Using a combination of experimental and computational investigations, we assemble a consistent mechanistic model for the oxygen reduction reaction (ORR) at molecularly well-defined graphite-conjugated catalyst (GCC) active sites featuring aryl-pyridinium moieties (N+-GCC). ORR catalysis at glassy carbon surfaces modified with N+-GCC fragments displays near-first-order dependence in O2 partial pressure and near-zero-order dependence on electrolyte pH. Tafel analysis suggests an equilibrium one-electron transfer process followed by a rate-limiting chemical step at modest overpotentials that transitions to a rate-limiting electron transfer sequence at higher overpotentials. Finite-cluster computational modeling of the N+-GCC active site reveals preferential O2 adsorption at electrophilic carbons alpha to the pyridinium moiety. Together, the experimental and computational data indicate that ORR proceeds via a proton-decoupled O2 activation sequence involving either concerted or stepwise electron transfer and adsorption of O2, which is then followed by a series of electron/proton transfer steps to generate water and turn over the catalytic cycle. The proposed mechanistic model serves as a roadmap for the bottom-up synthesis of highly active N-doped carbon ORR catalysts.Keywords: density functional theory; electrocatalysis; mechanistic studies; N-doped carbon; oxygen reduction;

Computational screens for oxygen evolution reaction (OER) catalysts based on Sabatier analysis have seen great success in recent years; however, the concept of using chemical descriptors to form a reaction coordinate has not been put under scrutiny for complex systems. In this paper, we examine critically the use of chemical descriptors as a method for conducting catalytic screens. Applying density functional theory calculations to a two-center metal oxide model system, we show that the Sabatier analysis is quite successful for predicting activities and capturing the chemical periodic trends expected for the first-row transition metal series, independent of the proposed mechanism. We then extend this analysis to heterodimer metallic systems—metal oxide catalysts with two different catalytically active metal centers—and find signs that the Sabatier analysis may not hold for these more complex systems. By performing a principal component analysis on the computed redox potentials, we show (1) that a single chemical descriptor inadequately describes heterodimer overpotentials and (2) mixed-metal overpotentials cannot be predicted using only pure-metal redox potentials. We believe that the analysis presented in this article shows a need to move beyond the simple chemical descriptor picture when studying more complex mixed metal oxide OER catalysts.

Organic photovoltaic (OPV) devices hold a great deal of promise for the emerging solar market. However, to unlock this promise, it is necessary to understand how OPV devices generate free charges. Here, we analyze the energetics and charge delocalization of the interfacial charges in poly(p-phenylenevinylene) (PPV)/[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) and poly(3-hexylthiophene-2,5-diyl) (P3HT)/PCBM devices. We find that, in the PPV system, the interface does not produce molecular disorder, but an interfacial electric field is formed upon the inclusion of environmental polarization that promotes charge separation. In contrast, the P3HT system shows a significant driving force for charge separation due to interfacial disorder confining the hole. However, this feature is overpowered by the polarization of the electronic environment, which generates a field that inhibits charge separation. In the two systems studied herein, electrostatic effects dominate charge separation, overpowering interfacially induced disorder. This suggests that, when balancing polymeric order with electrostratic effects, the latter should take priority.

•A new method for solving chemical reaction kinetics with disorder in the rates (unimolecular or bimolecular) is presented.•The method uses a mean-field approximation to quickly compute self-consistent steady state populations.•We illustrate the proposed method with a working example of H2 production on a heterogeneous surface.We propose a method to quickly compute steady state populations of species undergoing a set of chemical reactions whose rate constants are heterogeneous. Using an average environment in place of an explicit nearest neighbor configuration, we obtain a set of equations describing a single fluctuating active site in the presence of an averaged bath. We apply this Mean Field Steady State (MFSS) method to a model of H2 production on a disordered surface for which the activation energy for the reaction varies from site to site. The MFSS populations quantitatively reproduce the KMC results across the range of rate parameters considered.Download high-res image (64KB)Download full-size image

We propose a calculation scheme that accelerates QM/MM simulations of solvated systems. This new approach is based on the adiabatic approximation whereby the solute degrees of freedom are separated from those of the solvent. More specifically, we assume that the solute electron density remains constant with respect to the relaxation of the solvent molecules. This allows us to achieve a dramatic speed-up of QM/MM calculations by discarding the slow self-consistent field cycle. We test this method by applying it to the calculation of the redox potential of aqueous transition metal ions. The root-mean-square deviation (RMSD) between the full solvation and adiabatic approximation is only 0.17 V. We find a RMSD from experimental values of 0.32 V for the adiabatic approximation as compared to 0.31 V for the full solvation model, so that the two methods are of essentially the same accuracy. Meanwhile, the adiabatic calculations are up to 10 times faster than the full solvation calculations, meaning that the method proposed here reduces the cost of QM/MM calculations while retaining the accuracy.

