Electron Transfer in Multiply Bridged Donor−Acceptor Molecules: Dephasing and Quantum Coherence

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

On the role of non-diagonal system-environment interactions in bridge-mediated electron transfer

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model are increasingly understood, the influence of off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here, we numerically investigate with quasi-adiabatic propagator path integral simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios, the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Furthermore, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales.

Polariton-Mediated Electron Transfer via Cavity Quantum Electrodynamics

We investigate the polariton-mediated electron transfer reaction in a model system with analytic rate constant theory and direct quantum dynamical simulations. We demonstrate that the photoinduced charge transfer reaction between a bright donor state and dark acceptor state can be significantly enhanced or suppressed by coupling the molecular system to the quantized radiation field inside an optical cavity. This is because the quantum light-matter interaction can influence the effective driving force and electronic couplings between the donor state, which is the hybrid light-matter excitation, and the molecular acceptor state. Under the resonance condition between the photonic and electronic excitations, the effective driving force can be tuned by changing the light-matter coupling strength; for an off-resonant condition, the same effect can be accomplished by changing the molecule-cavity detuning. We further demonstrate that using both the electronic coupling and light-matter coupling helps to extend the effective couplings across the entire system, even for the dark state that carries a zero transition dipole. Theoretically, we find that both the counter-rotating terms and the dipole self-energy in the quantum electrodynamics Hamiltonian are important for obtaining an accurate polariton eigenspectrum as well as the polariton-mediated charge transfer rate constant, especially in the ultrastrong coupling regime.

Quantum coherence in ultrafast photo-driven charge separation

Coherent interactions are prevalent in photodriven processes, ranging from photosynthetic energy transfer to superexchange-mediated electron transfer, resulting in numerous studies aimed towards identifying and understanding these interactions. A key motivator of this interest is the non-statistical scaling laws that result from coherently traversing multiple pathways due to quantum interference. To that end, we employed ultrafast transient absorption spectroscopy to measure electron transfer in two donor-acceptor molecular systems comprising a p-(9-anthryl)-N,N-dimethylaniline chromophore/electron donor and either one or two equivalent naphthalene-1,8:4,5-bis(dicarboximide) electron acceptors at both ambient and cryogenic temperatures. The two-acceptor compound shows a statistical factor of 2.1 ± 0.2 rate enhancement at room temperature and a non-statistical factor of 2.6 ± 0.2 rate enhancement at cryogenic temperatures, suggesting correlated interactions between the two acceptors with the donor and with the bath modes. Comparing the charge recombination rates indicates that the electron is delocalized over both acceptors at low temperature but localized on a single acceptor at room temperature. These results highlight the importance of shielding the system from bath fluctuations to preserve and ultimately exploit the coherent interactions.

Computational construction of the electronic Hamiltonian for photoinduced electron transfer and Redfield propagation

The construction of open-system diabatic Hamiltonians relevant for the investigation of electron transfer processes is a computational challenge. Here all relevant parameters for Redfield propagations are extracted fromab initiocomputations.

Fine tuning of electron transfer and spin chemistry parameters in triarylamine-bridge-naphthalene diimide dyads by bridge substituents

The photoinduced charge separation and charge recombination in a set of four molecular dyads consisting of a triarylamine donor and a naphthalene diimide acceptor were investigated by time resolved transient absorption spectroscopy with fs and ns time resolution. In these dyads the donor and acceptor are bridged by a meta-conjugated diethynylbenzene bridge whose electronic nature was tuned by small electron donating (OMe, Me) or electron withdrawing (Cl, CN) substituents. While the formation of the transient charge separated states is complete within tens of ps, charge recombination is biphasic with a shorter component of several hundred ns and a longer component of several microseconds. This behaviour could be rationalized by assuming an equilibrium of singlet and triplet charge separated states. Magnetic field dependent measurements showed a strong influence on the biphasic decay kinetics and also a pronounced level crossing effect in the magnetic field affected reaction yield (MARY) spectra caused by a significant exchange coupling. An analysis of the observed kinetics using classical kinetic rate equations yields rate constants for charge separation and charge recombination as well as the exchange interaction splitting in the radical ion pair, all of them showing a delicate dependence on the bridge substituents.

