Dependence of charge transfer reorganization energy on carrier localisation in organic molecular crystals

Taking the organic molecular material dithiophene-tetrathiafulvalene (DT-TTF) as an example of a high mobility organic molecular material, we use density functional calculations to calculate the dependency of the reorganization energy associated with charge carrier transport on: (i) the geometric and electronic responsiveness of the local molecular crystal environment, and, (ii) the local spatial extent of the charge carrier. We find that in our most realistic extended models the charge transfer reorganization energy is strongly dependent on carrier localization. In particular, whereas highly localized carriers are found to be highly susceptible to their charge transfer efficiency being affected by changes in the local crystal environment, more delocalized carriers are better able to maintain their low reorganization energies. Considering that maintaining a relatively small charge transfer reorganization energy magnitude is an important factor in achieving high carrier mobilities, we suggest that those materials better able to sustain carriers with short-range thermally resistant intermolecular delocalisation should be sought for device applications.     

Theoretically Rational Designs of Transport Organic Semiconductors Based on Heteroacenes

A Marcus electron transfer theory coupled with an incoherent polaron hopping and charge diffusion model in combining with first‐principle quantum chemistry calculation was applied to investigating the effects of heteroatom on the intermolecular charge transfer rate for a series of heteroacene molecules. The influences of intermolecular packing and charge reorganization energy were discussed. It was found that the sulphur and nitrogen substituted heteroacenes were intrinsically hole‐transporting materials due to the reduced hole reorganization energy and the enhanced overlap between HOMOs. For the oxygen‐substituted heteroacene, it was found that both the electronic couplings and the reorganization energies for holes and electrons were comparative, indicating the application potential of ambipolar devices. Most interestingly, for the boron‐substituted heteroacenes, theoretical calculations predicted a promising electron‐transport material, which is rare for organic materials. These findings provide insights into rationally designing organic semiconductors with specific properties.     

Reorganization energies of ferrocene-peptide monolayers

To deepen understanding of the electron transfer through a peptide backbone, we have investigated a series of noncyclic and cyclic ferrocene-peptide (Fc-peptide) cystamine conjugates immobilized on the gold microelectrode. Interaction of the ferrocenium group with BF4-, ClO4-, and PF6- as counterions was explored and the electron-transfer rates and reorganization energies were determined by variable temperature cyclic voltammetry. The highest reorganization energy was observed for the BF4- counterion, which has the weakest ability to associate with the ferrocenium cation. In addition, the more rigid cyclic Fc-peptide conjugates have a smaller reorganization energy ranging from 0.3 to 0.5 eV compared to less rigid noncyclic Fc-peptide cystamine conjugates which have higher reorganization energies in the range of 0.5-1.0 eV, which suggests that the dynamic properties of the conjugate play a role in mediating electron transfer in these systems.     

Absolute rates of hole transfer in DNA

Absolute rates of hole transfer between guanine nucleobases separated by one or two A:T base pairs in stilbenedicarboxamide-linked DNA hairpins were obtained by improved kinetic analysis of experimental data. The charge-transfer rates in four different DNA sequences were calculated using a density-functional-based tight-binding model and a semiclassical superexchange model. Site energies and charge-transfer integrals were calculated directly as the diagonal and off-diagonal matrix elements of the Kohn-Sham Hamiltonian, respectively, for all possible combinations of nucleobases. Taking into account the Coulomb interaction between the negative charge on the stilbenedicarboxamide linker and the hole on the DNA strand as well as effects of base pair twisting, the relative order of the experimental rates for hole transfer in different hairpins could be reproduced by tight-binding calculations. To reproduce quantitatively the absolute values of the measured rate constants, the effect of the reorganization energy was taken into account within the semiclassical superexchange model for charge transfer. The experimental rates could be reproduced with reorganization energies near 1 eV. The quantum chemical data obtained were used to discuss charge carrier mobility and hole-transport equilibria in DNA.     

Cyanation: providing a three-in-one advantage for the design of n-type organic field-effect transistors

The theoretical work presented here demonstrates that, when substitution takes place at appropriate positions, cyanation could be a useful tool for reducing the internal reorganization energy of molecules. A molecular-orbital-based explanation is given for this fundamentally important phenomenon. Some of the cyanated pentacene derivatives (nCN-PENT-n) not only have internal reorganization energies for electron transfer (lambda(-)) smaller than that of pentacene, but the lambda(-) values are even of the same magnitude as the internal reorganization energy for hole transfer (lambda(+)) of pentacene, a small value that few organic compounds have surpassed. In addition, cyanation raises the electron affinity of the parent compound and may afford good electronic couplings between neighboring molecules, because of its ability in promoting pi-stacking. For the design of high performance n-Type Organic field-effect transistors, high electron affinities, large intermolecular electronic couplings, and small reorganization energies are necessary. Cyanation may help in all three aspects. Two cyanated trialkylsilylethynyl pentacene derivatives with known pi-stacking structures are predicted to provide reasonably small internal reorganization energies, large electronic couplings, and high electron affinities. They have the potential to outperform N-fluoroalkylated dicyanoperylene-3,4:9,10-bis(dicarboximides) (PDI-FCN(2)) in terms of electron mobility.     

