Intra-strand phosphate-mediated pathways in microsolvated double-stranded DNA.

We argue that dry DNA charge transport in molecular junctions, over distances of tens of nanometers, can take place via independent intra-strand pathways involving the phosphate groups. Such pathways explain recent single-molecule experiments that compare currents in intact and nicked 100 base-pair double-stranded DNA. We explore the conditions that favor independent intra-strand transport channels with the participation of the phosphate groups, as opposed to purely base-mediated transport involving the pi-stacked bases and inter-strand transitions. Our computations demonstrate how long-distance transport pathways in DNA are tuned by the degree of solvation, which affects the level of dynamic disorder in the pi-stacking, and the energies of phosphate-group molecular orbitals.

Molecular Wires for Efficient Long-Distance Triplet Energy Transfer.

We propose design rules for building organic molecular bridges that enable coherent long-distance triplet-exciton transfer. Using these rules, we describe example polychromophoric structures with low inner-sphere exciton reorganization energies, low static and dynamic disorder, and enhanced π-stacking interactions between nearest-neighbor chromophores. These features lead to triplet-exciton eigenstates that are delocalized over several units at room temperature. The use of such bridges in donor-bridge-acceptor assemblies enables fast triplet-exciton transport over very long distances that is rate-limited by the donor-bridge injection and bridge-acceptor trapping rates.

The Role of Bridge-State Intermediates in Singlet Fission for Donor-Bridge-Acceptor Systems: A Semianalytical Approach to Bridge-Tuning of the Donor-Acceptor Fission Coupling.

We describe a semianalytical/computational framework to explore structure-function relationships for singlet fission in Donor (D)-Bridge (B)-Acceptor (A) molecular architectures. The aim of introducing a bridging linker between the D and A molecules is to tune, by modifying the bridge structure, the electronic pathways that lead to fission and to D-A-separated correlated triplets. We identify different bridge-mediation regimes for the effective singlet-fission coupling in the coherent tunneling limit and show how to derive the dominant fission pathways in each regime. We describe the dependence of these regimes on D-B-A many-electron state energetics and on D-B (A-B) one-electron and two-electron matrix elements. This semianalytical approach can be used to guide computational and experimental searches for D-B-A systems with tuned singlet fission rates. We use this approach to interpret the bridge-resonance effect of singlet fission that has been observed in recent experiments.

Backbone charge transport in double-stranded DNA.

Understanding charge transport in DNA molecules is a long-standing problem of fundamental importance across disciplines1,2. It is also of great technological interest due to DNA's ability to form versatile and complex programmable structures. Charge transport in DNA-based junctions has been reported using a wide variety of set-ups2-4, but experiments so far have yielded seemingly contradictory results that range from insulating5-8 or semiconducting9,10 to metallic-like behaviour11. As a result, the intrinsic charge transport mechanism in molecular junction set-ups is not well understood, which is mainly due to the lack of techniques to form reproducible and stable contacts with individual long DNA molecules. Here we report charge-transport measurements through single 30-nm-long double-stranded DNA (dsDNA) molecules with an experimental set-up that enables us to address individual molecules repeatedly and to measure the current-voltage characteristics from 5 K up to room temperature. Strikingly, we observed very high currents of tens of nanoamperes, which flowed through both homogeneous and non-homogeneous base-pair sequences. The currents are fairly temperature independent in the range 5-60 K and show a power-law decrease with temperature above 60 K, which is reminiscent of charge transport in organic crystals. Moreover, we show that the presence of even a single discontinuity ('nick') in both strands that compose the dsDNA leads to complete suppression of the current, which suggests that the backbones mediate the long-distance conduction in dsDNA, contrary to the common wisdom in DNA electronics2-4.

Initial-state preparation effects in time-resolved electron paramagnetic resonance experiments.

