Ultrafast Electron Transfer with Symmetrical Quasi-classical Dynamics based on Mapping Hamiltonian and Quantum Dynamics based on ML-MCTDH

Symmetrical quasi-classical (SQC) method based on mapping Hamiltonian is an efficient approach that is potentially useful to treat the nonadiabatic dynamics of very large systems. We try to evaluate the performance of this method in the ultrafast electron transfer processes involving a few of electronic states and a large number of vibrational modes. The multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method was used to get the accurate dynamical results for benchmark. Although the population dynamics in the longtime limit show differences in the ML-MCTDH and SQC calculations, the SQC method gives acceptable results.     

Multilayer multiconfiguration time-dependent Hartree method: implementation and applications to a Henon-Heiles hamiltonian and to pyrazine

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6×10(7)time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5×10(5) coefficients and requiring a shorter computation time.     

A unified theory for charge-carrier transport in organic crystals

To characterize the crossover from bandlike transport to hopping transport in molecular crystals, we study a microscopic model that treats electron-phonon interactions explicitly. A finite-temperature variational method combining Merrifield's transformation with Bogoliubov's theorem is developed to obtain the optimal basis for an interacting electron-phonon system, which is then used to calculate the bandlike and hopping mobilities for charge carriers. Our calculations on the one dimensional (1D) Holstein model at T=0 K and finite temperatures show that the variational basis gives results that compared favorably to other analytical methods. We also study the structures of polaron states at a broad range of parameters including different temperatures. Furthermore, we calculate the bandlike and hopping mobilities of the 1D Holstein model in different parameters and show that our theory predicts universal power-law decay at low temperatures and an almost temperature independent behavior at higher temperatures, in agreement with experimental observations. In addition, we show that as the temperature increases, hopping transport can become dominant even before the polaron state changes its character. Thus, our result indicates that the self-trapping transition studied in conventional polaron theories does not necessarily correspond to the bandlike to hopping transition in the transport properties in organic molecular crystals. Finally, a comparison of our 1D results with experiments on ultrapure naphthalene crystals suggests that the theory can describe the charge-carrier mobilities quantitatively across the whole experimental temperature range.     

Dynamics of a Holstein polaron with off-diagonal coupling

Dynamics of a one-dimensional Holstein polaron with off-diagonal exciton-phonon coupling is studied by employing the Dirac-Frenkel time-dependent variational principle. The trial state used is the Davydov D(2) Ansatz with two sets of variational parameters, one for each constituting particle in the linearly coupled exciton-phonon system. Validity of the approach is carefully checked by quantifying how faithfully the trial state follows the Schro?dinger equation. A close examination of variational outputs reveals fine details of polaron dynamics and intricacies of dynamic exciton-phonon correlations. In the absence of diagonal coupling, the change in the polaron effective mass hinges on the sign of the transfer integral due to the antisymmetric nature of the off-diagonal coupling. The role of the off-diagonal coupling switches from being an agent of transport at moderate coupling strengths to that of localization at large coupling strengths. Increasing the phonon bandwidth leads to a reduced polaron effective mass at the zone center and an overall lowering of the polaron band.     

Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach

The recently proposed multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) approach to evaluating reactive quantum dynamics is applied to two model condensed-phase proton transfer reactions. The models consist of a one-dimensional double-well "system" that is bilinearly coupled to a "bath" of harmonic oscillators parameterized to represent a condensed-phase environment. Numerically exact quantum-mechanical flux correlation functions and thermal rate constants are obtained for a broad range of temperatures and system-bath coupling strengths, thus demonstrating the efficacy of the ML-MCTDH approach. Particular attention is focused on the regime where low temperatures are combined with weak system-bath coupling. Under such conditions it is found that long propagation times are often required and that quantum coherence effects may prevent a rigorous determination of the rate constant.     

Time-dependent ion selectivity in capacitive charging of porous electrodes

In a combined experimental and theoretical study, we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl(2) mixtures, when the concentration of Na(+) ions in the water is five times the Ca(2+)-ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na(+) cations are preferentially adsorbed in the EDLs, and later, they are gradually replaced by the minority, divalent Ca(2+) cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is short-circuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca(2+)/Na(+)-ratio of a factor of 300 is achieved. The phenomenon of time-dependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay between the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations.     