Enhancing Singlet Fission Dynamics by Suppressing Destructive Interference between Charge-Transfer Pathways

We apply a real-time path-integral approach to investigate the charge-transfer (CT)-mediated singlet fission quantum dynamics in a model pentacene dimer. Our path-integral method gives reliable fission dynamics across various reaction regimes as well as a broad range of reorganization energies and temperatures. With this method, we investigated the destructive interference between the two CT-mediated fission pathways and discovered two mechanisms that can suppress this deleterious effect. First, increasing the energy gap between the two CT states effectively shuts down the high-lying CT pathway, leaving a better functioning low-lying CT pathway with a minimum amount of destructive interference. Second, intermolecular vibrations induce electronic coupling fluctuations, such that the destructive cancellations due to the different signs in static electronic couplings are suppressed. Our numerical results suggest that these two effects can enhance the fission rate up to three times. These findings reveal promising design principles for more efficient singlet fission materials.

Effects of the Backbone and Chemical Linker on the Molecular Conductance of Nucleic Acid Duplexes

Scanning tunneling microscope break junction measurements are used to examine how the molecular conductance of nucleic acids depends on the composition of their backbone and the linker group to the electrodes. Molecular conductances of 10 base pair long homoduplexes of DNA, aeg-PNA, γ-PNA, and a heteroduplex of DNA/aeg-PNA with identical nucleobase sequence were measured. The molecular conductance was found to vary by 12 to 13 times with the change in backbone. Computational studies show that the molecular conductance differences between nucleic acids of different backbones correlate with differences in backbone structural flexibility. The molecular conductance was also measured for duplexes connected to the electrode through two different linkers, one directly to the backbone and one directly to the nucleobase stack. While the linker causes an order-of-magnitude increase in the overall conductance for a particular duplex, the differences in the electrical conductance with backbone composition are preserved. The highest molecular conductance value, 0.06G₀, was measured for aeg-PNA duplexes with a base stack linker. These findings reveal an important new strategy for creating longer and more complex electroactive, nucleic acid assemblies.

Constructive quantum interference in a bis-copper six-porphyrin nanoring

The exchange interaction, J, between two spin centres is a convenient measure of through bond electronic communication. Here, we investigate quantum interference phenomena in a bis-copper six-porphyrin nanoring by electron paramagnetic resonance spectroscopy via measurement of the exchange coupling between the copper centres. Using an analytical expression accounting for both dipolar and exchange coupling to simulate the time traces obtained in a double electron electron resonance experiment, we demonstrate that J can be quantified to high precision even in the presence of significant through-space coupling. We show that the exchange coupling between two spin centres is increased by a factor of 4.5 in the ring structure with two parallel coupling paths as compared to an otherwise identical system with just one coupling path, which is a clear signature of constructive quantum interference.

Quantum interference in charge transport is attracting interest with applications in nanoelectronics and quantum computing. Here, the authors present a method for quantifying electronic transmission through molecules, and demonstrate constructive quantum interference in a molecule with two identical, parallel coupling paths.

Vibrational control of electron-transfer reactions: a feasibility study for the fast coherent transfer regime

Electron donors are connectedvialeft and right bridges to electron acceptors. Following electron-transfer initiation, the IR excitation of selected bridge vibrational modes can tune the directionality of electron transfer.

Microscopic theory of singlet exciton fission. II. Application to pentacene dimers and the role of superexchange

We apply our theoretical formalism for singlet exciton fission, introduced in the previous paper [T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, J. Chem. Phys. 138, 114102 (2013)] to molecular dimers of pentacene, a widely studied material that exhibits singlet fission in the crystal phase. We address a longstanding theoretical issue, namely whether singlet fission proceeds via two sequential electron transfer steps mediated by charge-transfer states or via a direct two-electron transfer process. We find evidence for a superexchange mediated mechanism, whereby the fission process proceeds through virtual charge-transfer states which may be very high in energy. In particular, this mechanism predicts efficient singlet fission on the sub-picosecond timescale, in reasonable agreement with experiment. We investigate the role played by molecular vibrations in mediating relaxation and decoherence, finding that different physically reasonable forms for the bath relaxation function give similar results. We also examine the competing direct coupling mechanism and find it to yield fission rates slower in comparison with the superexchange mechanism for the dimer. We discuss implications for crystalline pentacene, including the limitations of the dimer model.

