Charlotte Brückner 1 Matthias Stolte 2 Frank Würthner 2 Jens Pflaum 3,4 Bernd Engels 1 1 INTRODUCTION

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1 Received: 19 April 2017 Revised: 6 June 2017 Accepted: 11 June 2017 DOI: /poc.3740 SPECIAL ISSUE ARTICLE QM/MM calculations combined with the dimer approach on the static disorder at organic organic interfaces of thin film organic solar cells composed of small molecules Charlotte Brückner 1 Matthias Stolte 2 Frank Würthner 2 Jens Pflaum 3,4 Bernd Engels 1 1 Institut für Theoretische Chemie, Universität Würzburg, Würzburg, Germany 2 Universität Würzburg, Institut für Organische Chemie and Center for Nanosystems Chemistry, Würzburg, Germany 3 Experimentelle Physik VI, Universität Würzburg, Würzburg, Germany 4 Bayerisches Zentrum für Angewandte Energieforschung (ZAE Bayern e.v.), Würzburg, Germany Correspondence Bernd Engels, Institut für Theoretische Chemie, Universität Würzburg, Emil Fischer Straße 42, Würzburg, Germany. bernd.engels@uni wuerzburg.de Funding information Deutsche Forschungsgemeinschaft, Grant/ Award Number: FOR1809, GRK2112 and SPP1355 Abstract A QM/MM approach using ωb97x D combined with AMOEBA calculations was used to analyze the energetic disorder in the vicinity of interfaces in amorphous organic heterostructures. Distributions of ground, excited, and cationic state energies as well as of ionization potentials and excitation energies, all being relevant quantities for the transport properties of thin films, were calculated. As already found for bulk amorphous organic semiconductors, local densities of states at molecular interfaces possess Gaussian shaped profiles with a significant amount of disorder. Assuming a disorder limited activation of exciton and charge transport, a decrease in the amount of disorder could improve the transport properties. Relating calculated disorders to molecular parameters revealed that in line with the Bässler model, especially the molecular polarity, its change upon electronic excitation, and the molecular polarizability are relevant quantities leading to energetically largely disordered films. Moreover, because of the different mechanisms of exciton and polaron delocalization, a given morphology with disordered charge transport levels gives not necessarily rise to disordered exciton transport levels and vice versa. 1 INTRODUCTION Disorder in molecular organic semiconductors has been recognized as a key parameter limiting the semiconductor's transport properties for both charges and excitons. [1] A random distribution of the molecules in a disordered amorphous film results in considerable variations in local intermolecular interactions. This gives rise to a distribution of ionization and excitation energies, the relevant quantities for charge and exciton transport, which depend among others on these intermolecular interaction energies. [2] According to the central limit theorem, resulting densities of states (DOSs) for excitons and charges have a Gaussian shape because intermolecular interaction energies are composed of many This article is published as part of a special issue to celebrate the 80 th birthday of Professor Waldemar Adam independently varying contributions. [3] The width of the Gaussian shaped DOSs, ie, the standard deviation of the Gaussian normal distribution σ, is referred to as the disorder parameter and characterizes the amount of site energy disorder, ie, of static disorder, in the semiconducting solid state system. [2] Based on this Gaussian DOS, the Bässler model describes charge transport in organic semiconductors as an incoherent hopping process between the normally distributed sites. [4] The expression disorder can be connected with geometrical and energetical disorder. In line with the Bässler nomenclature, in the following the expression, disorder is always used to characterize the energetic disorder unless otherwise noted. Although experimentally detected field and temperature dependent charge carrier mobilities confirm the predictions of the Bässler model in principle, no direct experimental proof for the Gaussian shaped DOS, particularly of charge carriers, in disordered molecular semiconductors J Phys Org Chem. 2017;30:e wileyonlinelibrary.com/journal/poc Copyright 2017 John Wiley & Sons, Ltd. 1of13

2 2of13 exists. [2] Evidence for the Gaussian distribution of the excitonic DOS is provided by various experimental studies, for example, via optical probing of excitonic transitions [3] Gaussian shaped absorption profiles and via time resolved measurements on dispersive exciton transport. [5,6] Via the calculation of local electric fields for a number of different hopping sites, it could be shown that the disorder parameter σ depends on the polarity and the polarizability of the transport material. [7] This result is supported by experiments demonstrating that polar side chains in polymeric semiconductors have a detrimental effect on charge carrier mobilities by increasing the disorder in the DOS. [2] A more profound understanding of these and other parameters influencing the disorder is