We explain a recent experimental observation that the time-resolved electron paramagnetic resonance spectra of an organic molecule for optical excitation within a highly absorbing region of the molecule has similar intensities to the spectra for optical excitation in a nonabsorbing region [D. L. Meyer et al., J. Phys. Chem. Lett. 8, 1677 (2017)]. We demonstrate that this phenomenon is due to an initial-state preparation effect of photoexcitation that leads to similar initial populations of triplet states for both optical excitation regions. Due to the low intersystem crossing rates, the initial triplet populations are not perturbed on the time scale of the experiment, so they determine the relative intensities of the paramagnetic resonance spectra. The effect is surprising given the weak spin-orbit interactions of organic molecules. Such initial-state preparation effects are likely to occur in systems where the intersystem crossing time scales are long compared to the time scale of the experiment.

Observing Donor-to-Acceptor Electron-Transfer Rates and the Marcus Inverted Parabola in Molecular Junctions.

A recurring theme in molecular electronics is the relationship between the intramolecular electron transfer rate in a donor-bridge-acceptor system and the conductance at low bias in the corresponding electrode-bridge-electrode junction. The similarities between through-bridge donor-to-acceptor electron tunneling and through-bridge electrode-to-electrode Landauer transport led to the suggestion of an approximate linear relationship between the rate and the conductance for any given bridge. A large body of work indicates that the two quantities are not necessarily linearly related, showing different behaviors as a function of temperature, voltage and bridge length. Apart from Landauer tunneling, incoherent hopping can be an important mechanism in molecular junctions. We propose a donor-bridge-acceptor molecular junction, functioning in the incoherent hopping regime, that is suited for establishing direct correlations between the electrode-to-electrode current and the intramolecular donor-to-acceptor electron transfer rate. We suggest that this type of junction may be used to observe the Marcus-inverted-parabola dependence of the intramolecular rate on energy gap by varying the bias voltage. The realization of such an experiment would enable meaningful comparisons between solution-phase electron transfer rates and molecular-junction currents for the same molecule.

Quantum interferences among Dexter energy transfer pathways.

Dexter energy transfer in chemical systems moves an exciton (i.e., an electron-hole pair) from a donor chromophore to an acceptor chromophore through a bridge by a combination of bonded and non-bonded interactions. The transition is enabled by both one-electron/one-particle and two-electron/two-particle interaction mechanisms. Assuming that there is no real intermediate state population of an electron, hole, or exciton in the bridge, the transport involves two states that are coupled non-adiabatically. As such, coherent quantum interferences arise among the Dexter energy coupling pathways. These interferences, while related to well understood interferences in single-electron transfer, are much richer because of their two particle nature: the transfer of a triplet exciton involves the net transfer of both an electron and a hole. Despite this additional complexity, simple rules can govern Dexter coupling pathway interferences in special cases. As in the case of single-electron transfer, identical parallel coupling pathways can be constructively interfering and may enhance the Dexter transfer rate. Because of the virtual particle combinatorics associated with two-particle superexchange, two parallel Dexter coupling routes may be expected to enhance Dexter couplings by more than a factor of two. We explore Dexter coupling pathway interferences in non-covalent assemblies, employing a method that enables the assessment of Dexter coupling pathway strengths and interferences, in the context of one-particle and two-particle coupling interactions.

How can infra-red excitation both accelerate and slow charge transfer in the same molecule?

A UV-IR-Vis 3-pulse study of infra-red induced changes to electron transfer (ET) rates in a donor-bridge-acceptor species finds that charge-separation rates are slowed, while charge-recombination rates are accelerated as a result of IR excitation during the reaction. We explore the underpinning mechanisms for this behavior, studying IR-induced changes to the donor-acceptor coupling, to the validity of the Condon approximation, and to the reaction coordinate distribution. We find that the dominant IR-induced rate effects in the species studied arise from changes to the density of states in the Marcus curve crossing region. That is, IR perturbation changes the probability of accessing the activated complex for the ET reactions. IR excitation diminishes the population of the activated complex for forward (activationless) ET, thus slowing the rate. However, IR excitation increases the population of the activated complex for (highly activated) charge recombination ET, thus accelerating the charge recombination rate.

