Incoherent Hopping Research Articles

Between Superexchange and Hopping: An Intermediate Charge-Transfer Mechanism in Poly(A)-Poly(T) DNA Hairpins

We developed a model for hole migration along relatively short DNA hairpins with fewer that seven adenine (A):thymine (T) base pairs. The model was used to simulate hole migration along poly(A)-poly(T) sequences with a particular emphasis on the impact of partial hole localization on the different rate processes. The simulations, performed within the framework of the stochastic surrogate Hamiltonian approach, give values for the arrival rate in good agreement with experimental data. Theoretical results obtained for hairpins with fewer than three A:T base pairs suggest that hole transfer along short hairpins occurs via superexchange. This mechanism is characterized by the exponential distance dependence of the arrival rate on the donor/acceptor distance, k(a) ≃ e(-βR), with β = 0.9 Å(-1). For longer systems, up to six A:T pairs, the distance dependence follows a power law k(a) ≃ R(-η) with η = 2. Despite this seemingly clear signature of unbiased hopping, our simulations show the complete delocalization of the hole density along the entire hairpin. According to our analysis, the hole transfer along relatively long sequences may proceed through a mechanism which is distinct from both coherent single-step superexchange and incoherent multistep hopping. The criterion for the validity of this mechanism intermediate between superexchange and hopping is proposed. The impact of partial localization on the rate of hole transfer between neighboring A bases was also investigated.

Photonics meets excitonics: natural and artificial molecular aggregates

AbstractOrganic molecules store the energy of absorbed light in the form of charge-neutral molecular excitations – Frenkel excitons. Usually, in amorphous organic materials, excitons are viewed as quasiparticles, localized on single molecules, which diffuse randomly through the structure. However, the picture of incoherent hopping is not applicable to some classes of molecular aggregates – assemblies of molecules that have strong near-field interaction between electronic excitations in the individual subunits. Molecular aggregates can be found in nature, in photosynthetic complexes of plants and bacteria, and they can also be produced artificially in various forms including quasi-one dimensional chains, two-dimensional films, tubes, etc. In these structures light is absorbed collectively by many molecules and the following dynamics of molecular excitation possesses coherent properties. This energy transfer mechanism, mediated by the coherent exciton dynamics, resembles the propagation of electromagnetic waves through a structured medium on the nanometer scale. The absorbed energy can be transferred resonantly over distances of hundreds of nanometers before exciton relaxation occurs. Furthermore, the spatial and energetic landscape of molecular aggregates can enable the funneling of the exciton energy to a small number of molecules either within or outside the aggregate. In this review we establish a bridge between the fields of photonics and excitonics by describing the present understanding of exciton dynamics in molecular aggregates.

Spectroscopic signatures of quantum-coherent energy transfer

One of the most surprising and significant advances in the study of the photosynthetic light-harvesting process is the discovery that the electronic energy transfer might involve long-lived electronic coherences, under physiologically relevant conditions. This means that the transfer of energy among different chromophores does not follow the expected classical incoherent hopping mechanism, but that quantum-mechanical laws can steer the migration of energy. The implications of such a quantum transport regime, although currently under debate, might have a tremendous impact on our way of thinking about natural and artificial light-harvesting. Central to these discoveries has been the development of new ultrafast spectroscopic techniques, in particular two-dimensional electronic spectroscopy, which is now the primary tool to obtain clear and definitive experimental proof of such effects. This review aims to provide an overview of the experimental techniques developed with the purpose of attaining a more detailed picture of the coherent and incoherent quantum dynamics relevant to energy transfer processes, not limited to the two-dimensional electronic spectroscopy. With the idea of summarizing the experimental and theoretical basic notions necessary to introduce the field, the connection between experimental observables and coherence dynamics will be analysed in detail for each technique, highlighting how electronic coherences could be manifested in different experimental signatures. Similarities and differences among coherent signals as well as advantages and disadvantages of each approach will be critically discussed. Current opinions and debated issues will be emphasised and some possible future directions to address still open questions will be suggested.