needed to rationally design materials with favorable transport properties because small energetic disorder is decisive for efficient exciton and charge transport in molecular semiconducting thin films of optoelectronic devices. [8 10] Computational chemistry provides ideal tools to deepen the understanding of the origin of disorder in organic semiconducting materials because the DOS is directly accessible from the calculations. Furthermore, it is in silico also possible to extend the disorder concept to interfaces between 2 semiconducting phases, where optical absorption measurements as well as investigations of charge carrier mobilities are experimentally barely feasible. Hence, theoretical studies are needed because insight into the formation of the energy landscapes of the transport states in the vicinity of these interfaces is particularly essential for a rationally guided design of efficient organic solar cells (OSCs) and organic light emitting diodes. [11] They are of special interest because the shapes of the interfacial DOS might deviate from a Gaussian one, and the parameters of interest might differ from the ones found for the corresponding bulk phases. Several computational studies have addressed the influence of disorder on charge transport in the bulk of organic semiconductors, for instance, by Gennett and coworkers [12] and by Brédas and coworkers. [13,14] Van Voorhis et al outlined that also disorder at organic organic interfaces is decisive and can significantly influence the character of the chargegeneration process. [15,16] Multiple investigations also focus on the fundamental relationship between interfacial disorder and the photoinduced charge transfer step. [17 19] In contrast, the influence of interfacial disorder on exciton and charge transport in the vicinity of organic organic interfaces has not yet been investigated in detail although fast exciton and charge transport in the interfacial region are prerequisites for efficient excitonto free charge conversion in OSCs. Moreover, to the best of our knowledge, there is no computational investigation including various molecular p type semiconductors to target site energy disorder in the vicinity of the interfacial region. To shed some light on this important issue, we present QM/MM calculations on disordered interfaces to calculate the DOS of ground, excited, and ionized state energies, and of ionization potentials and excitation energies. The interfaces were generated in precedent molecular dynamics (MD) simulations [20,21] and are composed of fullerene C 60 and a variety of molecular p type semiconductors with different polarity and various structural motifs (Figure 1). Thus, besides the more conventional organic semiconductor molecules such as anthracene and rubrene, we also included quadrupolar diketopyrrolopyrrole DPP and squaraine and even two highly dipolar merocyanines because, recently, these dyes and pigments afforded surprisingly good electronic and optoelectronic performances as active semiconducting compounds in organic transistors and solar cells. [32] For the dipolar merocyanines, we chose [31] HB194 and MD353 [33] because, despite their rather different electronic structure, both dyes could be used successfully as donor materials in bulk heterojunction solar cells in combination with C 60 fullerene and its derivative PCBM. Here, HB194 is a more polyene like dye that shows a strong increase of the dipole moment upon optical excitation whereas MD353 possesses almost equal dipole moments in the ground and excited state, leading to narrow cyanine type absorption bands. [34] Disorder parameters resulting from the computed DOS were related to the molecular properties. 2 THEORETICAL APPROACH BRÜCKNER ET AL. Disordered interface structures were generated in MD simulations as described in our previous works. [20,21] Starting with a single monolayer taken from the experimental crystal structure, some vacancies are created. Subsequently, disorder is generated in a short MD simulation. In the next step, a second crystal slice with vacancies is accelerated onto the first layer in a next MD step. A harmonic potential applied between the newly added molecules and already deposited film was used to mimic adhesion forces. The cycle is repeated for the p type molecules several times. Subsequently, the fullerene layers are deposited on top using the same iterative procedure. Starting from the 3 basic crystallographic planes of the p type semiconductor, we created 3 different systems to ensure a more complete sampling. For the fullerene, only one slice was taken because the 3 crystallographic orientations are identical in the cubic faces centered crystal structures. [35] Perpendicular to the interface, the systems have 4 to 5 layers for the p type semiconductor and for the fullerene. The horizontal extensions are determined as the least common multiple of the unit cell dimensions of the p type semiconductor and the fullerene, respectively. Taking the anthracen fullerene interface as an example, the horizontal extension is about 45 Å 45 Å. Its thickness is about 50 Å. The dimensions of all other systems are given in table 8 of the supporting information of Brückner et al. [20] It is worth emphasizing that disorder was also generated in materials like anthracene, DIP, or merocyanines, which

