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We report the preparation of high-quality, solvent-free [6,6]-Phenyl C61 butyric acid methyl ester (PCBM) large single crystals (size up to 0.5 mm) by slow drying of a chlorobenzene solution at room temperature. The monoclinic structure containing four PCBM molecules per unit cell was successfully solved (R factor = 0.0512) via micro-focused X-ray diffraction and employed as a reliable experimental model for further molecular dynamics simulations. We find that the first peak of the simulated fullerene-fullerene radial distribution function is centred at 10.05 A, giving a nearest neighbour coordination number of 7.0. The work reported herein provides the structural basis for a fundamental understanding of charge transport in this important functional material that is particularly relevant to organic solar cells.

We employ a periodic plane-wave implementation of constrained density functional theory to describe electron tunnelling between oxygen vacancy defects in MgO. We find that calculated electron transfer parameters, and therefore electron tunnelling rates, depend sensitively on the fraction of Hartree-Fock exchange (HFX) used to approximate the exchange-correlation functional. In particular, we show that the exponential decay constant for electronic coupling (β) is proportional to the square-root of the band gap of MgO. Therefore, it is essential to use an exchange-correlation functional which predicts the correct band gap for accurate prediction of electron tunnelling rates. We also present a scheme for the correction of finite size effects for electronic coupling due to the interaction with periodic images, and discuss the sensitivity of the results with respect to the charge constraint used. The computationally demanding calculations presented in this work have only become feasible owing to recent advances in both computer hardware and code parallelisation and demonstrate that the first principles modelling of long-range electron transfer in wide-gap oxides is now possible.

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.

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction Ag(+)-->Ag(2+)+e(-) in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of Ag(+). Diabatic free energy curves of reduced (R) and oxidized (O) states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of Ag(+) and Ag(2+) are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of Ag(+) and find different values for the reorganization free energy of R (1.4 eV) and O (0.9 eV). The computed reorganization free energy of Ag(2+) is in good agreement with the experimental estimate of 0.9-1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for Ag(+) is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation. [on SciFinder (R)]

The thermochemistry of the RuO(4)(2-)+MnO(4)(-)--RuO(4)(-)+MnO(4)(2-) redox reaction in aqueous solution is studied by separate density-functional-based ab initio molecular-dynamics simulations of the component half reactions RuO(4)(2-)--RuO(4)(-)+e(-) and MnO(4)(2-)--MnO(4)(-)+e(-). We compare the results of a recently developed grand-canonical method for the computation of oxidation free energies to the predictions by the energy-gap relations of the Marcus theory that can be assumed to apply to these reactions. The calculated redox potentials are in good agreement. The subtraction of the half-reaction free energies gives an estimate of the free energy of the full reaction. The result obtained from the grand-canonical method is -0.4 eV, while the application of the Marcus theory gives -0.3 eV. These should be compared to the experimental value of 0.0 eV. Size effects, in response to increasing the number of water molecules in the periodic model system from 30 to 48, are found to be small ( approximately 0.1 eV). The link to the Marcus theory also has enabled us to compute reorganization free energies for oxidation. For both the MnO(4)(2-) and RuO(4)(2-) redox reactions we find the same reorganization free energy of 0.8 eV (1.0 eV in the larger system). The results for the free energies and further analysis of solvation and electronic structure confirm that these two tetrahedral oxoanions show very similar behavior in solution in spite of the central transition-metal atoms occupying a different row and column in the periodic table.

Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron-phonon couplings.Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms "flickering" polarons, objects that are delocalized over 10-20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed "transient delocalization", this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.