Electronic and Charge Transport Properties of peri-Xanthenoxanthene: The Effects of Heteroatoms and Phenyl Substitutions

The electronic and charge transport properties of peri-xanthenoxanthene (PXX) and its phenyl-substitued derivative (Ph-PXX) are explored via quantum chemical calculations. To gain a better understanding of the physical properties of PXX, a comparative study is performed for its analogue, that is, anthanthrene. By employing Marcus electron transfer theory coupled with an incoherent charge hopping and diffusion model, we estimate the charge mobilties of PXX and Ph-PXX. Our calculated results indicate that the introduction of a heteroatom (oxygen) at the reactive sites of anthanthrene can stabilize the extended π-system and improve the effiecient charge injection in electronic devices. The phenyl substitution of PXX makes a remarkable change of charge transport characteristics from a p-type semiconductor to an n-type semiconductor, which shed light on molecular design for an n-type semiconductor through simple chemical structural modification.

Hall-effect mobility of pentacene films prepared by the thermal evaporating method with different substrate temperature

We studied the Hall-effect mobility of pentacene films prepared by the thermal evaporating method with different substrate temperature. A crossover from coherent bandlike charge transport with mobilities up to several tens of cm2/V-s at low temperature to an incoherent hopping motion at high temperature is observed. The carrier mobilities of pentacene exhibit a hopping-to-band transition around room temperature. An exhibition of high mobility of pentacene films prepared with substrate temperature of 90 °C is attributed to the increased spacing between molecules.

Avoiding dark states in open quantum systems by tailored initializations

We study the transport of excitations on a network of three coupled two-level systems that are subjected to an environment that induces incoherent hopping between the nodes. The two end nodes are coupled to a source while the central node is coupled to a drain. A common feature of these networks is the existence of a dark state that blocks the transport to the drain. Here we propose a means to avoid this state by a suitable initialization of the system, induced by a source that is common to both coupled nodes.

Monte Carlo simulation based on dynamic disorder model in organic semiconductors: From coherent to incoherent transport

The dynamic disorder model for charge carrier transport in organic semiconductors has been extensively studied in recent years. Although it is successful on determining the value of bandlike mobility in the organic crystalline materials, the incoherent hopping, the typical transport characteristic in amorphous molecular semiconductors, cannot be described. In this work, the decoherence process is taken into account via a phenomenological parameter, say, decoherence time, and the projective and Monte Carlo method are applied for this model to determine the waiting time and thus the diffusion coefficient. It is obtained that the type of transport is changed from coherent to incoherent with a sufficiently short decoherence time, which indicates the essential role of decoherence time in determining the type of transport in organics. We have also discussed the spatial extent of carriers for different decoherence time, and the transition from delocalization (carrier resides in about 10 molecules) to localization is observed. Based on the experimental results of spatial extent, we estimate that the decoherence time in pentacene has the order of 1 ps. Furthermore, the dependence of diffusion coefficient on decoherence time is also investigated, and corresponding experiments are discussed.

Organic magnetoresistance and spin diffusion in organic semiconductor thin film devices

AbstractWe review recent work in the field of organic spintronics, focusing on our own contributions to this field. There are two principle magnetoresistance effects that occur in organic devices. (i) Organic magnetoresistance (OMAR), which occurs in nonmagnetic organic semiconductor devices. For example, in devices made from the prototypical small molecule Alq3 OMAR reaches values of 10% or more at room temperature. (ii) Organic spin‐valve effects that occur in devices that employ ferromagnetic electrodes for spin‐polarized current injection and detection. We undertake an analysis of these two types of magnetoresistance with the goal of identifying the dominant spin‐scattering mechanism. Analysis of OMAR reveals that hyperfine coupling is the dominant spin‐coupling mechanism. Spin–orbit coupling, on the other hand, is important only in organic semiconductor materials containing heavy atoms. We explore the reasons why spin–orbit coupling is relatively unimportant in hydrocarbon materials. Next, we present a theory for spin diffusion in disordered organic semiconductors based on hyperfine coupling, taking into account a combination of incoherent carrier hopping and coherent spin precession in the random hyperfine magnetic fields. We compare our findings with experimental values for the spin‐diffusion length. Finally, we demonstrate a criterion that allows the determination whether the organic spin‐valves operate in the tunneling or injection regimes. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Exponential Distance Dependence of Photoinitiated Stepwise Electron Transfer in Donor–Bridge–Acceptor Molecules: Implications for Wirelike Behavior