Theoretical study of long oligothiophene dications: bipolaron vs polaron pair vs triplet state

A series of oligothiophene dications (from the sexithiophene dication to the 50-mer oligothiophene dication, nT2+, n = 6-50) were studied. Density functional theory (DFT) at the B3LYP/6-31G(d) level and, in some cases, also at BLYP/6-31Gd, was applied to study the singlet and triplet states of the whole series. We found that the singlet state is the ground state for all oligothiophene dications up to the 20-mer, and that the singlet and triplet states are degenerate for longer oligomers. Thus, the triplet state is never a pure ground state for these dications. We found that, for short oligothiophenes dication (e.g., 6T2+), the bipolaron state is the more important state, with only a small contribution made by the polaron pair state. For medium size oligothiophene dications (e.g., 14T2+), both the bipolaron state and the polaron-pair state contribute to the electronic structure. Finally, in long oligothiophene dications, such as 30T2+ and 50T2+, the contribution from the polaron pair state becomes dominant, and these molecules can be considered as consisting of two independent cation radicals or a polaron pair. Results from isodesmic reactions show that the stability of oligothiophene cation radicals over dications is inversely proportional to chain length. Small oligothiophene dications (n = 6-12) were studied at the CASSCF(m,m)/6-31G(d) (m = 4, 6, and 10) level. The major conclusions of this paper regarding the relative energy of the singlet state versus the triplet state and regarding the relative stability of the bipolaron versus the polaron pair were also supported by CASSCF calculations.     

Thermoelectric power of superionic conductors

A technique for the calculation of the thermoelectric power in many-particle systems exhibiting hopping conduction is presented. It is shown that the combination of thermopower and conductivity data provides very useful information about the microscopic nature of the ion hopping process in solid electrolytes. There are two main qualitative features of the transport data. In most systems the heat of transport (determined from the thermopower) and the activation energy for conduction are nearly equal, and in systems exhibiting lattice gas order-disorder transitions, these parameters may change across the phase boundary. An extended polaron lattice gas model is presented which is consistent with these features of the data and which allows a determination of the relative strengths of static barrier and polaron effects on the hopping. The results of the model suggest that polaron coupling is relatively small in most materials except for those based on organic halides.     

Base sequence effects on transport in DNA

Given the success of the polaron model based on solvation in accounting for the width of a hole polaron on an all-adenine (A) sequence on DNA, we extend the calculations to other sequences. We find excellent agreement with the free energy differences measured by Lewis et al. (J. Am. Chem. Soc. 2000, 122, 12037-12038) between a guanine (G) cation and a pair of bases, GG, or a triple of bases, GGG, in all cases surrounded by As, by treating AGGA and AGGGA as solvated polarons. There is additional support for hole polaron formation in DNA from experiments in which oxidative damage due to injected holes is investigated in sequences involving Gs and As. Theory and comparison with transport measurements on repeated sequences involving multiple thymines (Ts) or combinations such as ATs or GCs, where C is cytosine, led to the suggestion that the basic sequences in these cases must be polarons whose wave functions have substantial amplitudes on both chains in a duplex. The size of an electron polaron in DNA is predicted to be similar to that of a hole polaron, approximately 4 or 5 bases. Although experiments have shown that polaron hopping is the dominant mode of charge transport in DNA with repeated sequences such as AGGA, further investigations, particularly of temperature dependence of site energies and transfer integrals, are needed to determine to what extent hole transport takes place by polaron hopping for arbitrary DNA sequences.     

Accurate quantum-mechanical rate constants for a linear response Azzouz-Borgis proton transfer model employing the multilayer multiconfiguration time-dependent Hartree approach

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is applied to simulate the quantum dynamics and thermal rate constant of the Azzouz-Borgis model of proton transfer in a polar solvent. To this end, the original atomistic potential is mapped to a system-bath model. Employing the flux correlation function formalism and importance sampling techniques, accurate quantum mechanical rate constants are obtained, which provide a benchmark for evaluating approximate approaches to study the quantum dynamics of condensed-phase chemical reactions. Furthermore, the validity of the mapping procedure is discussed based on the comparison of the classical dynamics of the original atomistic Azzouz-Borgis model and the mapped system-bath model.     

Polaron-exciton model of resonance energy transfer

It is shown that F?rster's expression for the electronic energy transfer rate can be recast in a form predicted for exciton motion that interacts strongly with molecular vibrations. Using a simple model based on the Kennard-Stepanov theory, F?rster's expression for the spectral overlap is shown to be of a thermally activated form, as obtained previously by multiphonon theory. In contrast, the high-frequency internal vibrations contribute a factor which results from tunneling through a potential barrier between potential curves in the configuration coordinate diagram. We thus show that resonance energy transfer is equivalent to phonon-assisted hopping of a trapped excitonic polaron.     