We evaluate the validity of the commonly assumed polaron hopping model for some of the most popular organic semiconductors, rubrene, pentacene, and C60. This model is based on the assumption that the charge carrier is localized, i.e., forms a polaron that hops from one molecule to the next. We have calculated the relevant intermolecular charge transfer parameters that determine whether a polaron forms or not: electronic coupling matrix element and reorganization energy for the above materials using quantum chemical calculations and molecular dynamics simulations. We find that neither for rubrene nor pentancene the hopping model is justified due to the relatively large electronic couplings between molecules in the respective herringbone layers. For C60 the coupling matrix elements are smaller, and a small but finite barrier for charge transport exists in any transport direction. Despite the theoretical problems surrounding the polaron transport model, we find that mobilities based on this model (as obtaine...

The interaction of amino acids with metal electrodes plays a crucial role in bioelectrochemistry and the emerging field of bionanoelectronics. Here we present benchmark calculations of the adsorption structure and energy of all natural amino acids on Au(111) in vacuum using a van-der-Waals density functional (revPBE-vdW) that showed good performance on the S22 set of weakly bound dimers (mean relative unsigned error (MRUE) wrt CCSD(T)/CBS = 13.3%) and adsorption energies of small organic molecules on Au(111) (MRUE wrt experiment = 11.2%). The vdW-DF results are then used to assess the accuracy of a popular force field for Au-amino acid interactions, GolP-CHARMM, which explicitly describes image charge interactions via rigid-rod dipoles. We find that while the force field underestimates adsorption distances, it does reproduce the binding energy rather well (MRUE wrt revPBE-vdW = 11.3%) with the MRUE decreasing in the order Cys, Metaminesaliphaticcarboxylicaromatic. We also present a parametrization of the bonding interaction between sulfur-containing molecules and the Au(111) surface and report force field parameters that are compatible with GolP-CHARMM. We believe the vdW-DF calculations presented herein will provide useful reference data for further force field development, and that the new Au-S bonding parameters will enable improved simulations of proteins immobilized on Au-electrodes via S-linkages.

A robust understanding of the mechanoelectric response of organic semiconductors is crucial for the development of materials for flexible electronics. In particular, the prospect of using external mechanical strain to induce a controlled modulation in the charge mobility of the material is appealing. Here we develop an accurate computational protocol for the prediction of the mechanical strain dependence of charge mobility. Ab initio molecular dynamics simulations with a van der Waals density functional are carried out to quantify the off-diagonal electronic disorder in the system as a function of strain by the explicit calculation of the thermal distributions of electronic coupling matrix elements. The approach is applied to a representative molecular organic semiconductor, single-crystal rubrene. We find that charge mobility along the high-mobility direction a⃗ increases with compressive strain, as one might expect. However, the increase is larger when compressive strain is applied in the perpendicular direction than in the parallel direction with respect to a⃗, in agreement with experimental reports. We show that this seemingly counterintuitive result is a consequence of a significantly greater suppression of electronic coupling fluctuations in the range of 50–150 cm–1, when strain is applied in the perpendicular direction. Thus our study highlights the importance of considering off-diagonal electron–phonon coupling in understanding the mechanoelectric response of organic semiconducting crystals. The computational approach developed here is well suited for the accurate prediction of strain–charge mobility relations and should provide a useful tool for the emerging field of molecular strain engineering.

Electron-transporting multi-heme cytochromes are essential to the metabolism of microbes that inhabit soils and carry out important biogeochemical processes. Recently the first crystal structure of a prototype bacterial deca-heme cytochrome (MtrF) has been resolved and its electrochemistry characterized. However, the molecular details of electron transport along heme chains in the cytochrome are difficult to access via experiment due to the nearly identical chemical nature of the heme cofactors. Here we employ large-scale molecular dynamics simulations to compute the redox potentials of the 10 hemes of MtrF in aqueous solution. We find that as a whole they fall within a range of ~0.3 V, in agreement with experiment. Individual redox potentials give rise to a free energy profile for electron transport that is approximately symmetric with respect to the center of the protein. Our calculations indicate that there is no significant potential bias along the orthogonal octa- and tetra-heme chains, suggesting that under aqueous conditions MtrF is a nearly reversible two-dimensional conductor.