3 BRÜCKNER ET AL. 3of13 FIGURE 1 Used p type molecular semiconductors. The semiconductors are arranged in groups of structurally similar compounds. They range from apolar aromatic hydrocarbons (anthracene, [22] rubrene, [23] and DIP [24] ), over triphenylamines [25 27] and donor acceptor donor compounds (squaraines, [28] and diketopyrrolopyrroles [29] ) to highly polar merocyanines (MD353, [30] and HB194 [31] ) would rather crystallize or form polycrystalline films in real samples. [36] In the MD simulations, no periodic boundary conditions were used to allow for a large amount of random conformational rearrangements. This ensures that later on, calculated disorder values represent an upper limit for real disorder parameters σ. A model that uses our systems as unit cells within a periodic boundary approach would be perfect because it would avoid edge effects but this is too expensive because of software and hardware limitations. To obtain converged values for the charge charge interactions, being of long range nature, the disordered interface structures [20,21] were used to construct supercells (Figure 2A) (for details of the construction process, see Supporting Information). In the originally disordered interface part, ie, the center cell of the supercell (Figure 2), dimers were cut out on the basis of a distance criterion (Figure 2B) based on the centers of mass. All data are given in table S1 of the supporting information of reference 20. The dimers were used as the quantum mechanical system for subsequent QM/MM calculations. Using dimers as the quantum mechanical system has the major advantage that delocalization of the excitation or charge over 2 monomers is possible. [37,38] Furthermore, intermolecular interactions are taken into account on a fully quantum mechanical level. [39,40] Ground state geometries and energies, excitation energies, and ionization potentials were calculated with the ωb97x D functional [41] that was shown to provide very accurate ground state geometries, excitation energies, and ionization potentials. [42 44] Furthermore, it yields reliable intermolecular potential energies for dimers composed of molecular semiconductors. [45,46] In well ordered but also in amorphous systems, excitons and charges are expected to be delocalized over several units. [2,47,48] Consequently, the computations of oligomers larger than dimers would be desirable, but such computations are too costly within the framework of the present study. The dimer approach accurately takes into account all interactions between both monomers but neglects distant interactions within a stack. [49] Some recent investigations show its accuracy for the description of absorption and emission spectra of exciton diffusion in PBI aggregates [50 52] and in DIP and PTCDA single crystals. [39,44] A comparison with monomer based approaches showing advantages and disadvantages of both approaches is presented in a recent review. [53]

4 4of13 BRÜCKNER ET AL. FIGURE 2 A, Construction of the supercell of sufficient size from the generated disordered interface models highlighted in pink in the supercell. B, Dimers cut out from the center cell. C, Definition of layers for the decomposition of the computed MM interaction energy Within the present study, the dimer was electrostatically embedded into the environment using a subtractive QM/ MM scheme. [54,55] Partial charges on all molecules in the MM part polarize the dimer QM system. These charges included in the quantum mechanical calculation were beforehand generated in electrostatic potential (ESP) fits [56] using the ωb97x D/cc pvdz density of the respective molecules. Thus, the electrostatic interaction energy of a given dimer with the environment was included on a quantum mechanical level. This is important since the ground, excited, and cationic state might interact differently with the same electrostatic environment. [57] Back polarization of the environment is not included. Apart from the electrostatic component, remaining parts of the interaction between the dimer and its environment were calculated on the MM level using the polarizable Atomic Multipole Optimized Energetics for Biomolecular Simulation (AMOEBA) force field. [58,59] It was sufficiently accurate so that special parametrizations were not necessary. [60,61] Final states energies E QM/MM were calculated from the dimer energies obtained in the QM calculation E QM (dimer) (which includes the electrostatic interaction energy with the environment) and the difference of the force field energies of the total system and the QM system E MM (total) E MM (dimer), the latter corrected for the electrostatic force field interaction energy calculated as the difference E MM, el (total) E MM, el (dimer). E QM=MM ¼ E QM ðdimerþþ E MM ðtotalþ E MM ðdimerþ E MM;el ðtotalþ E MM;el ðdimerþ Andrienko et al demonstrated