A Nonequilibrium Molecular Dynamics Study of Infrared Perturbed Electron Transfer.

Infrared (IR) excitation is known to change electron-transfer kinetics in molecules. We use nonequilibrium molecular dynamics (NEqMD) simulations to explore the molecular underpinnings of how vibrational excitation may influence nonadiabatic electron-transfer. NEqMD combines classical molecular dynamics simulations with nonequilibrium semiclassical initial conditions to simulate the dynamics of vibrationally excited molecules. We combine NEqMD with electronic structure computations to probe IR effects on electron transfer rates in two molecular species, dimethylaniline-guanosine-cytidine-anthracene (DMA-GC-Anth) and 4-(pyrrolidin-1-yl)phenyl-2,6,7-triazabicyclo[2.2.2]octatriene-10-cyanoanthracen-9-yl (PP-BCN-CA). In DMA-GC-Anth, the simulations find that IR excitation of the NH2 scissoring motion and the subsequent intramolecular vibrational energy redistribution (IVR) do not significantly alter the mean-squared donor-acceptor (DA) coupling interaction. This finding is consistent with earlier computational analysis of static systems. In PP-BCN-CA, IR excitation of the bridging C═N bond changes the bridge-mediated coupling for charge separation and recombination by ∼30-40%. The methods described here enable detailed explorations of how IR excitation may perturb charge-transfer processes at the molecular scale.

Dexter energy transfer pathways.

Energy transfer with an associated spin change of the donor and acceptor, Dexter energy transfer, is critically important in solar energy harvesting assemblies, damage protection schemes of photobiology, and organometallic opto-electronic materials. Dexter transfer between chemically linked donors and acceptors is bridge mediated, presenting an enticing analogy with bridge-mediated electron and hole transfer. However, Dexter coupling pathways must convey both an electron and a hole from donor to acceptor, and this adds considerable richness to the mediation process. We dissect the bridge-mediated Dexter coupling mechanisms and formulate a theory for triplet energy transfer coupling pathways. Virtual donor-acceptor charge-transfer exciton intermediates dominate at shorter distances or higher tunneling energy gaps, whereas virtual intermediates with an electron and a hole both on the bridge (virtual bridge excitons) dominate for longer distances or lower energy gaps. The effects of virtual bridge excitons were neglected in earlier treatments. The two-particle pathway framework developed here shows how Dexter energy-transfer rates depend on donor, bridge, and acceptor energetics, as well as on orbital symmetry and quantum interference among pathways.

Two-Electron Transfer Pathways.

The frontiers of electron-transfer chemistry demand that we develop theoretical frameworks to describe the delivery of multiple electrons, atoms, and ions in molecular systems. When electrons move over long distances through high barriers, where the probability for thermal population of oxidized or reduced bridge-localized states is very small, the electrons will tunnel from the donor (D) to acceptor (A), facilitated by bridge-mediated superexchange interactions. If the stable donor and acceptor redox states on D and A differ by two electrons, it is possible that the electrons will propagate coherently from D to A. While structure-function relations for single-electron superexchange in molecules are well established, strategies to manipulate the coherent flow of multiple electrons are largely unknown. In contrast to one-electron superexchange, two-electron superexchange involves both one- and two-electron virtual intermediate states, the number of virtual intermediates increases very rapidly with system size, and multiple classes of pathways interfere with one another. In the study described here, we developed simple superexchange models for two-electron transfer. We explored how the bridge structure and energetics influence multielectron superexchange, and we compared two-electron superexchange interactions to single-electron superexchange. Multielectron superexchange introduces interference between singly and doubly oxidized (or reduced) bridge virtual states, so that even simple linear donor-bridge-acceptor systems have pathway topologies that resemble those seen for one-electron superexchange through bridges with multiple parallel pathways. The simple model systems studied here exhibit a richness that is amenable to experimental exploration by manipulating the multiple pathways, pathway crosstalk, and changes in the number of donor and acceptor species. The features that emerge from these studies may assist in developing new strategies to deliver multiple electrons in condensed-phase redox systems, including multiple-electron redox species, multimetallic/multielectron redox catalysts, and multiexciton excited states.