Duplex polarons in DNA

In earlier work we calculated the wavefunction and energy of the solvated polaron in DNA with a simple model in which the charge was taken to be on a single chain of bases at the center of the double helix. To better approximate the actual situation, we have now extended the calculations to the case in which the charge is distributed on two chains of bases, complementary to each other, one on each side of the center. The binding energy of the resulting polaron is somewhat larger than that obtained for the single-chain polaron, the result of each chain of the polaron being closer to some of the polarization charge it induces. Carrying out the calculations for a number of different sequences, we find that the polaron wavefunction is predominantly on one of the two chains, this usually being the one on which the charge was originally placed, despite the availability of lower energy sites on the other chain. This finding is in agreement with recent experiments of Schuster's group(Joy, A.; Ghosh, A. K.; Schuster, G. B. J. Am. Chem. Soc. 2006, 128, 5346-5347). Thus, in contradiction to the ideas of many researchers, there is no transport in which a hole zigzags from one chain to the other, as has been suggested for a sequence of guanines and cytosines (GCGCGC....), for example.     

Polaron effects and electric field dependence of the charge carrier mobility in conjugated polymers

Charge transport in conjugated polymers has been investigated using Monte Carlo simulations implemented on top of the Marcus theory for donor-acceptor transition rates. In particular, polaron effects and the dependency of the mobility on the temperature and the applied electric field have been studied. The conclusions are that while the qualitative temperature dependence is similar to that predicted by Miller-Abrahams theory in the Gaussian disorder model (GDM), the electric field dependence is characterized by a crossover into the Marcus inverted region, not present in the GDM. Furthermore, available analytical approximations to describe the electric field dependence of the mobility in Marcus theory fail to fit the simulation data and hence cannot be used to directly draw conclusions about the importance of polaron effects for charge transport in conjugated polymers.     

Experimental and theoretical study of three new benzothiazole-fused carbazole derivatives

Three new D-π-A type compounds, each containing one benzothiazole ring as an electron acceptor and one N-ethylcarbazole group as electron donor, were synthesized and characterized by elemental analysis, NMR, MS and thermogravimetric analysis. The absorption and emission spectra of three compounds were experimentally determined in several solvents and were simultaneously computed using density functional theory (DFT) and time-dependent density functional theory (TDDFT). The calculated reorganization energy for hole and electron indicates that three compounds are in favor of hole transport than electron transport. The calculated absorption and emission wavelengths are well coincident with the measured data. The calculated lowest-lying absorption spectra can be mainly attributed to intramolecular charge transfer (ICT). And the calculated fluorescence spectra can be mainly described as originating from an excited state with intramolecular charge transfer (ICT) character. The results show that three compounds exhibited excellent thermal stability and high fluorescence quantum yields, indicating their potential applications as excellent optoelectronic material in optical field.     

Kinetic Monte Carlo model of charge transport in hematite (alpha-Fe(2)O(3))

The mobility of electrons injected into iron oxide minerals via abiotic and biotic electron transfer processes is one of the key factors that control the reductive dissolution of such minerals. Building upon our previous work on the computational modeling of elementary electron transfer reactions in iron oxide minerals using ab initio electronic structure calculations and parametrized molecular dynamics simulations, we have developed and implemented a kinetic Monte Carlo model of charge transport in hematite that integrates previous findings. The model aims to simulate the interplay between electron transfer processes for extended periods of time in lattices of increasing complexity. The electron transfer reactions considered here involve the IIIII valence interchange between nearest-neighbor iron atoms via a small polaron hopping mechanism. The temperature dependence and anisotropic behavior of the electrical conductivity as predicted by our model are in good agreement with experimental data on hematite single crystals. In addition, we characterize the effect of electron polaron concentration and that of a range of defects on the electron mobility. Interaction potentials between electron polarons and fixed defects (iron substitution by divalent, tetravalent, and isovalent ions and iron and oxygen vacancies) are determined from atomistic simulations, based on the same model used to derive the electron transfer parameters, and show little deviation from the Coulombic interaction energy. Integration of the interaction potentials in the kinetic Monte Carlo simulations allows the electron polaron diffusion coefficient and density and residence time around defect sites to be determined as a function of polaron concentration in the presence of repulsive and attractive defects. The decrease in diffusion coefficient with polaron concentration follows a logarithmic function up to the highest concentration considered, i.e., approximately 2% of iron(III) sites, whereas the presence of repulsive defects has a linear effect on the electron polaron diffusion. Attractive defects are found to significantly affect electron polaron diffusion at low polaron to defect ratios due to trapping on nanosecond to microsecond time scales. This work indicates that electrons can diffuse away from the initial site of interfacial electron transfer at a rate that is consistent with measured electrical conductivities, but that the presence of certain kinds of defects will severely limit the mobility of donated electrons.     