the importance of the longrange character of electrostatic interactions and the very slow convergence of charge charge and charge quadrupole interactions. [62] To verify that the constructed supercells are sufficiently large to obtain converged values for the interaction energies of the QM system with the environment (and to keep our calculations computationally feasible for AMOEBA), we divided the supercell into layers (innermost interface area, 2 outer monomer layers, 2 outer fullerene layers, Figure 2C). We calculated the interaction energy of each layer with the dimer separately. This implies the drawback that three body effects between different layers (eg, via polarization) are not included. However, our calculations reveal that the polarization contribution to the total force field interaction energy is always very small. Moreover, calculations between the dimer and the outermost layers yield interaction energies of less than 0.1 kcal/mol (see Supporting Information), which is far below the accuracy of the used methods. It should be noted that no dielectric shielding was applied, ie, the vacuum dielectric constant was employed. Nevertheless, our findings suggest that the size of the constructed supercells is sufficient to obtain converged values for all site energies.

5 BRÜCKNER ET AL. AMOEBA parameters for the ground state of all molecules were obtained from the generalized distributed multipole analysis (GDMA) of Stone et al. [63] These parameters are used for all molecules in the environment, ie, in the MM part, and for the 2 monomers of the QM dimer system if ground state energies have to be calculated. The generated parameters had been evaluated by a comparison to density functional theory (DFT) D curves, [45,64,65] where a very good coincidence was found (see Supporting Information). Because of the adopted subtractive QM/MM scheme, AMOEBA parameters for excited and ionized dimers are necessary to calculate the MM interaction energies of cationic and excited dimers with the environment. Interactions between neutrally excited states (vs charge transfer states) and the environment can be assumed to be quite similar to interactions between the respective ground state and the environment because the excited state is not charged and the environment does not necessarily feel all local density variations upon electronic excitation of the dimer system. [39] This assumption was verified for all molecules by comparing the solvent shifts of the molecular ground and the first bright excited state upon solvating the molecule with a state specific solvation model (see Supporting Information). It was observed that solvent shifts were essentially equal for the ground and the excited state of the respective molecules. This shows that interactions of both states of a given molecule with the environment are similar. Hence, to a good approximation, ground state force field parameters can be also used to calculate interactions of excited states with the environment. [39] For the merocyanine HB194 (Figure 1), a push pull dye where considerably charge shifting takes place upon excitation, the error introduced by this approximation was additionally analyzed in more detail. Two different parameter sets were used for the QM system when calculating the MM interaction energy with the environment. On the one hand, interaction energies were calculated using groundstate parameters for the excited dimer. On the other hand, excited state parameters were generated in GDMA analyses individually conducted for all excited dimers using the (nonequivalent) excited state densities of the respective dimers. The MM interaction energies with the environment were calculated using these dimer specific parameters and compared to the interaction energies calculated with ground state parameters. The results (see Supporting Information) show that the interaction energies obtained with the 2 sets of parameter are almost equal for all dimers. This validates the adopted approach. In contrast to the excited states, neutral ground state parameters cannot be used for ionized compounds because the total charge of the compound changes, inducing large modifications of the interactions with the environment. [61] This is again confirmed by comparing the solvent shifts of the ground state and the ionized state of all molecules modeled by state specific solvation models (see Supporting Information). The response of the ionized state to changes in the environment differs significantly from that of the neutral ground state. Therefore, to calculate ionization energies and cationic state energies in a subtractive QM/MM scheme, a GDMA analysis was performed for each ionized dimer, and dimer specific force field parameters were obtained. These parameters are used to calculate the MM interaction energy of the ionized dimer with its environment, for which regular ground state parameters are used. From the QM/MM calculations, both absolute energies and energy differences, ie, excitation energies and ionization potentials are calculated. All absolute energies are referenced to the lowest overall energy value. 