Effects Of Dynamic Disorder Research Articles

Impact of static and dynamic disorder effects on the charge transport properties of merocyanine single crystals

Static and dynamic disorder effects impact the charge transport properties of merocyanine single crystals. While thermal disorder enhances the hole transfer rates, polarization phenomena lower the hole mobility and modify the transport topology.

Unraveling the role of thermal fluctuations on the exciton structure of the cryptophyte PC612 and PC645 photosynthetic antenna complexes.

Protein scaffolds play a crucial role in tuning the light harvesting properties of photosynthetic pigment-protein complexes, influencing pigment-protein and pigment-pigment excitonic interactions. Here, we investigate the influence of thermal dynamic effects on the protein tuning mechanisms of phycocyanin PC645 and PC612 antenna complexes of cryptophyte algae, featuring closed or open quaternary structures. We employ a dual molecular dynamics (MD) strategy that combines extensive classical MD simulations with multiple short Born-Oppenheimer quantum/molecular mechanical (QM/MM) simulations to accurately account for both static and dynamic disorder effects. Additionally, we compare the results with an alternative protocol based on multiple QM/MM geometry optimizations of the pigments. Subsequently, we employ polarizable QM/MM calculations using time-dependent density functional theory (TD-DFT) to compute the excited states, and we adopt the full cumulant expansion (FCE) formalism to describe the absorption and circular dichroism spectra. Our findings indicate that thermal effects have only minor impacts on the energy ladder in PC612, despite its remarkable flexibility owing to an open quaternary structure. In striking contrast, thermal effects significantly influence the properties of PC645 due to the absence of a hydrogen bond controlling the twist of ring D in PCB β82 bilins, as well as the larger impact of fluctuations on the excited states of MBV pigments, which possess a higher conjugation length compared to other bilin types. Overall, the dual MD protocol combined with the FCE formalism yields excellent spectral properties for PC612 and PC645, and the resultant excitonic Hamiltonians pave the way for future investigations concerning the implications of open and closed quaternary structures on phycocyanin light harvesting properties.

Effects of dynamic disorder on thermoelectric transport in soft materials

A model is developed that accounts for the effects of thermal disorder (both static and dynamic) in predicting the thermoelectric (TE) performance of weakly bonded semiconductors. With dynamic disorder included, the model is found to fit well with experimental results found in the literature for the density-of-states and the energy-dependent carrier mobility, which are key for assessing TE properties. The model is then used to analyze the concentration-dependent TE properties of the prototypical small molecular semiconductor rubrene. At low (e.g., intrinsic) carrier concentrations, where Fermi level pinning occurs, dynamic disorder is found to reduce electrical conductivity (σ), Seebeck coefficient (S), and thermoelectric power factor (PF) to values that are much lower than those traditionally predicted by static disorder models. As carrier concentration (p) increases, S exhibits nonlinear behavior, increasing well above the conventional S vs log(p) relationship before reaching a peak value (Speak∼1550μV/K). A critical carrier concentration (pcrit.≈4.299×10−4 molar ratio) is observed near Speak at which thermoelectric transport transitions from trap-limited behavior at low concentrations to conventional band behavior at high concentrations. Above this value, σ and PF are reduced compared to the perfect crystal and static-only conditions, causing a drop in the maximum PF by factors of 3 and 2.3, respectively. This PF reduction, while not as large as the PF reduction that occurs for low carrier concentration, is found to occur in a high concentration regime (p>pcrit.) that contains the PF maximum and has remained inaccessible to experimentalists due to dopant limitations that are worsened in the presence of dynamic disorder.

Simple evaluation of dynamic disorder effects on exciton transport.

Exciton transport in molecular materials is usually well described by Fermi's golden rule within the Condon approximation. However, when collective or molecular vibrations are thermally accessible, dynamic disorder effects have a sizable impact on the predicted exciton transfer rates and need to be considered for quantitative evaluation. In this work, we derive an analytic expression for the distribution of the electronic couplings that gives direct access to averaged quantities without the need to perform explicit calculations for a distribution of structural conformations. The distribution of exciton couplings and transfer rates obtained by this simple model in the study of singlet exciton transfer in the crystal naphthalene are in very good agreement with the data generated from molecular dynamics.