Donor-bridge-acceptor (D-B-A) systems in which a 3,5-dimethyl-4-(9-anthracenyl)julolidine (DMJ-An) chromophore and a naphthalene-1,8:4,5-bis(dicarboximide) (NI) acceptor are linked by oligomeric 2,7-fluorenone (FN(n)) bridges (n = 1-3) have been synthesized. Selective photoexcitation of DMJ-An quantitatively produces DMJ(+•)-An(-•), and An(-•) acts as a high-potential electron donor. Femtosecond transient absorption spectroscopy in the visible and mid-IR regions showed that electron transfer occurs quantitatively in the sequence: DMJ(+•)-An(-•)-FN(n)-NI → DMJ(+•)-An-FN(n)(-•)-NI → DMJ(+•)-An-FN(n)-NI(-•). The charge-shift reaction from An(-•) to NI(-•) exhibits an exponential distance dependence in the nonpolar solvent toluene with an attenuation factor (β) of 0.34 Å(-1), which would normally be attributed to electron tunneling by the superexchange mechanism. However, the FN(n)(-•) radical anion was directly observed spectroscopically as an intermediate in the charge-separation mechanism, thereby demonstrating conclusively that the overall charge separation involves the incoherent hopping (stepwise) mechanism. Kinetic modeling of the data showed that the observed exponential distance dependence is largely due to electron injection onto the first FN unit followed by charge hopping between the FN units of the bridge biased by the distance-dependent electrostatic attraction of the two charges in D(+•)-B(-•)-A. This work shows that wirelike behavior does not necessarily result from building a stepwise, energetically downhill redox gradient into a D-B-A molecule.

Multistep hopping and extracellular charge transfer in microbial redox chains

Dissimilatory metal-reducing bacteria are microorganisms that gain energy by transferring respiratory electrons to extracellular solid-phase electron acceptors. In addition to its importance for physiology and natural environmental processes, this form of metabolism is being investigated for energy conversion and fuel production in bioelectrochemical systems, where microbes are used as biocatalysts at electrodes. One proposed strategy to accomplish this extracellular charge transfer involves forming a conductive pathway to electrodes by incorporating redox components on outer cell membranes and along extracellular appendages known as microbial nanowires within biofilms. To describe extracellular charge transfer in microbial redox chains, we employed a model based on incoherent hopping between sites in the chain and an interfacial treatment of electrochemical interactions with the surrounding electrodes. Based on this model, we calculated the current-voltage (I-V) characteristics and found the results to be in good agreement with I-V measurements across and along individual microbial nanowires produced by the bacterium Shewanella oneidensis MR-1. Based on our analysis, we propose that multistep hopping in redox chains constitutes a viable strategy for extracellular charge transfer in microbial biofilms.

Excitation energy migration in covalently linked perylene bisimide macrocycles

A series of acetylene-linked perylene bisimide (PBI) macrocycles 3a–d with various ring sizes from trimer to hexamer have been synthesised by a palladium-catalysed homocoupling reaction of perylene bisimide 1. Photophysical properties of these PBI macrocycles have been examined by steady-state absorption, fluorescence, fluorescence lifetime, fluorescence anisotropy decay, and transient absorption measurements. Both pump-power dependence on the femtosecond transient absorption and the transient absorption anisotropy decay profiles are directly related with the excitation energy migration processes within PBI macrocycles where the exciton-exciton annihilation time and the polarization anisotropy decay time are well described in terms of the Forster-type incoherent energy hopping model. Consequently, the excitation energy hopping times of macrocycles become slower and then saturated as the ring size increases. Nevertheless, the intrinsically large transition dipole moment of PBI leads to fast energy transfer processes as compared to other artificial light-harvesting complexes such as those constructed from porphyrin building blocks.

Revisiting electronic couplings and incoherent hopping models for electron transport in crystalline C60 at ambient temperatures

We assess the validity of incoherent hopping models that have previously been used to describe electron transport in crystalline C(60) at room temperature. To this end we present new density functional theory based calculations of the electron transfer parameter defining these models. Specifically, we report electronic coupling matrix elements for several ten thousand configurations that are thermally accessible to the C(60) molecules through rotational diffusion around their lattice sites. We find that the root-mean-square fluctuations of the electronic coupling matrix element (11 meV) are almost as large as the average value (14 meV) and that the distribution is well approximated by a Gaussian. Importantly, due to the small reorganisation energy of the C(60) dimer (≈0.1 eV), the ET is almost activationless for the majority of configurations. Yet, for a small but significant fraction of orientations the coupling is so strong compared to reorganisation energy that no charge-localised state exists, a situation that is aggravated if zero-point motion of the nuclei is taken into account. The present calculations indicate that standard hopping models do not provide a sound description of electron transport in C(60), which might be the case for many other organics as well, and that approaches are needed that solve the electron dynamics directly.