3 COMPUTATIONAL DETAILS 5of13 The generation of the disordered interfaces is described in our previous investigations. [20,21] Among the 3 generated interfaces per molecule, the largest heterojunction system of each p type semiconductor with fullerene C 60 was selected (see other works [20,21] ). All force field calculations were performed using the Tinker program package. [66] In the energy calculations with AMOEBA, [58,59] no cutoff was used. Monomer geometries obtained with quantum mechanical methods were superposed onto the force field geometries. Multireference approaches deliver very accurate groundstate properties [67] and reactions [68] as well as excitation energies [38,69] but are too expensive for the given systems. Hence, we rely on density functional approaches, which were carefully tested to be sufficiently accurate for the treated questions. [42] All monomer geometries were optimized at the ωb97x D/cc pvdz level of theory. [70] An ultrafine grid was used for the optimizations. Excitation energies and ionization potentials were obtained with ωb97x D/cc pvdz as well. For all ESP fits, the Merz Kollmann scheme was applied. [71] The GDMA analyses were conducted using the ωb97x D/cc pvdz densities of the respective states. This density along with its gradients was also used to calculate molecular polarizabilities. Both the state specific solvation model implemented by Improta et al [72,73] and the perturbative correction of Mennucci et al [74] were used to quantitatively assess solvent shifts of ground, excited, and cationic states. Similar results were obtained. Calculations with linear response solvation were conducted for further comparison (see Supporting Information). [75] Relaxed dipole moments for the molecular ground states were obtained with SCS MP2/cc pvtz. [70,76 78] Excitedstate dipole moments were computed using SCS CC2/ccpVDZ. [70,79,80]

6 6of13 All quantum mechanical DFT calculations were conducted with the Gaussian program package. [81] Turbomole was used for the calculation of molecular properties. [82] 4 RESULTS AND DISCUSSION The discussion is organized as follows. In a first step, shapes of the densities of ground, excited, and ionized states in the vicinity of organic organic interfaces are calculated. The disorder parameter σ is only meaningful if the DOSs are Gaussians. Furthermore, only if the DOSs are broad, ie, if the disorder is significant, transport is disorder limited. [2] In a second step, the distributions of ground, excited, and ionized state energies are investigated and related to molecular parameters. In a third step, the disorder of the relevant excitonic and polaronic transport levels ionization potentials and excitation energies is analyzed. Its physical origin is elucidated, and distinct structure property relationships are identified. Densities of states for disordered interfaces composed of C 60 and the respective p type molecular semiconductors, displayed in Figure 1, were calculated. For 3 representative molecules, the apolar DIP molecule, the TAA compound, a three dimensional dye featuring some donor acceptor character, and the highly dipolar (μ g = 12.8 D) merocyanine [34] MD353, the computed DOSs are shown in Figure 3. Evidently, the DOSs have Gaussian profiles irrespective of the FIGURE 3 Distribution of ground state energies (ground state disorder) obtained from the QM/MM calculations (diamonds). As the reference (0), we used the energy of the dimer with the lowest state energy. Gaussian normal distributions obtained from the mean and the standard deviation of the ground state energies (solid lines). For clarity, the normalization of the Gaussian profiles was omitted BRÜCKNER ET AL. electronic nature of the individual molecule the diamonds coincide very well with the normal distributions for all 3 molecular entities. Moreover, computed densities of excited and ionized states have equal shapes, and comparable results are obtained for all molecules. Therefore, the densities of ground states at organic organic interfaces are much alike to Gaussian shaped DOSs in disordered organic bulk phases underlying the Bässler model for charge carrier transport. [2] Gaussian distributions are also found for state energy differences for ionization potentials and excitation energies, ie, for polaronic and excitonic transport energies (Figure 4). This could be expected since energy differences between Gaussian distributions should be normally distributed as well. Apparently, on a molecular scale, disregarding band bending on a mesoscale, state energies and resulting energy differences are normally distributed even in the presence of a morphological discontinuity such as an organic organic interface. This means that the local DOS in the vicinity of interfaces is still dominated by the same mechanisms also determining the distributions of state energies in amorphous organic bulk phases. Most importantly for the following discussion, because of the Gaussian shape of the DOSs, the definition of disorder as a standard deviation can also be used