Organic molecules with charge-transfer (CT) excited states are widely used in industry and are especially attractive as candidates for fabrication of energy efficient OLEDs, as they can harvest energy from nonradiative triplets by means of thermally activated delayed fluorescence (TADF). It is therefore useful to have computational protocols for accurate estimation of their electronic spectra in order to screen candidate molecules for OLED applications. However, it is difficult to predict the photophysical properties of TADF molecules with LR-TDDFT, as semilocal LR-TDDFT is incapable of accurately modeling CT states. Herein, we study absorption energies, emission energies, zero–zero transition energies, and singlet–triplet gaps of TADF molecules using a restricted open-shell Kohn–Sham (ROKS) approach instead and discover that ROKS calculations with semilocal hybrid functionals are in good agreement with experiments—unlike TDDFT, which significantly underestimates energy gaps. We also propose a cheap computational protocol for studying excited states with large CT character that is found to give good agreement with experimental results without having to perform any excited-state geometry optimizations.

Thermally activated delayed fluorescence (TADF) is becoming an increasingly important OLED technology that extracts light from nonemissive triplet states via reverse intersystem crossing (RISC) to the bright singlet state. Here we present the rather surprising finding that in TADF materials that contain a mixture of donor and acceptor molecules the electron–hole separation fluctuates as a function of time. By performing time-resolved photoluminescence experiments, both with and without a magnetic field, we observe that at short times the TADF dynamics are insensitive to magnetic field, but a large magnetic field effect (MFE) occurs at longer times. We explain these observations by constructing a quantum mechanical rate model in which the electron and hole cycle between a near-neighbor exciplex state that shows no MFE and a separated polaron-pair state that is not emissive but does show magnetic field dependent dynamics. Interestingly, the model suggests that only a portion of TADF in these blends comes from direct RISC from triplet to singlet exciplex. A substantial contribution comes from an indirect path, where the electron and hole separate, undergo RISC from hyperfine interactions, and then recombine to form a bright singlet exciplex. These observations have a significant impact on the design rules for TADF materials, as they imply a separate set of electronic parameters that can influence efficiency.

Water splitting by artificial catalysts is a critical process in the production of hydrogen gas as an alternative fuel. In this paper, we examine the essential role of theoretical calculations, with particular focus on density functional theory (DFT), in understanding the water-splitting reaction on these catalysts. First, we present an overview of DFT thermochemical calculations on water-splitting catalysts, addressing how these calculations are adapted to condensed phases and room temperature. We show how DFT-derived chemical descriptors of reactivity can be surprisingly good estimators for reactive trends in water-splitting catalysts. Using this concept, we recover trends for bulk catalysts using simple model complexes for at least the first-row transition-metal oxides. Then, using the CoPi cobalt oxide catalyst as a case study, we examine the usefulness of simulation for predicting the kinetics of water splitting. We demonstrate that the appropriate treatment of solvent effects is critical for computing accurate redox potentials with DFT, which, in turn, determine the rate-limiting steps and electrochemical overpotentials. Finally, we examine the ability of DFT to predict mechanism, using ruthenium complexes as a focal point for discussion. Our discussion is intended to provide an overview of the current strengths and weaknesses of the state-of-the-art DFT methodologies for condensed-phase molecular simulation involving transition metals and also to guide future experiments and computations toward the understanding and development of novel water-splitting catalysts.

We introduce ForceBalance, a method and free software package for systematic force field optimization with the ability to parametrize a wide variety of functional forms using flexible combinations of reference data. We outline several important challenges in force field development and how they are addressed in ForceBalance, and present an example calculation where these methods are applied to develop a highly accurate polarizable water model. ForceBalance is available for free download at https://simtk.org/home/forcebalance.