Bimolecular recombination kinetics and interfacial electronic structures of poly[2-methoxy-5-(2-ethyl-hexyloxy)-p-phenylene vinylene] on gold studied using two-photon photoemission spectroscopy

Photoexcitation kinetics and interfacial electronic structures of poly[2-methoxy-5(2-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV) film on gold have been investigated using two-photon photoemission spectroscopy (2PPE). The authors directly probed a fixed intermediate state located at 0.95 eV above the Fermi level (or 2.95 eV below the vacuum level), assigned to a charged polaron. Based on the power law slope and the 2PPE spectra with laser intensity, they found that the polaron follows a second order bimolecular annihilation process. The 2PPE yield dramatically increases with increasing photon energy. They attribute this to an enhanced dissociation of hotter excitons at higher excitation levels. The work function of MEH-PPV/Au is measured to be 3.9 eV, 1.2 eV downshift from the clean gold, attributable to interface dipole effects. The energy gap between the intermediate polaron state and the hole polaron level is estimated to be 2.45 eV.     

Reconstruction of the free energy in the metastable region using the path ensemble

By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent distributions from which we reconstruct the free energy as a function of the magnetic field, temperature, and system size. From the reconstructed free energy, we obtain the free-energy barrier that is associated with the transition from a metastable state to the stable equilibrium state. Although mean-field theory predicts a sharp transition between the metastable and the unstable region where the free-energy barrier is zero, the results for the nearest-neighbor Ising model show that the free-energy barrier does not go to zero.     

Electronic structure and microscopic charge‐transport properties of a new‐type diketopyrrolopyrrole‐based material

Recently, diketopyrrolopyrrole (DPP)‐based materials have attracted much interest due to their promising performance as a subunit in organic field effect transistors. Using density functional theory and charge‐transport models, we investigated the electronic structure and microscopic charge transport properties of the cyanated bithiophene‐functionalized DPP molecule (compound 1 ). First, we analyzed in detail the partition of the total relaxation (polaron) energy into the contributions from each vibrational mode and the influence of bond‐parameter variations on the local electron–vibration coupling of compound 1 , which well explains the effects of different functional groups on internal reorganization energy (λ). Then, we investigated the structural and electronic properties of compound 1 in its isolated molecular state and in the solid state form, and further simulated the angular resolution anisotropic mobility for both electron‐ and hole‐transport using two different simulation methods: (i) the mobility orientation function proposed in our previous studies (method 1); and (ii) the master equation approach (method 2). The calculated electron‐transfer mobility (0.00003–0.784 cm² V^?1 s^?1 from method 1 and 0.02–2.26 cm² V^?1 s^?1 from method 2) matched reasonably with the experimentally reported value (0.07–0.55 cm² V^?1 s^?1). To the best of our knowledge, this is the first time that the transport parameters of compound 1 were calculated in the context of band model and hopping models, and both calculation results suggest that the intrinsic hole mobility is higher than the corresponding intrinsic electron mobility. Our calculation results here will be instructive to further explore the potential of other higher DPP‐containing quinoidal small molecules. © 2015 Wiley Periodicals, Inc.     

Theoretical study of the benzene excimer using time-dependent density functional theory

A theoretical characterization of the potential energy surfaces of the singlet benzene excimer states derived from the B2u monomer excited state has been performed using time-dependent density functional theory. The excited-state potential energy surfaces were initially characterized by computations along the parallel and perpendicular intermolecular translational coordinates. These calculations predict that the lowest excited state for parallel translation is bound with a minimum at 3.15 angstroms and with a binding energy of 0.46 eV, while the perpendicular translational coordinate was essentially found to be a repulsive state. At the calculated minimum distance, the effect of in-plane rotation, out-of-plane rotation, and slipped-parallel translation were examined. The rotational calculations predict that deviations from the D6h geometry lead to a destabilization of the excimer state; however, small angular variations in the range of 0 degrees -10 degrees are predicted to be energetically feasible. The slipped-parallel translational calculations also predict a destabilizing effect on the excimer state and were found to possess barriers to this type of dissociation in the range of 0.50-0.61 eV. When compared to experimentally determined values for the benzene excimer energetics, the calculated values were found to be in semiquantitative agreement. Overall, this study suggests that the time-dependent density functional theory method can be used to characterize the potential energy surfaces and the energetics of aromatic excimers with reasonable accuracy.