Ab Initio Molecular Dynamics Assessment on the Mixed Ionic–Electronic Transport for Crystalline Poly(3-Hexylthiophene) Using Full Explicit Lithium-Based Dopants and Additives

Here, we report ab initio molecular dynamics calculations dealing with mixed ionic–electronic transport in a poly(3-hexylthiophene) crystalline supercell, including the use of full explicit lithium-based dopants and additives. Up to now and to the best of our knowledge, the use of full explicit dopants and additives for both ionic and electronic transport calculations has remained practically unexplored probably due to their high computational cost. The use of fewer artifacts and other common assumptions in our calculations allowed us to reveal some interesting behavior associated with the presence of lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) dopants and dimethoxyethane (DME) additives on the mixed ionic–electronic transport in a wide temperature range. Our ionic and electronic conductivity calculations show a good correlation with the experimental reports of similar mixed ionic–electronic conductors in the very recent literature. For the electronic transport, our transfer integral (J) and reorientation energies (λ) values showed increment respect to typical unexplicit-doped calculations. Furthermore, we also introduce the role of the explicit dopant in the interchain, intrachain, “effective” doping, and charge-transfer complex bonding distances, and their associated static and dynamic disorder effects on electronic transport. These new insights can be extremely helpful to unravel not only the doping mechanism but also, and simultaneously, the mixed ionic–electronic transport mechanism for organic semiconductors. Advancing in the fundamental understanding of mixed ionic–electronic organic conductors is a key to boosting their properties for different applications going from energy storage to bioelectronic devices.

Maximizing the Carrier Mobilities of Metal-Organic Frameworks Comprising Stacked Pentacene Units.

Charge transport properties of metal–organic frameworks (MOFs) are of distinct interest for (opto)electronic applications. In contrast to the situation in molecular crystals, MOFs allow an extrinsic control of the relative arrangement of π-conjugated entities through the framework architecture. This suggests that MOFs should enable materials with particularly high through-space charge carrier mobilities. Such materials, however, do not yet exist, despite the synthesis of MOFs with, for example, seemingly ideally packed stacks of pentacene-bearing linkers. Their rather low mobilities have been attributed to dynamic disorder effects. Using dispersion-corrected density functional theory calculations, we show that this is only part of the problem and that targeted network design involving comparably easy-to-implement structural modifications have the potential to massively boost charge transport. For the pentacene stacks, this is related to the a priori counterintuitive observation that the electronic coupling between neighboring units can be strongly increased by increasing the stacking distance.

Impact of Fluoroalkylation on the n-Type Charge Transport of Two Naphthodithiophene Diimide Derivatives.

In this work, we investigate two recently synthesized naphthodithiophene diimide (NDTI) derivatives featuring promising n-type charge transport properties. We analyze the charge transport pathways and model charge mobility with the non-adiabatic hopping mechanism using the Marcus-Levich-Jortner rate constant formulation, highlighting the role of fluoroalkylated substitution in α (α-NDTI) and at the imide nitrogen (N-NDTI) position. In contrast with the experimental results, similar charge mobilities are computed for the two derivatives. However, while α-NDTI displays remarkably anisotropic mobilities with an almost one-dimensional directionality, N-NDTI sustains a more isotropic charge percolation pattern. We propose that the strong anisotropic charge transport character of α-NDTI is responsible for the modest measured charge mobility. In addition, when the role of thermally induced transfer integral fluctuations is investigated, the computed electron–phonon couplings for intermolecular sliding modes indicate that dynamic disorder effects are also more detrimental for the charge transport of α-NDTI than N-NDTI. The lower observed mobility of α-NDTI is therefore rationalized in terms of a prominent anisotropic character of the charge percolation pathways, with the additional contribution of dynamic disorder effects.

Theoretical study of synergetic effect between halogenation and pyrazine substitutions on transport properties of silylethynylated pentacene

Combining quantum-tunneling-effect-enabled hopping theory with kinetic Monte Carlo simulation and dynamic disorder effects, the charge transport properties of a series of N-hetero 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN) derivatives with halogen substitutions were studied.