Coherence in electron transfer pathways

Central to the view of electron-transfer reactions is the idea that nuclear motion generates a transition state geometry at which the electron/hole amplitude propagates coherently from the electron donor to the electron acceptor. In the weakly coupled or nonadiabatic regime, the electron amplitude tunnels through an electronic barrier between the donor and acceptor. The structure of the barrier is determined by the covalent and noncovalent interactions of the bridge. Because the tunneling barrier depends on the nuclear coordinates of the reactants (and on the surrounding medium), the tunneling barrier is highly anisotropic, and it is useful to identify particular routes, or pathways, along which the transmission amplitude propagates. Moreover, when more than one such pathway exists, and the paths give rise to comparable transmission amplitude magnitudes, one may expect to observe quantum interferences among pathways if the propagation remains coherent. Given that the effective tunneling barrier height and width are affected by the nuclear positions, the modulation of the nuclear coordinates will lead to a modulation of the tunneling barrier and hence of the electron flow. For long distance electron transfer in biological and biomimetic systems, nuclear fluctuations, arising from flexible protein moieties and mobile water bridges, can become quite significant. We discuss experimental and theoretical results that explore the quantum interferences among coupling pathways in electron-transfer kinetics; we emphasize recent data and theories associated with the signatures of chirality and inelastic processes, which are manifested in the tunneling pathway coherence (or absence of coherence).

Steering electrons on moving pathways

Electron transfer (ET) reactions provide a nexus among chemistry, biochemistry, and physics. These reactions underpin the "power plants" and "power grids" of bioenergetics, and they challenge us to understand how evolution manipulates structure to control ET kinetics. Ball-and-stick models for the machinery of electron transfer, however, fail to capture the rich electronic and nuclear dynamics of ET molecules: these static representations disguise, for example, the range of thermally accessible molecular conformations. The influence of structural fluctuations on electron-transfer kinetics is amplified by the exponential decay of electron tunneling probabilities with distance, as well as the delicate interference among coupling pathways. Fluctuations in the surrounding medium can also switch transport between coherent and incoherent ET mechanisms--and may gate ET so that its kinetics is limited by conformational interconversion times, rather than by the intrinsic ET time scale. Moreover, preparation of a charge-polarized donor state or of a donor state with linear or angular momentum can have profound dynamical and kinetic consequences. In this Account, we establish a vocabulary to describe how the conformational ensemble and the prepared donor state influence ET kinetics in macromolecules. This framework is helping to unravel the richness of functional biological ET pathways, which have evolved within fluctuating macromolecular structures. The conceptual framework for describing nonadiabatic ET seems disarmingly simple: compute the ensemble-averaged (mean-squared) donor-acceptor (DA) tunneling interaction, <H(DA)(2)>, and the Franck-Condon weighted density of states, rho(FC), to describe the rate, (2pi/variant Planck's over 2pi)<H(DA)(2)>rho(FC). Modern descriptions of the thermally averaged electronic coupling and of the Franck-Condon factor establish a useful predictive framework in biology, chemistry, and nanoscience. Describing the influence of geometric and energetic fluctuations on ET allows us to address a rich array of mechanistic and kinetic puzzles. How strongly is a protein's fold imprinted on the ET kinetics, and might thermal fluctuations "wash out" signatures of structure? What is the influence of thermal fluctuations on ET kinetics beyond averaging of the tunneling barrier structure? Do electronic coupling mechanisms change as donor and acceptor reposition in a protein, and what are the consequences for the ET kinetics? Do fluctuations access minority species that dominate tunneling? Can energy exchanges between the electron and bridge vibrations generate vibronic signatures that label some of the D-to-A pathways traversed by the electron, thus eliminating unmarked pathways that would otherwise contribute to the DA coupling (as in other "which way" or double-slit experiments)? Might medium fluctuations drive tunneling-hopping mechanistic transitions? How does the donor-state preparation, in particular, its polarization toward the acceptor and its momentum characteristics (which may introduce complex rather than pure real relationships among donor orbital amplitudes), influence the electronic dynamics? In this Account, we describe our recent studies that address puzzling questions of how conformational distributions, excited-state polarization, and electronic and nuclear dynamical effects influence ET in macromolecules. Indeed, conformational and dynamical effects arise in all transport regimes, including the tunneling, resonant transport, and hopping regimes. Importantly, these effects can induce switching among ET mechanisms.