Long-range electron tunnelling in oligo-porphyrin molecular wires

Short chains of porphyrin molecules can mediate electron transport over distances as long as 5-10 nm with low attenuation. This means that porphyrin-based molecular wires could be useful in nanoelectronic and photovoltaic devices, but the mechanisms responsible for charge transport in single oligo-porphyrin wires have not yet been established. Here, based on electrical measurements of single-molecule junctions, we show that the conductance of the oligo-porphyrin wires has a strong dependence on temperature, and a weak dependence on the length of the wire. Although it is widely accepted that such behaviour is a signature of a thermally assisted incoherent (hopping) mechanism, density functional theory calculations and an accompanying analytical model strongly suggest that the observed temperature and length dependence is consistent with phase-coherent tunnelling through the whole molecular junction.

Bulk photovoltaic effect of LiNbO3:Fe and its small-polaron-based microscopic interpretation

Based on recent experimental evidence on the electronic and optical properties of Fe${}_{\mathrm{Li}}^{2+}$ and Nb${}_{\mathrm{Nb}}^{4+}$ in LiNbO${}_{3}$:Fe, both strongly determined by their small polaron character, a microscopic model is presented accounting for the main features of the bulk photovoltaic effect (BPVE) in this material. The relative sizes of the components of the photovoltaic tensor are explained on an atomic basis. Optical small polaron transfer from Fe${}_{\mathrm{Li}}^{2+}$ to Nb${}_{\mathrm{Nb}}^{5+}$ conduction band states and the subsequent coherent bandlike electron transport, terminated by the formation of Nb${}_{\mathrm{Nb}}^{4+}$ free small polarons within about ${10}^{\ensuremath{-}13}$ s, characterize the first steps of the BPVE. These free polarons, transported by thermally activated incoherent hopping, are then trapped by deeper defects such as Nb${}_{\mathrm{Li}}^{5+}$ and Fe${}_{\mathrm{Li}}^{3+}$ impurities. The model allows us to explain the strong increase of the ionization probability of Fe${}_{\mathrm{Li}}^{2+}$ and the coherent transport length with photon energy. The low mobility of the Nb${}_{\mathrm{Nb}}^{4+}$ conduction polarons appears to be the reason for the high open-circuit photovoltaic fields attainable in LiNbO${}_{3}$.

Theoretical Study of Coherent Excitation Energy Transfer in Cryptophyte Phycocyanin 645 at Physiological Temperature

Recent two-dimensional photon-echo experiments suggest that excitation energy transfer in light harvesting systems occurs coherently rather than by incoherent hopping. The signature quantum beating of coherent energy transfer has been observed even at ambient temperatures. In this letter, we use an iterative linearized density matrix (ILDM) propagation approach to study this dynamics in a realistic multistate system−bath model. Our calculations reproduce the observed 400 fs decoherence time, and studies that vary the system Hamiltonian and structured spectral density describing the chromophore network−protein environment interactions give results that enable us to explore the role of initial coherence in energy transfer efficiency of the model network. Our findings suggest that the initial coherence has only a slight effect on energy transfer in this model system. We explore energy transfer optimization of different chromophores in the network by controlling environmental properties. This study points to the importance of stochastic resonance behavior in determining optimal network throughput.

Probing Coherence in Synthetic Cyclic Light-Harvesting Pigments

A series of π-extended cyclic thiophene oligomers of 12, 18, 24, and 30 repeat units have been studied using methods of ultrafast time-resolved absorption, fluorescence upconversion, and three-pulse photon echo. These measurements were conducted in order to examine the structure-function relationships that may affect the coherence between chromophores within the organic macrocycles. Our results indicate that an initial delocalized state can be seen upon excitation of the cyclic thiophenes. Anisotropy measurements show that this delocalized state decays on an ultrafast time scale and is followed by the presence of incoherent hopping. From the use of a phenomenological model, we conclude that our ultrafast anisotropy decay measurements suggest that the system does not reside in the Förster regime and coherence within the system must be considered. Three-pulse photon echo peak shift experiments reveal a clear dependence of initial peak shift with ring size, indicating a weaker coupling to the bath (and stronger intramolecular interactions) as the ring size is increased. Our results suggest that the initial delocalized state increases with ring size to distances (and number of chromophores) comparable to the natural light-harvesting system.

