure ionic liquid in agreement with recent experimental observations. The nonmonotonic behavior of the capacitance as a function of ion concentration results from the competition between the independent motion of solvated ions in the dilute regime and solvation fluctuations in the concentrated regime. Mirroring the capacitance, we find that the characteristic decay length of charge density correlations away from the electrode is also nonmonotonic. The correlation length first decreases with ion concentration as a result of better electrostatic screening but increases with ion concentration as a result of enhanced steric interactions. When charge fluctuations induced by correlated ion-solvent fluctuations are large relative to those induced by the pure ionic liquid, such capacitive behavior is expected to be generic.

*Chem Rev ; 116(13): 7698-726, 2016 07 13.*

##### RESUMO

The interfaces of neat water and aqueous solutions play a prominent role in many technological processes and in the environment. Examples of aqueous interfaces are ultrathin water films that cover most hydrophilic surfaces under ambient relative humidities, the liquid/solid interface which drives many electrochemical reactions, and the liquid/vapor interface, which governs the uptake and release of trace gases by the oceans and cloud droplets. In this article we review some of the recent experimental and theoretical advances in our knowledge of the properties of aqueous interfaces and discuss open questions and gaps in our understanding.