We investigate and assign a previously reported unexpected transition in the metal–organic framework Zn2(NDC)2(DPNI) (1; NDC = 2,6-naphthalenedicarboxylate, DPNI = dipyridyl-naphthalenediimide) that displays linear arrangements of naphthalenediimide ligands. Given the longitudinal transition dipole moment of the DPNI ligands, J-coupling seemed possible. Photophysical measurements revealed a broad, new transition in 1 between 400 and 500 nm. Comparison of the MOF absorption spectra with that of a charge transfer (CT) complex formed by manual grinding of DPNI and H2NDC led to the assignment of the new band in 1 as arising from an interligand CT. Constrained density functional theory utilizing a custom long-range-corrected hybrid functional was employed to determine which ligands were involved in the CT transition. On the basis of relative oscillator strengths, the interligand CT was assigned as principally arising from π-stacked DPNI/NDC dimers rather than the alternative orthogonal pairs within the MOF.Keywords: charge transfer; constrained DFT; J-coupling; Koopman’s theorem; metal−organic frameworks;

Exciton dissociation at organic semiconductor interfaces is an important process for the design of future organic photovoltaic (OPV) devices, but at present, it is poorly understood. On the one hand, exciton breakup is very efficient in many OPVs. On the other, electron–hole pairs generated by an exciton should be bound by Coulombic attraction, and therefore difficult to separate in materials of such low dielectric. In this paper, we highlight several electrostatic effects that appear commonly at organic/organic interfaces. Using QM/MM simulations, we demonstrate that the electric fields generated in this fashion are large enough to overcome typical electron–hole binding energies and thus explain the high efficiencies of existing OPV devices without appealing to the existence of nonthermal (“hot”) carrier distributions. Our results suggest that the classical picture of flat bands at organic/organic interfaces is only qualitatively correct. A more accurate picture takes into account the subtle effects of electrostatics on interfacial band alignment.

The nonlocal correlation functional VV10, developed recently in our group, describes the whole range of dispersion interactions in a seamless and general fashion using only the electron density as input. The VV10 functional has a simple analytic form that can be adjusted for pairing with the exchange functional of choice. In this paper, we use several benchmark data sets of weakly interacting molecular complexes to test the accuracy of two VV10 variants, differing in their treatment of the exchange component. For the sake of comparison, several other density functionals suitable for noncovalent interactions were also tested against the same benchmarks. We find that the “default’’ version of VV10 with semilocal exchange gives very accurate geometries and binding energies for most van der Waals complexes but systematically overbinds hydrogen-bonded complexes. The alternative variant of VV10 with long-range corrected hybrid exchange performs exceptionally well for all types of weak bonding sampled in this study, including hydrogen bonds.

We present a quantum mechanical/molecular mechanical (QM/MM) explicit solvent model for the computation of standard reduction potentials E0. The QM/MM model uses density functional theory (DFT) to model the solute and a polarizable molecular mechanics (MM) force field to describe the solvent. The linear response approximation is applied to estimate E0 from the thermally averaged electron attachment/detachment energies computed in the oxidized and reduced states. Using the QM/MM model, we calculated one-electron E0 values for several aqueous transition-metal complexes and found substantially improved agreement with experiment compared to values obtained from implicit solvent models. A detailed breakdown of the physical effects in the QM/MM model indicates that hydrogen-bonding effects are mainly responsible for the differences in computed values of E0 between the QM/MM and implicit models. Our results highlight the importance of including solute–solvent hydrogen-bonding effects in the theoretical modeling of redox processes.

Current bilayer organic photovoltaics cannot be made thick enough to absorb all incident solar radiation because of the short diffusion lengths (≈10 nm) of singlet excitons. Thus, the diffusion length sets an upper bound on the efficiency of these devices. By contrast, triplet excitons can have very long diffusion lengths (as large as 10 μm) in organic solids, leading some to speculate that triplet excitonic solar cells could be more efficient than their singlet counterparts. In this paper, we examine the nature of singlet and triplet exciton diffusion. We demonstrate that although there are fundamental physical upper bounds on the distance singlet excitons can travel by hopping, there are no corresponding limits on triplet diffusion lengths. This conclusion strongly supports the idea that triplet diffusion should be more controllable than singlet diffusion in organic photovoltaics. To validate our predictions, we model triplet diffusion by purely ab inito means in various crystals, achieving good agreement with experimental values. We further show that in at least one example (tetracene), triplet diffusion is fairly robust to disorder in thin films, as a result of the formation of semicrystalline domains and the high internal reorganization energy for triplet hopping. These results support the potential usefulness of triplet excitons in achieving maximum organic photovoltaic device efficiency.

Charge transfer (CT) states and excitons are important in energy conversion processes that occur in organic light emitting devices (OLEDS) and organic solar cells. An ab initio density functional theory (DFT) method for obtaining CT−exciton electronic couplings between CT states and excitons is presented. This method is applied to two organic heterodimers to obtain their CT−exciton coupling and adiabatic energy surfaces near their CT−exciton diabatic surface crossings. The results show that the new method provides a new window into the role of CT states in exciton−exciton transitions within organic semiconductors.

