Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

Simulation of Temperature-Dependent Charge Transport in Organic Semiconductors with Various Degrees of Disorder.

Different trends in the temperature dependence of the mobility can be observed in organic semiconductors, which constitutes a serious challenge for theoretical approaches. In this work, we apply an atomistic bottom-up simulation for the calculation of temperature-dependent mobilities of a broad selection of materials, ranging from single crystal to amorphous solid. We evaluate how well the method is able to distinguish temperature dependences of different materials and how the findings relate to experimental observations. The applied method is able to cover the full range of temperature dependencies from activated transport in amorphous materials to band-like transport in crystals. In well-characterized materials, we find good agreement with the experiment and a band-like temperature dependence. In less-ordered materials, we find discrepancies from the experiment that indicated that experimentally studied materials possess a higher degree of disorder than do the simulated defect-free morphologies.

Multi-Scale Approach to Non-Adiabatic Charge Transport in High-Mobility Organic Semiconductors.

A linear scaling QM/MM model for studying charge transport in high-mobility molecular semiconductors is presented and applied to an anthracene single crystal and a hexabenzocoronene derivative in its liquid crystalline phase. The model includes both intra- and intermolecular electron-phonon couplings, long-range interactions with the environment, and corrections to the self-interaction error of density functional theory. By performing Ehrenfest simulations of the cationic system, hole mobilities are derived and compared to the experiment. A detailed picture of the charge carrier dynamics is given, and the performance of our method is discussed.

Charge carrier mobilities in organic semiconductors: crystal engineering and the importance of molecular contacts.

We have conducted a combined experimental and theoretical study on the optimization of hexa-peri-hexabenzocoronene (HBC) as organic semiconductor. While orientations with high electronic coupling are unfavorable in the native liquid crystalline phase of HBC, we enforced such orientations by applying external constraints. To this end, self-assembled monolayers (SAMs) were formed by a non-conventional preparation method on an Au-substrate using electrochemical control. Within these SAMs the HBC units are forced into favorable orientations that cannot be achieved by unconstrained crystallization. For simulating the charge transport we applied a recently developed approach, where the molecular structure and the charge carrier are propagated simultaneously during a molecular dynamics simulation. Experiments as well as simulations are mutually supportive of an improved mobility in these novel materials. The implication of these findings for a rational design of future organic semiconductors will be discussed.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT and FODFTB against high-level ab initio calculations. II.

A new database (HAB7-) of electronic coupling matrix elements (Hab) for electron transfer in seven medium-sized negatively charged π-conjugated organic dimers is introduced. Reference data are obtained with spin-component scaled approximate coupled cluster method (SCS-CC2) and large basis sets. Assessed DFT-based approaches include constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), self-consistent charge density functional tight-binding (FODFTB) and the recently described analytic overlap method (AOM). This complements the previously reported HAB11 database where only cationic dimers were considered. The CDFT method in combination with a functional based on PBE and including 50% of exact exchange (HFX) was found to provide best estimates, with a mean relative unsigned error (MRUE) of 8.2%. CDFT couplings systematically increase with decreasing fraction of HFX as a consequence of increasing delocalisation of the SOMO orbital. The FODFT method is found to be very robust underestimating electronic couplings by 28%. The FODFTB and AOM methods, although orders of magnitude more efficient in terms of computational effort than the DFT approaches, perform well with reasonably small errors of 54% and 29%, respectively, translating in errors in the non-adiabatic electron transfer rate of a factor of 2.4 and 1.7, respectively. We discuss carefully various sources of errors and the scope and limitations of all assessed methods taking into account the results obtained for both HAB7- and HAB11 databases.

Fragment orbital based description of charge transfer in peptides including backbone orbitals.

Charge transfer in peptides and proteins can occur on different pathways, depending on the energetic landscape as well as the coupling between the involved orbitals. Since details of the mechanism and pathways are difficult to access experimentally, different modeling strategies have been successfully applied to study these processes in the past. These can be based on a simple empirical pathway model, efficient tight binding type atomic orbital Hamiltonians or ab initio and density functional calculations. An interesting strategy, which allows an efficient calculations of charge transfer parameters, is based on a fragmentation of the system into functional units. While this works well for systems like DNA, where the charge transfer pathway is naturally divided into distinct molecular fragments, this is less obvious for charge transfer along peptide and protein backbones. In this work, we develop and access a strategy for an effective fragmentation approach, which allows one to compute electronic couplings for large systems along nanosecond time scale molecular dynamics trajectories. The new methodology is applied to a solvated peptide, for which charge transfer properties have been studied recently using an empirical pathway model. As could be expected, dynamical effects turn out to be important, which emphasizes the importance of using effective quantum approaches which allow for sufficient sampling. However, the computed rates are orders of magnitude smaller than experimentally determined, which indicates the shortcomings of present modeling approaches.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT, and FODFTB against high-level ab initio calculations.

We introduce a database (HAB11) of electronic coupling matrix elements (H(ab)) for electron transfer in 11 π-conjugated organic homo-dimer cations. High-level ab inito calculations at the multireference configuration interaction MRCI+Q level of theory, n-electron valence state perturbation theory NEVPT2, and (spin-component scaled) approximate coupled cluster model (SCS)-CC2 are reported for this database to assess the performance of three DFT methods of decreasing computational cost, including constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), and self-consistent charge density functional tight-binding (FODFTB). We find that the CDFT approach in combination with a modified PBE functional containing 50% Hartree-Fock exchange gives best results for absolute H(ab) values (mean relative unsigned error = 5.3%) and exponential distance decay constants ß (4.3%). CDFT in combination with pure PBE overestimates couplings by 38.7% due to a too diffuse excess charge distribution, whereas the economic FODFT and highly cost-effective FODFTB methods underestimate couplings by 37.6% and 42.4%, respectively, due to neglect of interaction between donor and acceptor. The errors are systematic, however, and can be significantly reduced by applying a uniform scaling factor for each method. Applications to dimers outside the database, specifically rotated thiophene dimers and larger acenes up to pentacene, suggests that the same scaling procedure significantly improves the FODFT and FODFTB results for larger π-conjugated systems relevant to organic semiconductors and DNA.

Charge transfer in model peptides: obtaining Marcus parameters from molecular simulation.

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.