Iterative linearized density matrix propagation for modeling coherent excitation energy transfer in photosynthetic light harvesting

Rather than incoherent hopping between chromophores, experimental evidence suggests that the excitation energy transfer in some biological light harvesting systems initially occurs coherently, and involves coherent superposition states in which excitation spreads over multiple chromophores separated by several nanometers. Treating such delocalized coherent superposition states in the presence of decoherence and dissipation arising from coupling to an environment is a significant challenge for conventional theoretical tools that either use a perturbative approach or make the Markovian approximation. In this paper, we extend the recently developed iterative linearized density matrix (ILDM) propagation scheme [E. R. Dunkel et al., J. Chem. Phys. 129, 114106 (2008)] to study coherent excitation energy transfer in a model of the Fenna-Matthews-Olsen light harvesting complex from green sulfur bacteria. This approach is nonperturbative and uses a discrete path integral description employing a short time approximation to the density matrix propagator that accounts for interference between forward and backward paths of the quantum excitonic system while linearizing the phase in the difference between the forward and backward paths of the environmental degrees of freedom resulting in a classical-like treatment of these variables. The approach avoids making the Markovian approximation and we demonstrate that it successfully describes the coherent beating of the site populations on different chromophores and gives good agreement with other methods that have been developed recently for going beyond the usual approximations, thus providing a new reliable theoretical tool to study coherent exciton transfer in light harvesting systems. We conclude with a discussion of decoherence in independent bilinearly coupled harmonic chromophore baths. The ILDM propagation approach in principle can be applied to more general descriptions of the environment.

Charge correlations in polaron hopping through molecules

In many organic molecules the strong coupling of excess charges to vibrational modes leads to the formation of polarons, i.e., a localized state of a charge carrier and a molecular deformation. Incoherent hopping of polarons along the molecule is the dominant mechanism of transport at room temperature. We study the far-from-equilibrium situation where, due to the applied bias, the induced number of charge carriers on the molecule is high enough such that charge correlations become relevant. We develop a diagrammatic theory that exactly accounts for all many-particle correlations functions for incoherent transport through a finite system. We compute the transport properties of short sequences of DNA by expanding the diagrammatic theory up to second order in the hopping parameters. The correlations qualitatively modify the I-V characteristics as compared to those approaches where correlations are dealt with in a mean-field type approximation only.

Transition from Tunneling to Hopping in Single Molecular Junctions by Measuring Length and Temperature Dependence

The charge transport characteristics of a family of long conjugated molecular wires have been studied using the scanning tunneling microscope break junction technique. The family consists of four wires ranging from 3.1 to 9.4 nm in length. The two shortest wires show highly length dependent and temperature invariant conductance behavior, whereas the longer two wires show weakly length dependent and temperature variant behavior. This trend is consistent with a model whereby conduction occurs by two different mechanisms in the family of wires: by a coherent tunneling mechanism in the shorter two and by an incoherent charge hopping process in the longer wires. The temperature dependence of the two conduction mechanisms gives rise to a phenomenon whereby at elevated temperatures longer molecules that conduct via charge hopping can yield a higher conductance than shorter wires that conduct via tunneling. The evolution of molecular junctions as the tip retracts has been studied and explained in context of the characteristics of individual transient current decay curves.

Pathway Analysis on DNA Charge Transfer through Adenine and Guanine Bridges

Long-range DNA charge transfer dynamics of 5′-GAnGAmG3-3′ (n = 1, 2, m = 1−3) sequences have been explored on a quantitative basis. First, the degree of coherence was determined in terms of coherence length. Second, relative contribution of charge transfer mechanisms such as incoherent (nearest-neighbor) hopping, through-bridge, and superexchange as well as G-hopping mechanism was assessed by the density matrix decomposition based on the path integral formalism. Finally, time evolution of individual trajectory contribution was investigated through pathway analysis. Although G-hopping pathways were indeed found to be crucial, we have also shown that the initial transfer is driven by the nearest-neighbor hopping pathways through energetically less favored adenines followed by G-hopping pathways. Therefore, not only the G-hopping pathways but also the through-adenine pathways govern the overall long-range DNA charge transfer. By placing guanines no farther than two adenines apart, one can fully utilize effic...