A theoretical description of charge reorganization energies in molecular organic P‐type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge‐transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP‐tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP‐EOM‐CCSD single‐point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X‐D and SOGGA11X yield accurate charge reorganization energies in comparison with IP‐EOM‐CCSD values. © 2016 Wiley Periodicals, Inc.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Structural variability and dynamics of the P3HT/PCBM interface and its effects on the electronic structure and the charge-transfer rates in solar cells

Using a range of realistic interface geometries obtained from a molecular dynamics simulation we study the effects of different microscopic atomic arrangements on the electronic structure and charge transfer rates of the prototypical photovoltaic interface between P3HT (poly(3-hexylthiophene)) and PCBM ([6,6]-phenyl-C(61)-butyric acid methyl ester). The electronic structures of charge-transfer (CT) states belong to two groups that can be denoted as "charge-separated" and "charge-bridging" states. For the former group of structures, which may lead to fully separated charges, the ranges and the average values of internal reorganization energy, the electronic coupling and the charge separated states energy are evaluated. A range and distribution of absolute charge separation (CS) and recombination (CR) rates are computed using the Marcus-Levich-Jortner rate equation. Due to the variety of P3HT/PCBM interface structures, a very broad range of CS (7.7 × 10(9)-1.8 × 10(12) s(-1)) and CR (2.5 × 10(5)-1.1 × 10(10) s(-1)) "instantaneous" rates are computed. However, the energetic parameters affecting the rate evolve in time due to the dynamic nature of the interface with a characteristic timescale of about 10 ns. For this reason the slowest CR instantaneous rates are not observed and the minimum CR rate observed is determined by the rate of conformational rearrangement at the interface. The combination of these observations provides a more general framework for the interpretation of experimental spectroscopic data, suggesting that the analysis based on simple first order rates may be insufficient to describe charge transfer in organic solar cell interfaces.     

Modulating charge-transfer interactions in topologically different porphyrin-C60 dyads

Control over the interchromophore separation, their angular relationship, and the spatial overlap of their electronic clouds in several ZnP-C(60) dyads (ZnP=zinc porphyrin) is used to modulate the rates of intramolecular electron transfer. For the first time, a detailed analysis of the charge transfer absorption and emission spectra, time-dependent spectroscopic measurements, and molecular dynamics simulations prove quantitatively that the same two moieties can produce widely different electron-transfer regimes. This investigation also shows that the combination of ZnP and C(60) consistently produces charge recombination in the inverted Marcus region, with reorganization energies that are remarkably low, regardless of the solvent polarity. The time constants of electron transfer range from the mus to the ps regime, the electronic couplings from a few tens to several hundreds of cm(-1), and the reorganization energies remain below 0.54 eV and can be as low as 0.16 eV.     

Experimental and calculation methods of studying the effect of second coordination sphere on standard rate constants of charge transfer for Cr(III)/Cr(II) redox couple in chloride melts

The cyclic voltammetry method was used to determine the standard rate constants of charge transfer (k _s) on a glassy carbon electrode for the Cr(III)/Cr(II) redox couple in the systems of NaCl-KCl-CrCl₃, KCl-CrCl₃, and CsCl-CrCl₃ in the temperature range of 973–1173 K. It was shown that k _s grows at an increase in the temperature and decreases as sodium cations are replaced by potassium and cesium cations in the second coordination sphere of chromium complexes. The calculations carried out using the PC GAMESS/Firefly quantum-chemical software by means of the DFT technique showed that the values of the charge transfer activation energy change monotonously in the series of Na-K-Cs in accordance with the ratio of reorganization energies. In its turn, this leads to monotonous variation of the charge transfer rate constants.     

Reorganization energy associated with small polaron mobility in iron oxide

The reorganization energy is an important quantity controlling electron transfer rates. The internal contribution arising from the energy to reorganize donor/acceptor bonds can be evaluated by the "direct" and "4-point" methods. We examine how spatial separation leading to the noninteracting character of the donor and acceptor affects the reorganization energy. We show that the direct method captures contributions from interaction of the donor and acceptor while the 4-point method does not, and the two methods converge at large separation. Comparing reorganization energies determined by the two methods yields a measure of the degree of interaction between the initial and final states. The analysis is illustrated in the characterization of small polarons in iron oxides.     