We present an investigation of the band levels and charge transfer (CT) states at the interface between two organic semiconductors, metal-free phthalocyanine (H2Pc) and 3,4,9,10-perylenetetracarboxylic bisbenzimidazole (PTCBI), using a combined quantum mechanics/molecular mechanics (QM/MM) technique. Near the organic–organic interface, significant changes from the bulk, as large as 0.2 eV, are found in the excited state energies, ionization potentials, and electron affinities, due to differences in molecular packing and polarizabilities of the two molecules. The changes in the ionization potential and electron affinity cause the CT states at the interface to be on average higher in energy than fully separated charges in the bulk materials despite having a typical local binding energy of 0.15 eV. Furthermore, we find that thermal fluctuations can induce variations of up to 0.1 eV in the CT binding energy. These results suggest that it is possible for bound interfacial CT states to dissociate in a barrierless fashion without involving “hot” CT states. This observation has direct relevance to the design of more efficient organic photovoltaics.

Charge separation (CS) and charge recombination (CR) rates in photosynthetic architectures are difficult to control, yet their ratio can make or break photon-to-current conversion efficiencies. A rational design approach to the enhancement of CS over CR requires a mechanistic understanding of the underlying electron-transfer (ET) process, including the role of the environment. Toward this goal, we introduce a QM/MM protocol for ET simulations and use it to characterize CR in the formanilide–anthraquinone dyad (FAAQ). Our simulations predict fast recombination of the charge-transfer excited state, in agreement with recent experiments. The computed electronic couplings show an electronic state dependence and are weaker in solution than in the gas phase. We explore the role of cis–trans isomerization on the CR kinetics, and we find strong correlation between the vertical energy gaps of the full simulations and a collective solvent polarization coordinate. Our approach relies on constrained density functional theory to obtain accurate diabatic electronic states on the fly for molecular dynamics simulations, while orientational and electronic polarization of the solvent is captured by a polarizable force field based on a Drude oscillator model. The method offers a unified approach to the characterization of driving forces, reorganization energies, electronic couplings, and nonlinear solvent effects in light-harvesting systems.

We report a catalytic mechanism for water oxidation in a cobalt oxide cubane model compound, in which the crucial O–O bond formation step takes place by direct coupling between two CoIV(O) metal oxo groups. Our results are based upon density functional theory (DFT) calculations and are consistent with experimental studies of the CoPi water oxidation catalyst. The computation of energetics and barriers for the steps leading up to and including the O–O bond formation uses an explicit solvent model within a hybrid quantum mechanics/molecular mechanics (QM/MM) framework, and captures the essential hydrogen-bonding effects and dynamical flexibility of this system.Keywords: electrocatalysis; mechanism; oxygen evolution; water oxidation; water splitting;

Organic semiconductors (OSCs) have recently received significant attention for their potential use in photovoltaic, light emitting diode, and field effect transistor devices. Part of the appeal of OSCs is the disordered, amorphous nature of these materials, which makes them more flexible and easier to process than their inorganic counterparts. In addition to their technological applications, OSCs provide an attractive laboratory for examining the chemistry of heterogeneous systems. Because OSCs are both electrically and optically active, researchers have access to a wealth of electrical and spectroscopic probes that are sensitive to a variety of localized electronic states in these materials. In this Account, we review the basic concepts in first-principles modeling of the electronic properties of disordered OSCs. There are three theoretical ingredients in the computational recipe. First, Marcus theory of nonadiabatic electron transfer (ET) provides a direct link between energy and kinetics. Second, constrained density functional theory (CDFT) forms the basis for an ab initio model of the diabatic charge states required in ET. Finally, quantum mechanical/molecular mechanical (QM/MM) techniques allow us to incorporate the influence of the heterogeneous environment on the diabatic states. As an illustration, we apply these ideas to the small molecule OSC tris(8- hydroxyquinolinato)aluminum (Alq3). In films, Alq3 can possess a large degree of short-range order, placing it in the middle of the order−disorder spectrum (in this spectrum, pure crystals represent one extreme and totally amorphous structures the opposite extreme). We show that the QM/MM recipe reproduces the transport gap, charge carrier hopping integrals, optical spectra, and reorganization energies of Alq3 in quantitative agreement with available experiments. However, one cannot specify any of these quantities accurately with a single number. Instead, one must characterize each property by a distribution that reflects the influence of the heterogeneous environment on the electronic states involved. For example, the hopping integral between a given pair of Alq3 molecules can vary by as much as a factor of 5 on the nanosecond timescale, but the integrals for two different pairs can easily differ by a factor of 100. To accurately predict mesoscopic properties such as carrier mobilities based on these calculations, researchers must account for the dynamic range of the microscopic inputs, rather than just their average values. Thus, we find that many of the computational tools required to characterize these materials are now available. As we continue to improve this computational toolbox, we envision a future scenario in which researchers can use basic information about OSC deposition to simulate device operation on the atomic scale. This type of simulation could allow researchers to obtain data that not only aids in the interpretation of experimental results but also guides the design of more efficient devices.