Turning charge transfer on and off in a molecular interferometer with vibronic pathways

Inelastic electron-transfer kinetics in molecules with electron donor and acceptor units connected by a bridge is expected to be sensitive to bridge-localized vibronic interactions. Here, we show how inelastic electron transfer may be turned on and off in a double-slit style experiment that uses the molecule as an interferometer. We describe donor-acceptor interactions in terms of interfering vibronic coupling pathways that can be actively selected ("labeled") when pathway-specific vibrations are excited by infrared radiation. Thus, inelastic tunneling may be actively controlled, and we suggest strategies for building molecular scale quantum interferometers and switches based on this phenomenon.

Optical switching of electric charge transfer pathways in porphyrin: a light-controlled nanoscale current router

We introduce a novel molecular junction based on a thiol-functionalized porphyrin derivative with two almost energetically degenerate equilibrium configurations. We show that each equilibrium structure defines a pathway of maximal electric charge transfer through the molecular junction and that these two conduction pathways are spatially orthogonal. We further demonstrate computationally how to switch between the two equilibrium structures of the compound by coherent light. The optical switching mechanism is presented in the relevant configuration subspace of the compound, and the corresponding potential and electric dipole surfaces are obtained by ab initio methods. The laser-induced isomerization takes place in two steps in tandem, while each step is induced by a two-photon process. The effect of metallic electrodes on the electromagnetic irradiation driving the optical switching is also investigated. Our study demonstrates the potential for using thiol-functionalized porphyrin derivatives for the development of a light-controlled nanoscale current router.

STRANGE EFFECT OF DISORDER ON ELECTRON TRANSPORT THROUGH A THIN FILM

A novel feature of electron transport is explored through a thin film of varying impurity density with the distance from its surface. The film, attached to two metallic electrodes, is described by simple tight-binding model and its coupling to the electrodes is treated through Newns–Anderson chemisorption theory. It is observed that in the strong disorder regime the amplitude of the current passing through the film increases with the increase of the disorder strength, while it decreases in the weak disorder regime. This anomalous behavior is completely opposite to that of conventional disordered systems. Our results also predict that the electron transport is significantly influenced by the finite size of the thin film.

ELECTRON TRANSPORT THROUGH MULTILEVEL QUANTUM DOT

Quantum transport properties through some multilevel quantum dots sandwiched between two metallic contacts are investigated by the use of Green's function technique. Here, we do parametric calculations, based on the tight-binding model, to study the transport properties through such bridge systems. The electron transport properties are significantly influenced by (a) the number of quantized energy levels in the dots, (b) the dot-to-electrodes coupling strength, (c) the location of the equilibrium Fermi energy E F , and (d) the surface disorder. In the limit of weak-coupling, the conductance (g) shows sharp resonance peaks associated with the quantized energy levels in the dots, while, they get substantial broadening in the strong-coupling limit. The behavior of the electron transfer through these systems becomes much more clearly visible from our study of the current–voltage (I–V) characteristics. In this context, we also describe the noise power of current fluctuations (S) and determine the Fano factor (F) which provides an important information about the electron correlation among the charge carriers. Finally, we explore a novel transport phenomenon by studying the surface disorder effect in which the current amplitude increases with the increase of the surface disorder strength in the strong disorder regime, while, the amplitude decreases in the limit of weak disorder. Such an anomalous behavior is completely opposite to that of bulk disordered system where the current amplitude always decreases with the disorder strength. It is also observed that the current amplitude strongly depends on the system size which reveals the finite quantum size effect.

QUANTUM TRANSPORT THROUGH SINGLE PHENALENYL MOLECULE: EFFECT OF INTERFACE STRUCTURE

The electronic transport characteristics through a single phenalenyl molecule sandwiched between two metallic electrodes are investigated by using Green's function technique. A parametric approach, based on the tight-binding model, is used to study the transport characteristics through such molecular bridge system. The electronic transport properties are significantly influenced by (a) the molecule-to-electrodes interface structure and (b) the molecule-to-electrodes coupling strength.