for the interfacial region. Moreover, as the Gaussian profiles are broad, resulting disorder parameters are large. Hence, disorder should considerably impede the microscopic transport processes in the vicinity of the interfaces, [2] the latter being relevant for the efficiency of organic thin film devices and thus underlining the importance of understanding and eliminating its physical origin. The mechanisms responsible for the broadening of ground, excited, and ionized state energies are discussed next. From Figures 3 and 4, it is obvious that the disorder of ground state energies is considerably larger than that of ionization potentials or excitation energies. This result is quite general and valid for all molecules shown in Figure 1. Visual inspection of dimers with different energies reveals that the spread in ground state energies is particularly induced by changes in the van der Waals interaction with the environment (see Supporting Information). The influence of the less dense packing at organic organic interfaces on their interfacial energy landscapes has often been stressed. [15,19] In accordance with these investigations, our computationally generated interface structures have lower packing densities in the interface region. However, the reduced density arises from strong variations in the local density rather than from an evenly spread decrease of the density. This means that there are still spatially very confined regions with a high packing density. Van der Waals interactions are of short range nature and highly distance dependent. [83] Therefore, they fall off quickly as soon as the packing density is reduced. Stabilizing van der Waals interactions (distance

7 BRÜCKNER ET AL. 7of13 FIGURE 4 Gaussian distribution of ionization potentials (left) and excitation energies (right). Diamonds result from QM/MM calculations, the solid lines are Gaussian fits dependence R 6 ) contribute, in average, approximately 80% to the total interaction energy of any dimer with its environment (see Supporting Information). Reducing this stabilizing contribution by decreasing the density significantly destabilizes ground state site energies. This means that the large disorder of ground state site energies at the interfaces results primarily from considerable packing density variations in the vicinity of the interface. As these density variations are typical for interfacial regions only, such large ground state site disorders are presumably a distinct interfacial effect. The upper panel in Figure 5 correlates computed groundstate disorder parameters with the disorder parameters calculated for excited state DOSs. It is evident that the disorders of ground and excited state energies are related for a given system (coefficient of determination R 2 : 88%). In view of the role of van der Waals interactions determining ground state disorder, this could be expected. Empirical parameterizations for the calculation of van der Waals interaction are usually assumed to be state independent, [84] which was shown to be a reasonable approximation, at least, for valence excited states. [85] Hence, it seems consistent that the van der Waals interactions due to local density variations in the interfacial region similarly affect the energetic spread of the ground and the excited states. It should be furthermore kept in mind that ground and excited state force field parameters were shown to be almost identical. Putting the result that ground and excited state disorder parameters are interconnected by the stabilizing van der Waals interactions on a more quantitative basis, the lower panel in Figure 5 shows the correlation between the excited state disorder and the molecular polarizabilities FIGURE 5 Upper panel: correlation of ground and excited state disorder. Lower panel: dependence of the disorder of the excited state energies on the polarizability of the molecules. Straight lines represent linear fits to the data points with the corresponding coefficients of determination R 2 calculated at the ωb97x D/cc pvdz level of theory. It is well known that the molecular polarizability depends among others on the system size. In accordance with this finding, large systems like the squaraine and the diketopyrrolopyrrole

8 8of13 dispose rather large ground and excited state disorders (Figure 5). From a molecular perspective, a larger molecule has a larger possibility of being subject to local density variations. Its van der Waals energy caused by the interaction with the local environment is subject to larger variations. In contrast, ground and excited state energies of small molecules cover only a narrow energy range even in disordered films (Figure 5). The ionized state disorder is similarly affected by molecular polarizabilities. However, because of the nonzero total charge of the ionized dimer, electrostatic interactions with the environment become increasingly important for the total degree of disorder. This is demonstrated by the results shown in Figure 6, which relates the disorder of ionized state energies of a given system to the ground state dipole