Charge transfer in organic molecules for solar cells: theoretical perspective

This tutorial review primarily illustrates rate theories for charge transfer and separation in organic molecules for solar cells. Starting from the Fermi's golden rule for weak electronic coupling, we display the microcanonical and canonical rates, as well as the relationship with the Marcus formula. The fluctuation effect of bridges on the rate is further emphasized. Then, several rate approaches beyond the perturbation limit are revealed. Finally, we discuss the electronic structure theory for calculations of the electronic coupling and reorganization energy that are two key parameters in charge transfer, and show several applications.     

Direct calculation of electron transfer parameters through constrained density functional theory

It is shown that constrained density functional theory (DFT) can be used to access diabatic potential energy surfaces in the Marcus theory of electron transfer, thus providing a means to directly calculate the driving force and the inner-sphere reorganization energy. We present in this report an analytic expression for the forces in constrained DFT and their implementation in geometry optimization, a prerequisite for the calculation of electron transfer parameters. The method is then applied to study the symmetric mixed-valence complex tetrathiafulvalene-diquinone radical anion, which is observed experimentally to be a Robin-Day class II compound but found by DFT to be in class III. Constrained DFT avoids this pitfall of over-delocalization and provides a way to find the charge-localized structure. In another application, driving forces and inner-sphere reorganization energies are calculated for the charge recombination (CR) reactions in formanilide-anthraquinone (FA-AQ) and ferrocene-formanilide-anthraquinone (Fc-FA-AQ). While the two compounds have similar reorganization energies, the driving force in FA-AQ is 1 eV larger than in Fc-FA-AQ, in agreement with experimental observations and supporting the experimental conclusion that the anomalously long-lived FA-AQ charge-separated state arises because the electron transfer is in the Marcus inverted region.     

Resonance Raman analysis of nonlinear solvent dynamics: betaine-30 in ethanol

Resonance Raman profiles for 14 vibrational modes of betaine-30 in ethanol at room temperature were measured at wavelengths within the first charge-transfer absorption band. The absorption spectrum and resonance Raman profiles were analyzed using time-dependent theory and a Brownian oscillator model modified to account for nonlinear solvent response; i.e., dependence of the solvent reorganization energy on the electronic state of the solute. As in our previous study of betaine-30 in acetonitrile, the solvent reorganization energy for the excited electronic state, determined from resonance Raman spectroscopy, was found to be smaller than that for the ground electronic state, determined from the absorption spectrum. The mode-dependent internal reorganization energies of betaine-30 in ethanol were found to be slightly larger than those of betaine-30 in acetonitrile. Temperature-dependent solvent reorganization energies for the ground electronic state were determined from analysis of the absorption line shape from 279 to 332 K and were found to decrease with increasing temperature. The influence of hydrogen bonding on the solvent and internal reorganization energy of betaine-30 is considered, and the physical basis for nonlinear solvent response is discussed.     

Density functional calculations of potential energy surface and charge transfer integrals in molecular triphenylene derivative HAT6

We investigate the effect of structural fluctuations on charge transfer integrals, overlap integrals, and site energies in a system of two stacked molecular 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT₆), which is a model system for conducting devices in organic photocell applications. A density functional based computational study is reported. Accurate potential energy surface calculations are carried out using an improved meta-hybrid density functional to determine the most stable configuration of the two weakly bound HAT₆ molecules. The equilibrium parameters in terms of the twist angle and co-facial separation are calculated. Adopting the fragment approach within the Kohn–Sham density functional framework, these parameters are combined to a lateral slide, to mimic structural/conformational fluctuations and variations in the columnar phase. The charge transfer and spatial overlap integrals, and site energies, which form the matrix element of the Kohn–Sham Hamiltonian are derived. It is found that these quantities are strongly affected by the conformational variations. The spatial overlap between stacked molecules is found to be of considerable importance since charge transfer integrals obtained using the fragment approach differ significantly from those using the dimer approach.     

Crystal packing and charge transport in single crystals of chrysene derivatives: Impact of halogenation

Crystal packing has strong influence on the charge mobility for organic semiconductors, so the elucidation of the structure-property relationship is important for the design of high-performance organic semiconductors. Halogen substitution has been shown to be a promising strategy to alter the crystal structure without significantly changing the molecular size in previous reports. This paper studies the influence of halogenation on charge transport in single crystals of chrysene derivatives from a theoretical standpoint. The structure-property relationship is first rationalized by investigating the reorganization energy and electronic coupling from the density functional theory calculations. Based on the Marcus charge transfer theory, the mobilities in the molecular monolayer are then calculated with the random walk simulation technique from which the angular resolution anisotropic mobilities are obtained on the fly. It is shown that the mobilities become much larger for holes than those for electrons in the molecular monolayer when the halogenation occurs. Furthermore, the intra-layer charge transport is little influenced by the inter-layer pathways in the single crystals of the halogenated chrysene derivatives, while the opposite case is shown for the crystal of the nonhalogenated chrysene derivative. The reason for the variations of charge transport is discussed theoretically.     