Charge transfer in dynamical biosystems, or the treachery of (static) images.

CONSPECTUS: The image is not the thing. Just as a pipe rendered in an oil painting cannot be smoked, quantum mechanical coupling pathways rendered on LCDs do not convey electrons. The aim of this Account is to examine some of our recent discoveries regarding biological electron transfer (ET) and transport mechanisms that emerge when one moves beyond treacherous static views to dynamical frameworks. Studies over the last two decades introduced both atomistic detail and macromolecule dynamics to the description of biological ET. The first model to move beyond the structureless square-barrier tunneling description is the Pathway model, which predicts how protein secondary motifs and folding-induced through-bond and through-space tunneling gaps influence kinetics. Explicit electronic structure theory is applied routinely now to elucidate ET mechanisms, to capture pathway interferences, and to treat redox cofactor electronic structure effects. Importantly, structural sampling of proteins provides an understanding of how dynamics may change the mechanisms of biological ET, as ET rates are exponentially sensitive to structure. Does protein motion average out tunneling pathways? Do conformational fluctuations gate biological ET? Are transient multistate resonances produced by energy gap fluctuations? These questions are becoming accessible as the static view of biological ET recedes and dynamical viewpoints take center stage. This Account introduces ET reactions at the core of bioenergetics, summarizes our team's progress toward arriving at an atomistic-level description, examines how thermal fluctuations influence ET, presents metrics that characterize dynamical effects on ET, and discusses applications in very long (micrometer scale) bacterial nanowires. The persistence of structural effects on the ET rates in the face of thermal fluctuations is considered. Finally, the flickering resonance (FR) view of charge transfer is presented to examine how fluctuations control low-barrier transport among multiple groups in van der Waals contact. FR produces exponential distance dependence in the absence of tunneling; the exponential character emerges from the probability of matching multiple vibronically broadened electronic energies within a tolerance defined by the rms coupling among interacting groups. FR thus produces band like coherent transport on the nanometer length scale, enabled by conformational fluctuations. Taken as a whole, the emerging context for ET in dynamical biomolecules provides a robust framework to design and interpret the inner workings of bioenergetics from the molecular to the cellular scale and beyond, with applications in biomedicine, biocatalysis, and energy science.

Long-range charge transport in single G-quadruplex DNA molecules.

DNA and DNA-based polymers are of interest in molecular electronics because of their versatile and programmable structures. However, transport measurements have produced a range of seemingly contradictory results due to differences in the measured molecules and experimental set-ups, and transporting significant current through individual DNA-based molecules remains a considerable challenge. Here, we report reproducible charge transport in guanine-quadruplex (G4) DNA molecules adsorbed on a mica substrate. Currents ranging from tens of picoamperes to more than 100 pA were measured in the G4-DNA over distances ranging from tens of nanometres to more than 100 nm. Our experimental results, combined with theoretical modelling, suggest that transport occurs via a thermally activated long-range hopping between multi-tetrad segments of DNA. These results could re-ignite interest in DNA-based wires and devices, and in the use of such systems in the development of programmable circuits.

Biological charge transfer via flickering resonance.