We examine the significance of hot exciton dissociation in two archetypical polymer−fullerene blend solar cells. Rather than evolving through a bound charge transfer state, hot processes are proposed to convert excitons directly into free charges. But we find that the internal quantum yields of carrier photogeneration are similar for both excitons and direct excitation of charge transfer states. The internal quantum yield, together with the temperature dependence of the current−voltage characteristics, is consistent with negligible impact from hot exciton dissociation.

We study the electronic coupling matrix element for triplet excitation energy-transfer processes with a number of different computational methods. For the first time, constrained density functional theory (CDFT) is applied to the problem of energy transfer, and results are compared with direct coupling calculations of broken symmetry and fragment densities, as well as the splitting method. A naïve calculation of the electronic coupling using diabatic and adiabatic energy differences is shown to yield erroneous results due to the fractional spin error present in both Hartree−Fock and commonly used DFT exchange−correlation functionals. Some potential issues concerning the splitting method with triplet references within Hartree−Fock and DFT are discussed. We find that only methods that compute the matrix element directly (either from CDFT, broken symmetry, or fragment states) appear to be robust. Several illustrative examples are presented.

We report a detailed study of luminescence switching in the fluorescent zinc sensor Zinpyr-1 by density functional methods. A two-pronged approach employing both time-dependent density functional theory (TDDFT) and constrained density functional theory (CDFT) is used to characterize low-lying electronically excited states of the sensor. The calculations indicate that fluorescence activation in the sensor is governed by a photoinduced electron transfer mechanism in which the energy level ordering of the excited states is altered by binding Zn2+. While the sensor is capable of binding two Zn2+ cations, a single Zn2+ ion appears to be sufficient to activate moderate fluorescence in aqueous solution at physiological pH. We show that it is reasonable to consider the tertiary amine as the effective electron donor in this system, although the pyridyl nitrogens each contribute some density to the xanthone ring. The calculations illustrate an important design principle: because protonation equilibria at receptor sites can play a determining role in the sensor’s fluorescence response, receptor sites with a pKa near the pH of the sample are to be disfavored if a sensor governed by a simple PET fluorescence quenching model is desired.

In this work we address the influence of the initial state on electron transfer dynamics by comparing two different ways of setting up the initial state, namely by taking an electron from the HOMO of a DFT ground state, or by using constrained DFT to self-consistently create the initial state. We solve the TDKS equations for the benzyl-pentafluorobenzene cation. The neutral molecule has a localised HOMO, which gives a natural partitioning in donor and acceptor group. We compare the electronic dynamics for varying angle between donor and acceptor and for varying basis set. We show that the methods lead to essentially equivalent results, but that the use of cDFT gives higher currents and a more consistent initial state with respect to variation of basis set and geometry.

We present a detailed theoretical study of the pathway for water oxidation in synthetic ruthenium-based catalysts. As a first step, we consider a recently discovered single center catalyst, where experimental observations suggest a purely single-center mechanism. We find low activation energies (<5 kcal/mol) for each rearrangement in the catalytic cycle. In the crucial step of O−O bond formation, a solvent water acts as a Lewis base and attacks a highly oxidized RuV=O. Armed with the structures and energetics of the single-center catalyst, we proceed to consider a representative Ru-dimer which was designed to form O2 via coupling between the two centers. We discover a mechanism that proceeds in analogous fashion to the monomer case, with all the most significant steps occurring at a single catalytic center within the dimer. This acid−base mechanism suggests a new set of strategies for the rational design of multicenter catalysts: rather than coordinating the relative orientations of the subunits, one can focus on coordinating solvation-shell water molecules or tuning redox potentials.

In this work we address the influence of the initial state on electron transfer dynamics by comparing two different ways of setting up the initial state, namely by taking an electron from the HOMO of a DFT ground state, or by using constrained DFT to self-consistently create the initial state. We solve the TDKS equations for the benzyl-pentafluorobenzene cation. The neutral molecule has a localised HOMO, which gives a natural partitioning in donor and acceptor group. We compare the electronic dynamics for varying angle between donor and acceptor and for varying basis set. We show that the methods lead to essentially equivalent results, but that the use of cDFT gives higher currents and a more consistent initial state with respect to variation of basis set and geometry.