Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions.

Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra.

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries.

Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.

Trion Formation Resolves Observed Peak Shifts in the Optical Spectra of Transition-Metal Dichalcogenides.

Monolayer transition-metal dichalcogenides (ML-TMDs) have the potential to unlock novel photonic and chemical technologies if their optoelectronic properties can be understood and controlled. Yet, recent work has offered contradictory explanations for how TMD absorption spectra change with carrier concentration, fluence, and time. Here, we test our hypothesis that the large broadening and shifting of the strong band-edge features observed in optical spectra arise from the formation of negative trions. We do this by fitting an ab initio based, many-body model to our experimental electrochemical data. Our approach provides an excellent, global description of the potential-dependent linear absorption data. We further leverage our model to demonstrate that trion formation explains the nonmonotonic potential dependence of the transient absorption spectra, including through photoinduced derivative line shapes for the trion peak. Our results motivate the continued development of theoretical methods to describe cutting-edge experiments in a physically transparent way.

Hot carrier extraction from 2D semiconductor photoelectrodes.

Hot carrier-based energy conversion systems could double the efficiency of conventional solar energy technology or drive photochemical reactions that would not be possible using fully thermalized, "cool" carriers, but current strategies require expensive multijunction architectures. Using an unprecedented combination of photoelectrochemical and in situ transient absorption spectroscopy measurements, we demonstrate ultrafast (<50 fs) hot exciton and free carrier extraction under applied bias in a proof-of-concept photoelectrochemical solar cell made from earth-abundant and potentially inexpensive monolayer (ML) MoS2. Our approach facilitates ultrathin 7 Å charge transport distances over 1 cm2 areas by intimately coupling ML-MoS2 to an electron-selective solid contact and a hole-selective electrolyte contact. Our theoretical investigations of the spatial distribution of exciton states suggest greater electronic coupling between hot exciton states located on peripheral S atoms and neighboring contacts likely facilitates ultrafast charge transfer. Our work delineates future two-dimensional (2D) semiconductor design strategies for practical implementation in ultrathin photovoltaic and solar fuel applications.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations.

The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

Compact and complete description of non-Markovian dynamics.

Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.

Macroscopic surface charges from microscopic simulations.

Attaining accurate average structural properties in a molecular simulation should be considered a prerequisite if one aims to elicit meaningful insights into a system's behavior. For charged surfaces in contact with an electrolyte solution, an obvious example is the density profile of ions along the direction normal to the surface. Here, we demonstrate that, in the slab geometry typically used in simulations, imposing an electric displacement field D determines the integrated surface charge density of adsorbed ions at charged interfaces. This allows us to obtain macroscopic surface charge densities irrespective of the slab thickness used in our simulations. We also show that the commonly used Yeh-Berkowitz method and the "mirrored slab" geometry both impose vanishing integrated surface charge densities. We present results both for relatively simple rocksalt (1 1 1) interfaces and the more complex case of kaolinite's basal faces in contact with an aqueous electrolyte solution.

Stabilization of AgI's polar surfaces by the aqueous environment, and its implications for ice formation.

Silver iodide is one of the most potent inorganic ice nucleating particles known, a feature generally attributed to the excellent lattice match between its basal Ag-(0001) and I-(0001[combining macron]) surfaces, and ice. This crystal termination, however, is a type-III polar surface, and its surface energy therefore diverges with crystal size unless a polarity compensation mechanism prevails. In this simulation study, we investigate to what extent the surrounding aqueous environment is able to provide such polarity compensation. On its own, we find that pure H2O is unable to stabilize the AgI crystal in a physically reasonable manner, and that mobile charge carriers such as dissolved ions, are essential. In other words, proximate dissolved ions must be considered an integral part of the heterogeneous ice formation mechanism. The simulations we perform utilize recent advances in simulation methodology in which appropriate electric and electric displacement fields are imposed. A useful by-product of this study is the direct comparison to the commonly used Yeh-Berkowitz method that this enables. Here we find that naive application of the latter leads to physically unreasonable results, and greatly influences the structure of H2O in the contact layer. We therefore expect these results to be of general importance to those studying polar/charged surfaces in aqueous environments.

Finite electric displacement simulations of polar ionic solid-electrolyte interfaces: Application to NaCl(111)/aqueous NaCl solution.

Tasker type III polar terminations of ionic crystals carry a net surface charge as well as a dipole moment and are fundamentally unstable. In contact with electrolytes, such polar surfaces can be stabilized by adsorption of counterions from the solution to form electric double layers. In a previous work [T. Sayer et al., J. Chem. Phys 147, 104702 (2017)], we reported on a classical force field based molecular dynamics study of a prototype model system, namely, a NaCl(111) slab interfaced with an aqueous NaCl solution on both sides. A serious hurdle in the simulation is that the finite width of the slab admits an electric field in the solid perturbing the theoretical charge balance at the interface of semi-infinite systems [half the surface charge density for NaCl(111)]. It was demonstrated that the application of a finite macroscopic field E canceling the internal electric field can recover the correct charge compensation at the interface. In the present work, we expand this method by applying a conjugate electric displacement field D. The benefits of using D instead of E as the control variable are two fold: it does not only speed up the convergence of the polarization in the simulation but also leads to a succinct expression for the biasing displacement field involving only structural parameters which are known in advance. This makes it feasible to study the charge compensating phenomenon of this prototype system with density functional theory based molecular dynamics, as shown in this work.

Charge compensation at the interface between the polar NaCl(111) surface and a NaCl aqueous solution.

Periodic supercell models of electric double layers formed at the interface between a charged surface and an electrolyte are subject to serious finite size errors and require certain adjustments in the treatment of the long-range electrostatic interactions. In a previous publication Zhang and Sprik [Phys. Rev. B 94, 245309 (2016)], we have shown how this can be achieved using finite field methods. The test system was the familiar simple point charge model of a NaCl aqueous solution confined between two oppositely charged walls. Here this method is extended to the interface between the (111) polar surface of a NaCl crystal and a high concentration NaCl aqueous solution. The crystal is kept completely rigid and the compensating charge screening the polarization can only be provided by the electrolyte. We verify that the excess electrolyte ionic charge at the interface conforms to the Tasker 1/2 rule for compensating charge in the theory of polar rock salt (111) surfaces. The interface can be viewed as an electric double layer with a net charge. We define a generalized Helmholtz capacitance CH which can be computed by varying the applied electric field. We find CH=8.23 µF cm-2, which should be compared to the 4.23 µF cm-2 for the (100) non-polar surface of the same NaCl crystal. This is rationalized by the observation that compensating ions shed their first solvation shell adsorbing as contact ions pairs on the polar surface.