A map of high-mobility molecular semiconductors.

The charge mobility of molecular semiconductors is limited by the large fluctuation of intermolecular transfer integrals, often referred to as off-diagonal dynamic disorder, which causes transient localization of the carriers' eigenstates. Using a recently developed theoretical framework, we show here that the electronic structure of the molecular crystals determines its sensitivity to intermolecular fluctuations. We build a map of the transient localization lengths of high-mobility molecular semiconductors to identify what patterns of nearest-neighbour transfer integrals in the two-dimensional (2D) high-mobility plane protect the semiconductor from the effect of dynamic disorder and yield larger mobility. Such a map helps rationalizing the transport properties of the whole family of molecular semiconductors and is also used to demonstrate why common textbook approaches fail in describing this important class of materials. These results can be used to rapidly screen many compounds and design new ones with optimal transport characteristics.

Computational study on hole conduction in normal alkanes: Anisotropy and effect of dynamic disorder

Despite its importance, carrier conduction in electrical insulators is poorly understood. This work presents a computational study of hole conduction in single crystalline alkanes (n-C18H38 and n-C36H74). Hole mobilities are computed with the combination of molecular dynamics simulation, quantum chemical calculation, and the kinetic Monte Carlo method. The hole hopping rate is computed by the Fermi golden rule rate kernel without high temperature approximation. A strong correlation between the anisotropy of hole mobility and crystalline morphology is found. Hole mobilities in the direction of the c axis are more than an order of magnitude larger than those in the a − b plane. At room temperature, hole mobility is increased by roughly a factor of 10 due to the thermal motion of molecules. Computed anisotropic hole mobilities are in reasonable agreement with experimental values when the effect of dynamic disorder is taken into account. The results strongly indicate that hole transfer in crystalline alkane occurs in the phonon-assisted transport regime.

Effects of dynamic disorder on exciton migration: Quantum diffusion, coherences, and energy transfer.

We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both same bath (when baths are spatially correlated) and independent bath (when baths are completely uncorrelated) limits. In the latter case, all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain time dependent population distribution by solving Kubo's quantum stochastic Liouville equation. In the Markovian limit, both energy transfer dynamics and mean square displacement of the exciton behave the similar way in same and independent bath cases. However, these two baths can give rise to a markedly different behavior in the non-Markovian limit. We note that previously only the same bath case has been studied in the non-Markovian limit. The other main results of our study include the following. (i) For an average, non-zero off-diagonal coupling value J, exciton migration remains coherent in same bath case even at long times while it becomes incoherent in independent bath case in the Markovian limit. (ii) Coherent transfer is manifested in an oscillatory behavior of the energy transfer dynamics accompanied by faster-than diffusive spread of the exciton from the original position. (iii) Agreement with available analytical expression of mean squared displacement is good in Markovian limit for independent bath (off-diagonal fluctuation) case but only qualitative in non-Markovian limit for which no complete analytical solution is available. (iv) We observe transition from coherent to incoherent transport in independent bath (diagonal fluctuation) case when the bath is made progressively more Markovian. We present an analytical study that shows coherence to propagate through excited bath states. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.

Computational Study of Excess Electron Mobility in High-Pressure Liquid Benzene

In recent years, excess electron transfer in organic liquids has attracted increasing interest owing to the emerging class of liquid organic semiconductors. In this study, to achieve a comprehensive understanding of electron conduction in liquids, we investigate hopping electron conduction in liquids from an atomistic viewpoint. High-pressure liquid benzene is chosen as a simple model system. Hopping electron mobility is computed using a combination of molecular dynamics simulations, quantum chemical calculations, and kinetic Monte Carlo methods. The computed electron mobility is in good agreement with the experimental values. Because the amplitude of the intermolecular vibration observed in liquids is larger compared to that in solids, the effect of dynamic disorder on electron mobility is investigated. The time scale of the change in electronic couplings due to the rotation of molecules is comparable to that of the electron residence time at each benzene molecule at the absence of change in the arrangement of a benzene dimer. Thus, the effect of dynamic disorder is evaluated by a Monte Carlo-based analysis. It is shown that the effect of dynamic disorder on electron mobility is small even though electronic couplings between molecules fluctuate by more than an order of magnitude.

