Galen T. Craven

Lagrangian Descriptors of Thermalized Transition States on Time-Varying Energy Surfaces.

Thermalized chemical reactions driven under dynamical load are characteristic of activated dynamics for arbitrary nonautonomous systems. Recent generalizations of transition state theory to obtain formally exact rates have required the construction of a time-dependent transition state trajectory. Here, we show that Lagrangian descriptors can be used to obtain this structure directly. By developing a phase space separatrix that is void of recrossings, these constructs allow for the principal criterion in the implementation of modern rate theories to be satisfied. Thus, the reactive flux over a time-varying barrier can be determined without ambiguity in chemical reactions. The generality of the formalism suggests that this approach is applicable to any activated system subjected to arbitrary driving and thermal fluctuations.

Electron transfer across a thermal gradient

Significance Electron transfer (ET) is a fundamental process that drives many physical, chemical, and biological transformations, as well as playing a ubiquitous role in the development of technologies for energy conversion and electronics. Recent advances in temperature measurement and control allow thermal gradients and heat flow to be addressed at the molecular level, making it possible to observe electron transfer across thermal gradients. Here, we develop a theory for ET between donor and acceptor sites, where each site has a different local temperature. The transfer of charge across the resulting thermal gradient is found to be coupled with an energy transfer mechanism that may alter heat conduction between sites, even for vanishing net electron current. Charge transfer is a fundamental process that underlies a multitude of phenomena in chemistry and biology. Recent advances in observing and manipulating charge and heat transport at the nanoscale, and recently developed techniques for monitoring temperature at high temporal and spatial resolution, imply the need for considering electron transfer across thermal gradients. Here, a theory is developed for the rate of electron transfer and the associated heat transport between donor–acceptor pairs located at sites of different temperatures. To this end, through application of a generalized multidimensional transition state theory, the traditional Arrhenius picture of activation energy as a single point on a free energy surface is replaced with a bithermal property that is derived from statistical weighting over all configurations where the reactant and product states are equienergetic. The flow of energy associated with the electron transfer process is also examined, leading to relations between the rate of heat exchange among the donor and acceptor sites as functions of the temperature difference and the electronic driving bias. In particular, we find that an open electron transfer channel contributes to enhanced heat transport between sites even when they are in electronic equilibrium. The presented results provide a unified theory for charge transport and the associated heat conduction between sites at different temperatures.

Chemical reactions induced by oscillating external fields in weak thermal environments

Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead time-dependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the time-varying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations.

Persistence of transition-state structure in chemical reactions driven by fields oscillating in time

Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition-state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition-state trajectory. This surface is recrossing-free for both Hamiltonian and dissipative dynamics. This is confirmed even for strongly anharmonic barriers using simulation. The power of transition-state theory is thereby applicable to chemical reactions and other activated processes even when the bottlenecks are time dependent and move across space.

Electron transfer at thermally heterogeneous molecule-metal interfaces

The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through the implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions for the rate constant and the electronic contribution to a heat transfer mechanism which is induced by the temperature gradient between a molecule and metal are constructed. The system of coupled dynamical equations describing the electronic and thermal currents are derived and examined over diverse ranges of reaction geometries and temperature gradients. It is shown that electron transfer across the molecule-metal interface is associated with heat transfer and that the electron exchange between metal and molecule makes a distinct contribution to the interfacial heat conduction even when the net electronic current vanishes.

Transition state theory for activated systems with driven anharmonic barriers

Classical transition state theory has been extended to address chemical reactions across barriers that are driven and anharmonic. This resolves a challenge to the naive theory that necessarily leads to recrossings and approximate rates because it relies on a fixed dividing surface. We develop both perturbative and numerical methods for the computation of a time-dependent recrossing-free dividing surface for a model anharmonic system in a solvated environment that interacts strongly with an oscillatory external field. We extend our previous work, which relied either on a harmonic approximation or on periodic force driving. We demonstrate that the reaction rate, expressed as the long-time flux of reactive trajectories, can be extracted directly from the stability exponents, namely, Lyapunov exponents, of the moving dividing surface. Comparison to numerical results demonstrates the accuracy and robustness of this approach for the computation of optimal (recrossing-free) dividing surfaces and reaction rates in systems with Markovian solvation forces. The resulting reaction rates are in strong agreement with those determined from the long-time flux of reactive trajectories.