Biological electron-transfer (ET) reactions are typically described in the framework of coherent two-state electron tunneling or multistep hopping. However, these ET reactions may involve multiple redox cofactors in van der Waals contact with each other and with vibronic broadenings on the same scale as the energy gaps among the species. In this regime, fluctuations of the molecular structures and of the medium can produce transient energy level matching among multiple electronic states. This transient degeneracy, or flickering electronic resonance among states, is found to support coherent (ballistic) charge transfer. Importantly, ET rates arising from a flickering resonance (FR) mechanism will decay exponentially with distance because the probability of energy matching multiple states is multiplicative. The distance dependence of FR transport thus mimics the exponential decay that is usually associated with electron tunneling, although FR transport involves real carrier population on the bridge and is not a tunneling phenomenon. Likely candidates for FR transport are macromolecules with ET groups in van der Waals contact: DNA, bacterial nanowires, multiheme proteins, strongly coupled porphyrin arrays, and proteins with closely packed redox-active residues. The theory developed here is used to analyze DNA charge-transfer kinetics, and we find that charge-transfer distances up to three to four bases may be accounted for with this mechanism. Thus, the observed rapid (exponential) distance dependence of DNA ET rates over distances of ≲ 15 Šdoes not necessarily prove a tunneling mechanism.

Review: Probing protein electron transfer mechanisms from the molecular to the cellular length scales.

The mechanisms of bridge-mediated electron transfer (ET) reactions vary from coherent deep tunneling to thermally activated hopping. This short review focuses on some developments in the study of protein ET mechanisms at the molecular and at the cellular levels. It explains experimental and theoretical work on the influence of electronic-energy and electronic-coupling fluctuations on ET rates and on the switch from the tunneling to the hopping regimes. It also describes recent work on extracellular ET, in particular on bacterial nanowires which support ET over micron length scales. Future directions in these research areas are discussed.

Physical constraints on charge transport through bacterial nanowires.

Extracellular appendages of the dissimilatory metal-reducing bacterium Shewanella oneidensis MR-1 were recently shown to sustain currents of 10(10) electrons per second over distances of 0.5 microns [El-Naggar et al., Proc. Natl. Acad. Sci. U. S. A., 2010, 107, 18127]. However, the identity of the charge localizing sites and their organization along the "nanowire" remain unknown. We use theory to predict redox cofactor separation distances that would permit charge flow at rates of 10(10) electrons per second over 0.5 microns for voltage biases of < or = IV, using a steady-state analysis governed by a non-adiabatic electron transport mechanism. We find the observed currents necessitate a multi-step hopping transport mechanism, with charge localizing sites separated by less than 1 nm and reorganization energies that rival the lowest known in biology.

Floquet analysis for vibronically modulated electron tunneling.

Electron tunneling provides the primary reaction channel for electron transfer (ET) in many molecular systems. The analysis of such systems therefore requires the consideration of electronic coherence and interference effects. A model system for which tunneling may be either symmetry forbidden or allowed is considered here in the presence of a driving infrared (IR) field. It was previously shown that inelastic tunneling allows ET in the symmetry forbidden system via vibronic interactions. We show here that explicit considerations of IR interactions with these systems further changes the ET kinetics. Analysis in the framework of Floquet theory reveals that interaction with an IR field may increase the probability of inelastic tunneling and thus enhance the ET rate for a system in which elastic ET is forbidden. It is shown that IR driving of a nuclear oscillator promotes the oscillator into excited states that couple more strongly to the tunneling electron. Furthermore, it is shown that IR driving may suppress the ET rate in this same system, depending on system energetics. In a model where elastic tunneling is symmetry allowed, we examine vibronic modulation of ET in the Floquet framework. ET rates are computed for symmetry allowed and forbidden model systems, and vibronic interactions are found to suppress or enhance ET in both systems. The inelastic ET rate may be enhanced over 4 orders of magnitude in the symmetry disfavored case or suppressed by 15% in the same system. Effects of IR on ET rates in the symmetry-allowed system are weaker with enhancements up to 34% over the undriven rate and suppression of about 3% with IR driving present. This study is the first theoretical and computational exploration of ET rate control by IR irradiation of the bridge.

Chiral control of current transfer in molecules.

Electron transmission through chiral molecules induced by circularly polarized light can be very different for mirror image structures. This behavior is described in terms of current transfer: the transfer of both charge and momentum. We review recent theoretical developments on the theory of current transfer and discuss related experimental studies of electron transmission through chiral molecular structures adsorbed on surfaces.

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).