Aditya N. Singh

Nanocrystals (NCs) serve as versatile building blocks for the creation of functional materials with NC self-assembly offering opportunities to enable novel material properties. Here, we demonstrate that PbS NCs functionalized with strongly negatively charged metal chalcogenide complex (MCC) ligands, such as Sn₂S₆^4- and AsS₄^3-, can self-assemble into all-inorganic superlattices with both long-range superlattice translational and atomic-lattice orientational order. Structural characterizations reveal that the NCs adopt an unexpected edge-to-edge alignment, and numerical simulation clarifies that orientational order is thermodynamically stabilized by many-body ion correlations originating from the dense electrolyte. Furthermore, we show that the superlattices of Sn₂S₆^4--functionalized PbS NCs can be fully disassembled back into the colloidal state, which is highly unusual for orientationally attached superlattices with atomic-lattice alignment. The reversible oriented attachment of NCs, enabling their dynamic assembly and disassembly into effectively single-crystalline superstructures, offers a pathway toward designing reconfigurable materials with adaptive and controllable electronic and optoelectronic properties.

The modern theory of rare events is grounded in near-equilibrium ideas, however, many systems of modern interest are sufficiently far from equilibrium that traditional approaches do not apply. Using the recently developed variational path sampling methodology, we study systems evolving within nonequilibrium steady states to elucidate how reactive processes are altered away from equilibrium. Variational path sampling provides access to ensembles of reactive events and a means of quantifying the relative importance of each dynamical degree of freedom in such processes. With it, we have studied the conformational change of a solute in an active bath. We illustrate how energy injection generically enhances the rates of rare events, even when energy is not directed into specific reactive modes. By studying the folding and unfolding transitions of a grafted polymer under shear, we illustrate how nonequilibrium reactive processes do not follow gradient paths due to the emergence of persistent currents. The breaking of detailed balance allows for the mechanisms of forward and backward reactions to be distinct, enabling unconventional pathways to be explored and designed, and states unstable in equilibrium to become stabilized kinetically away from it. The analysis presented in this work establishes some basic principles for understanding the mechanism through which rates are perturbed by nonconservative forces, and how probability currents can stabilize thermodynamically unfavorable states, and is made possible by the use of a numerical method that does not invoke proximity to equilibrium.

This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space and leveraging the theory of large deviations, they provide a perspective from which dynamical phenomena can be studied with the same types of ensemble reweighting ideas that have been used for static equilibrium properties. Applications to chemical, material, and biophysical systems are highlighted.

The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analog of the committor that solves a generalized bridge problem to the splitting probability that solves a boundary value problem under a bistable assumption. By invoking stochastic optimal control and spectral theory, we derive a general form for the optimal controller of a bridge process that connects two metastable states expressed in terms of the splitting probability. This formalism offers an alternative perspective into the role of the committor and its gradients in that they encode force fields that guarantee reactivity, generating trajectories that are statistically identical to the way that a system would react autonomously.

Chemical reactions are dynamical processes involving the correlated reorganization of atomic configurations, driving the conversion of an initial reactant into a result product. By virtue of the metastability of both the reactants and products, chemical reactions are rare events, proceeding fleetingly. Reaction pathways can be modelled probabilistically by using the notion of reactive density in the phase space of the molecular system. Such density is related to a function known as the committor function, which describes the likelihood of a configuration evolving to one of the nearby metastable regions. In theory, the committor function can be obtained by solving the backward Kolmogorov equation (BKE), which is a partial differential equation (PDE) defined in the full dimensional phase space. However, using traditional methods to solve this problem is not practical for high dimensional systems. In this work, we propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of states that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based PDE solver to obtain an approximation solution of a restricted BKE, even when the dimension of the problem is very high. The resulting solution provides an approximation for the committor function that encodes mechanistic information for the reaction, paving a new way for understanding of complex chemical reactions and evaluation of reaction rates.

We present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

We use molecular dynamics simulations to study the thermodynamics and kinetics of alanine dipeptide isomerization at the air–water interface. Thermodynamically, we find an affinity of the dipeptide to the interface. This affinity arises from stabilizing intramolecular interactions that become unshielded as the dipeptide is desolvated. Kinetically, we consider the rate of transitions between the α_L and β conformations of alanine dipeptide and evaluate it as a continuous function of the distance from the interface using a recent extension of transition path sampling, TPS+U. The rate of isomerization at the Gibbs dividing surface is suppressed relative to the bulk by a factor of 3. Examination of the ensemble of transition states elucidates the role of solvent degrees of freedom in mediating favorable intramolecular interactions along the reaction pathway of isomerization. Near the air–water interface, water is less effective at mediating these intramolecular interactions.

The noble elements constitute the simplest group of atoms. At low temperatures or high pressures, they freeze into the face-centered cubic (fcc) crystal structure (except helium). This paper investigates neon, argon, krypton, and xenon by molecular dynamics using the simplified atomic potentials recently proposed by Deiters and Sadus [J. Chem. Phys. 150, 134504 (2019)], which are parameterized using data from accurate ab initio quantum-mechanical calculations by the coupled-cluster approach at the single-double-triple level. We compute the fcc freezing lines and find good agreement with the empirical values. At low pressures, predictions are improved by including many-body corrections. Hidden scale invariance of the potential-energy function is established by showing that mean-squared displacement and the static structure factor are invariant along the lines of constant excess entropy (isomorphs). The isomorph theory of melting [Pedersen et al., Nat. Commun. 7, 12386 (2016)] is used to predict from simulations at a single state point the freezing line’s shape, the entropy of melting, and the Lindemann parameter of the crystal at melting. Finally, our results suggest that the body-centered cubic crystal is the thermodynamically stable phase at high pressures.

The phase separation of oppositely-charged polyelectrolytes in solution is of current interest . In this work we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different forcefields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all forcefields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water does not play a significant role. For fully charged peptides, we find that the driving force for association is entropic in all cases when small ions either neutralize the poly-ions, or are in excess. The removal of all counterions switches the driving force, making complexation energetic. This suggests that the entropy of complexation is dominated by the counterions. When only 6 residues of a 11-mer are charged, however, the driving force is enthalpic in salt-free conditions. The simulations shed insight into the mechanism of complex coacervation and the importance of realistic models for the polyions.