Modeling the heterogeneous catalytic activity of a single nanoparticle using a first passage time distribution formalism

Metal nanoparticles are heterogeneous catalysts and have a multitude of non-equivalent, catalytic sites on the nanoparticle surface. The product dissociation step in such reaction schemes can follow multiple pathways. Proposed here for the first time is a completely analytical theoretical framework, based on the first passage time distribution, that incorporates the effect of heterogeneity in nanoparticle catalysis explicitly by considering multiple, non-equivalent catalytic sites on the nanoparticle surface. Our results show that in nanoparticle catalysis, the effect of dynamic disorder is manifested even at limiting substrate concentrations in contrast to an enzyme that has only one well-defined active site.

单分子拉伸力实验中DNA解链动力学无序效应的介观统计研究

Recent single molecule pulling experiments on DNA unzipping have revealed a heavy-tailed rupture force distribution, indicating dynamic disorder. Here we present a theoretical framework based on a generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and power-law memory kernel to study the kinetics of DNA unzipping to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. Such a GLE-fGn strategy is associated with the slow conformational fluctuations of macromolecules. By using the Kramers rate theory, we have obtained analytical formulae for the time-dependent rate coefficient k ( t , F ), and the distribution of rupture force p ( F ) which demonstrates a fat tail at high force as functions of time t and force F . In addition, through fitting our results to data from single molecule pulling experiments on DNA unzipping, we estimate the kinetic parameters and qualify the extent of disorder. Our work provides a plausible interpretation for the evidence of dynamic disorder in force-induced DNA unzipping, compared to two other models based on Bell model and Langevin equation (LE) approach.

Effect of dynamic disorder on charge carrier dynamics in Ph4DP and Ph4DTP molecules

Electronic structure calculations were used to study the charge transport and optical properties of 2,2′,6,6′-tetraphenyldipyranylidene (Ph4DP) and its sulfur analogue 2,2′,6,6′-tetraphenyldithiopyranylidene (Ph4DTP) based molecules.

Effects of dynamic disorder on exciton delocalization and photoinduced charge separation in DNA

The nature of electronically excited states in DNA is analyzed in detail using a combination of quantum mechanical (QM) semiempirical calculations and molecular dynamics (MD). For this purpose, we consider homogeneous π stacks extracted from the MD trajectory of a poly(A)·poly(T) oligomer. The environment is accounted for within the QM/MM scheme. The effects of structural fluctuations on exciton delocalization and photoinduced charge separation are explored using the quantitative analysis of the electron density in the excited states. We distinguish the effects generated by the vibronic interactions within nucleobases and by the environment of the π stack. While in ideal B-DNA stacks (A-T)n singlet excited states are spread over all intrastrand nucleobases, the average exciton length is ~0.75n, thermal fluctuations decrease considerably the extent of delocalization. The QM/MD model predicts that the excitons in (A-T)n stacks are spread over 3 bases (for n = 4 and 6, the average exciton length is found to be 2.6 ± 0.3 and 2.8 ± 0.3, respectively). We show that the main factor reducing the exciton length is the vibronic interactions within nucleobases whereas fluctuations of the π stack environment play a relatively minor role. The oscillator strength of electronic transitions from the ground state to charge-separated states Ak(+)Ak±1(-) and Tk(+)Tk±1(-) is found to be strong enough to populate directly these states by UV absorption at E = 5.0-5.3 eV. In contrast, the direct formation of interstrand charge transfer states Ai(+)Tj(-) is predicted to be unlikely.

Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Macromolecular transitions are subject to large fluctuations of rate constant, termed as dynamic disorder. The individual or intrinsic transition rates and activation free energies can be extracted from single-molecule pulling experiments. Here we present a theoretical framework based on a generalized Langevin equation with fractional Gaussian noise and power-law memory kernel to study the kinetics of macromolecular transitions to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. By using the Kramers' rate theory, we have calculated the fluctuating rate constant of molecular transition, as well as the experimentally accessible quantities such as the force-dependent mean lifetime, the rupture force distribution, and the speed-dependent mean rupture force. Particular attention is paid to the discrepancies between the kinetics with and without dynamic disorder. We demonstrate that these discrepancies show strong and nontrivial dependence on the external force or the pulling speed, as well as the barrier height of the potential of mean force. Our results suggest that dynamic disorder is an important factor that should be taken into account properly in accurate interpretations of single-molecule pulling experiments.

Stochastic Conformational Pumping: A Mechanism for Free-Energy Transduction by Molecules

Proteins and other macromolecules can act as molecular machines that convert energy from one form to another through cycles of conformational transitions. In a macroscopically fluctuating environment or at the single-molecule level, the probability for a molecule to be in any state j fluctuates, and the probability current from any other state i to state j is given as the sum of a steady-state current and a pumped current, I(ij)=I(ss)(ij)+F(ij)dP(j)/dt, where F(ij) is the fraction of the fluctuating current into and out of state j coming directly from state i, and dP(j)/dt is the rate of change of the probability for the molecule to be in state j. If the fluctuations arise from an equilibrium source, microscopic reversibility guarantees that the time average of the pumped current is zero. If, however, the fluctuations arise due to the action of a nonequilibrium source, the time average of the pumped current is not in general zero and can be opposite in sign to the steady-state current. The pumped current provides a mechanism by which fluctuations, whether generated externally or arising from an internal nonequilibrium chemical reaction, can do electrical, mechanical, or chemical work on a system by coupling into the equilibrium conformational transitions of a protein. In this review I examine work elaborating the mechanism of stochastic pumping and also discuss a thermodynamically consistent approach for modeling the effects of dynamic disorder on enzymes and other proteins.

Effect of dynamic disorder on charge transport along a pentacene chain

The lattice equation of motion and a numerical solution of the time-dependent Schr\"odinger equation provide us with a microscopic picture of charge transport in highly ordered molecular crystals. We have chosen the pentacene single crystal as a model system, and we study charge transport as a function of phonon-mode time-dependent fluctuations in the intermolecular electron transfer integral. For comparison, we include similar fluctuations also in the intramolecular potentials. The variance in these energy quantities is closely related to the temperature of the system. The pentacene system is shown to be very sensitive to fluctuation in the intermolecular transfer integral, revealing a transition from adiabatic to nonadiabatic polaron transport for increasing temperatures. The extension of the polaron at temperatures above 200 K is limited by the electron localization length rather than the interplay between the electron transfer integral and the electron-phonon coupling strength.

Ge‐based skutterudites MPt4Ge12: A comparative 195Pt NMR study

AbstractThe new Ge‐based skutterudites MPt4Ge12 are investigated by 195Pt NMR. They form with M = Ba, Sr, La, Ce, Pr, Nd, Sm, Eu, Th and U and in contrast to some pnictide skutterudites they remain metallic independent of the filler ion. Here we show that, consistent with the Korringa theory, the residual shift 195K(T → 0) scales with the density of states N(EF) and with the electronic specific heat coefficient γ. For the heavy filler ions La and Th an unusual 195K(T) dependence was found which might be associated to the effect of dynamic disorder (rattling). For paramagnetic CePt4Ge12 a Curie–Weiss‐like behaviour in both the shift 195K(T) and the bulk susceptibility χ(T) confirms the Ce3+‐4f1‐state at high temperatures. At low temperatures 195K(T) passes through a maximum at around 60 K and saturates below 10 K. This is interpreted being due to an unstable Ce valence, like, e.g. in CeSn3. Further evidence comes from the spin‐lattice relaxation where 195(1/T1) starts to deviate from its low‐temperature linear Korringa‐type of behaviour at around 60 K. We discuss our findings in the context of a dense Kondo system with valence fluctuations. For the van‐Vleck paramagnet SmPt4Ge12 at low‐temperatures, surprisingly, the shift is of the same order as for CePt4Ge12. It also passes through a maximum but at much lower temperatures (∼6 K).