A new molecular dataset called HAB79 is introduced to provide ab initio reference values for electronic couplings (transfer integrals) and to benchmark density functional theory (DFT) and density functional tight-binding (DFTB) calculations. The HAB79 dataset is composed of 79 planar heterocyclic polyaromatic hydrocarbon molecules frequently encountered in organic (opto)electronics, arranged to 921 structurally diverse dimer configurations. We show that CASSCF/NEVPT2 with a minimal active space provides a robust reference method that can be applied to the relatively large molecules of the dataset. Electronic couplings are largest for cofacial dimers, in particular, sulfur-containing polyaromatic hydrocarbons, with values in excess of 0.5 eV, followed by parallel displaced cofacial dimers. V-shaped dimer motifs, often encountered in the herringbone layers of organic crystals, exhibit medium-sized couplings, whereas T-shaped dimers have the lowest couplings. DFT values obtained from the projector operator-based diabatization (POD) method are initially benchmarked against the smaller databases HAB11 (HAB7-) and found to systematically improve when climbing Jacob���s ladder, giving mean relative unsigned errors (MRUEs) of 27.7% (26.3%) for the generalized gradient approximation (GGA) functional BLYP, 20.7% (15.8%) for hybrid functional B3LYP, and 5.2% (7.5%) for the long-range corrected hybrid functional omega-B97X. Cost-effective POD in combination with a GGA functional and very efficient DFTB calculations on the dimers of the HAB79 database give a good linear correlation with the CASSCF/NEVPT2 reference data, which, after scaling with a multiplicative constant, gives reasonably small MRUEs of 17.9% and 40.1%, respectively, bearing in mind that couplings in HAB79 vary over 4 orders of magnitude. The ab initio reference data reported here are expected to be useful for benchmarking other DFT or semi-empirical approaches for electronic coupling calculations.

The electronic and charge transport properties of porphyrin and tetra-indole porphyrinoid single layer covalent organic frameworks (COFs) are investigated by means of density functional theory calculations. Ultrathin diacetylene-linked COFs based on oxidized tetra-indole cores are narrow gap 2D semiconductors, featuring a pronounced anisotropic electronic band structure due to the combination of dispersive and flat band characteristics, while registering high room temperature charge carrier mobilities. The capability of bandgap and charge carrier localization tuning via the careful selection of fourfold porphyrin and porphyrinoid cores and twofold articulated linkers is demonstrated, with the majority of systems exhibiting electronic gap values between 1.75 eV and 2.3 eV. Tetra-indoles are also capable of forming stable monolayers via non-articulated core fusing, resulting in 2D morphologies with extended π-conjugation and semi-metallic behavior.

The development of highly efficient methods for the calculation of electronic coupling matrix elements between the electron donor and acceptor is an important goal in theoretical organic semiconductor research. In Paper I [F. Gajdos, S. Valner, F. Hoffmann, J. Spencer, M. Breuer, A. Kubas, M. Dupuis, and J. Blumberger, J. Chem. Theory Comput. 10, 4653 (2014)], we introduced the analytic overlap method (AOM) for this purpose, which is an ultrafast electronic coupling estimator parameterized to and orders of magnitude faster than density functional theory (DFT) calculations at a reasonably small loss in accuracy. In this work, we reparameterize and extend the AOM to molecules containing nitrogen, oxygen, fluorine, and sulfur heteroatoms using 921 dimer configurations from the recently introduced HAB79 dataset. We find again a very good linear correlation between the frontier orbital overlap, calculated ultrafast in an optimized minimum Slater basis, and DFT reference electronic couplings. The new parameterization scheme is shown to be transferable to sulfur-containing polyaromatic hydrocarbons in experimentally resolved dimeric configurations. Our extension of the AOM enables high-throughput screening of very large databases of chemically diverse organic crystal structures and the application of computationally intense non-adiabatic molecular dynamics methods to charge transport in state-of-the-art organic semiconductors, e.g., non-fullerene acceptors.