Prediction of reorganization free energies for biological electron transfer: a comparative study of Ru-modified cytochromes and a 4-helix bundle protein

The acceleration of electron transfer (ET) rates in redox proteins relative to aqueous solutes can be attributed to the protein's ability to reduce the nuclear response or reorganization upon ET, while maintaining sufficiently high electronic coupling. Quantitative predictions of reorganization free energy remain a challenge, both experimentally and computationally. Using density functional calculations and molecular dynamics simulation with an electronically polarizable force field, we report reorganization free energies for intraprotein ET in four heme-containing ET proteins that differ in their protein fold, hydrophilicity, and solvent accessibility of the electron-accepting group. The reorganization free energies for ET from the heme cofactors of cytochrome c and b(5) to solvent exposed Ru-complexes docked to histidine residues at the surface of these proteins fall within a narrow range of 1.2-1.3 eV. Reorganization free energy is significantly lowered in a designed 4-helix bundle protein where both redox active cofactors are protected from the solvent. For all ET reactions investigated, the major components of reorganization are the solvent and the protein, with the solvent contributing close to or more than 50% of the total. In three out of four proteins, the protein reorganization free energy can be viewed as a collective effect including many residues, each of which contributing a small fraction. These results have important implications for the design of artificial electron transport proteins. They suggest that reorganization free energy may in general not be effectively controlled by single point mutations, but to a large extent by the degree of solvent exposure of the ionizable cofactors.     

Charge transfer reactions of organic ions containing oxygen: Correlation between reaction energetics and cross sections

Cross sections for charge transfer reactions of organic ions containing oxygen have been obtained using time-of-flight techniques. Charge transfer cross sections have been determined for reactions of 2.0 to 3.4 keV ions produced by electron impact ionization of oxygen containing molecules such as methanol, ethanal and ethanol. Experimental cross section magnitudes have been correlated with reaction energy defects computed from ion recombination energies and target ionization energies. Large cross sections are observed for reacting systems with small energy defects.     

Molecular origin of differences in hole and electron mobility in amorphous Alq3--a multiscale simulation study

In order to determine the molecular origin of the difference in electron and hole mobilities of amorphous thin films of Alq(3) (meridional Alq(3) (tris(8-hydroxyquinoline) aluminium)) we performed multiscale simulations covering quantum mechanics, molecular mechanics and lattice models. The study includes realistic disordered morphologies, polarized site energies to describe diagonal disorder, quantum chemically calculated transfer integrals for the off-diagonal disorder, inner sphere reorganization energies and an approximative scheme for outer sphere reorganization energies. Intermolecular transfer rates were calculated via Marcus-theory and mobilities were simulated via kinetic Monte Carlo simulations and by a Master Equation approach. The difference in electron and hole mobility originates from the different localization of charge density in the radical anion (more delocalized) compared to the radical cation (more confined). This results in higher diagonal disorder for holes and less favourable overlap properties for the hole transfer integrals leading to an overall higher electron mobility.     

Structural dynamics and energy flow in Rydberg-excited clusters of N,N-dimethylisopropylamine

In molecular beams, the tertiary amine N,N-dimethylisopropyl amine can form molecular clusters that are evident in photoelectron and mass spectra obtained upon resonant multiphoton ionization via the 3p and 3s Rydberg states. By delaying the ionization pulse from the excitation pulse we follow, in time, the ultrafast energy relaxation dynamics of the 3p to 3s internal conversion and the ensuing cluster evaporation, proton transfer, and structural dynamics. While evaporation of the cluster occurs in the 3s Rydberg state, proton transfer dominates on the ion surface. The mass-spectrum shows protonated species that arise from a proton transfer from the alpha-carbon of the neutral parent molecule to the N-atom of its ionized partner in the dimer. DFT calculations support the proton transfer mechanism between tightly bonded cluster components. The photoelectron spectrum shows broad peaks, ascribed to molecular clusters, which have an instantaneous shift of about 0.5 eV toward lower binding energies. That shift is attributed to the charge redistribution associated with the induced dipoles in surrounding cluster molecules. A time-dependent shift that decreases the Rydberg electron binding energy by a further 0.4 eV arises from the structural reorganization of the cluster solvent molecules as they react to the sudden creation of a charge.