Transition state geometry of driven chemical reactions on time-dependent double-well potentials

Reaction rates across time-dependent barriers are difficult to define and difficult to obtain using standard transition state theory approaches because of the complexity of the geometry of the dividing surface separating reactants and products. Using perturbation theory (PT) or Lagrangian descriptors (LDs), we can obtain the transition state trajectory and the associated recrossing-free dividing surface. With the latter, we are able to determine the exact reactant population decay and the corresponding rates to benchmark the PT and LD approaches. Specifically, accurate rates are obtained from a local description regarding only direct barrier crossings and to those obtained from a stability analysis of the transition state trajectory. We find that these benchmarks agree with the PT and LD approaches for obtaining recrossing-free dividing surfaces. This result holds not only for the local dynamics in the vicinity of the barrier top, but also for the global dynamics of particles that are quenched at the reactant or product wells after their sojourn over the barrier region. The double-well structure of the potential allows for long-time dynamics related to collisions with the outside walls that lead to long-time returns in the low-friction regime. This additional global dynamics introduces slow-decay pathways that do not result from the local transition across the recrossing-free dividing surface associated with the transition state trajectory, but can be addressed if that structure is augmented by the population transfer of the long-time returns.

Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order

The occupied volume of a penetrable hard rod (HR) system in one dimension is probed through the use of molecular dynamics simulations. In these dynamical simulations, collisions between penetrable rods are governed by a stochastic penetration algorithm (SPA), which allows for rods to either interpenetrate with a probability δ, or collide elastically otherwise. The limiting values of this parameter, δ = 0 and δ = 1, correspond to the HR and the ideal limits, respectively. At intermediate values, 0 < δ < 1, mixing of mutually exclusive and independent events is observed, making prediction of the occupied volume nontrivial. At high hard core volume fractions φ0, the occupied volume expression derived by Rikvold and Stell [J. Chem. Phys. 82, 1014 (1985)] for permeable systems does not accurately predict the occupied volume measured from the SPA simulations. Multi-body effects contribute significantly to the pair correlation function g2(r) and the simplification by Rikvold and Stell that g2(r) = δ in the penetrative region is observed to be inaccurate for the SPA model. We find that an integral over the penetrative region of g2(r) is the principal quantity that describes the particle overlap ratios corresponding to the observed penetration probabilities. Analytic formulas are developed to predict the occupied volume of mixed systems and agreement is observed between these theoretical predictions and the results measured from simulation.

Electrothermal Transistor Effect and Cyclic Electronic Currents in Multithermal Charge Transfer Networks

A theory is developed to describe the coupled transport of energy and charge in networks of electron donor-acceptor sites which are seated in a thermally heterogeneous environment, where the transfer kinetics are dominated by Marcus-type hopping rates. It is found that the coupling of heat and charge transfer in such systems gives rise to exotic transport phenomena which are absent in thermally homogeneous systems and cannot be described by standard thermoelectric relations. Specifically, the directionality and extent of thermal transistor amplification and cyclical electronic currents in a given network can be controlled by tuning the underlying temperature gradient in the system. The application of these findings toward the optimal control of multithermal currents is illustrated on a paradigmatic nanostructure.

Electron-transfer-induced and phononic heat transport in molecular environments

A unified theory of heat transport in environments that sustain intersite phononic coupling and electron hopping is developed. The heat currents generated by both phononic transport and electron transfer between sites characterized by different local temperatures are calculated and compared. Using typical molecular parameters we find that the electron-transfer-induced heat current can be comparable to that of the standard phononic transport for donor-acceptor pairs with efficient bidirectional electron transfer rates (relatively small intersite distance and favorable free-energy difference). In most other situations, phononic transport is the dominant heat transfer mechanism.