moment of the respective molecular p type semiconductor. We included only those molecules from Figure 1 with ground state dipole moments significantly deviating from zero. All other ionizedstate disorders were averaged. Figure 6 clearly shows that the larger the ground state dipole moments, the larger the disorder of ionized states. The presence of large dipole moments in the environment leads to strongly varying local electric fields. Such local electric fields modulate uncharged ground and excited states only to a small extent but lead to pronounced differences in ionized state interactions and energies. From the results shown in Figures 5 and 6, it can be concluded that molecular polarizability increases the energetic disorder of ground, excited, and ionized states, whereas the presence of dipole moments in the environment influences particularly ionized state energies. Therefore, completely in line with literature findings for bulk organic materials, [2] the energetic site disorder in the organic phases adjacent to organic organic interfaces increases with the molecular polarizability and the dipole moment. As mentioned above, for exciton and charge transport at and across organic organic interfaces, the energetic FIGURE 6 Correlation of the disorder parameter σ calculated for the QM/MM ionized state energies with the ground state molecular dipole moment BRÜCKNER ET AL. distributions of ionization potentials and excitation energies are decisive, which are addressed next. [12] Since an excitation (ionization) accompanied by the polarization and deformation of the surrounding lattice corresponds to an exciton (a polaron), [1] it seems reasonable to associate the disorder of excitation energies (ionization potentials) with the disorder of excitonic (polaronic) transport levels. The distribution of these transport levels determines the efficiency of the corresponding transport processes. Fast exciton transport is necessary to enable the exciton to reach the interface within its radiative lifetime whereas high carrier mobilities ensure rapid charge separation after the photoinduced charge transfer step. [17] Disorder parameters calculated for ionization potentials and excitation energies are listed in Table 1 and correlated in Figure 7. As mentioned above, disorder parameters for ionization potentials and excitation energies are smaller than the deviations of state energies (Table 1 and Figure 7, comparison with Figure 5). This is because the van der Waals interactions dominating ground /excited /ionized state disorder are similar for all of these states. Depending on the local packing density, both states involved in the transport process, ie, the ground state and the excited or the ionized state, experience either very stabilizing van der Waals interactions or comparably small van der Waals interactions. Upon subtracting the state energies, the influence of site dependent van der Waals interactions levels out. This is in line with findings that percolation pathways improve charge transport properties of OSCs [86,87] although they necessarily induce significant local density variations and therefore, a significantly broadened DOS for ground and excited state energies. The disorder of excitation energies equals 53 mev in average. In contrast, the disorder for ionization energies is considerably larger with an average value of 227 mev. This becomes also evident from the plot in Figure 7 (upper panel) TABLE 1 Calculated disorder parameters for excitation energies (exciton transport levels) and ionization potentials (polaron transport levels) in the vicinity of interfaces composed of fullerene C 60 and various molecular p type semiconductors Molecule σ(ee), mev σ(ip), mev Anthracene Rubrene 2 82 DIP HB MD TBA 9 82 TAA TAM Diketopyrrolopyrrole Squaraine 7 71 Average

9 BRÜCKNER ET AL. 9of13 FIGURE 7 Upper panel: correlation of Gaussian disorder for the ionization potentials and excitation energies. Lower panel: correlation of QM disorder part of ionization potentials and excitation energies calculated. For more explanations see Figure 8 and text where the molecules are colored according to their classification in Figure 1 (hydrocarbons, triarylamines, donoracceptor donor compounds, merocyanines). The disorder relation between ionization potential (polaron transport) and excitation energy (exciton transport) is specific for a given system but is approximately 4 times larger for ionization potentials compared with excitation energies. HB194 possesses the broadest DOS with a disorder parameter of 169 mev for excitation energies and of 656 mev for ionization potentials. These maximal values compare well with calculated widths for the hole state DOS in polar polymers of 660 mev. [12] Experimentally characterized disorder parameters for bulk semiconducting phases are usually within an energy range of 50 to 150 mev. [2] While the calculated disorder of excitation energies in the vicinity of the interfaces lies within this range, the disorder of ionization potentials is considerably larger. This is partially due to the inclusion of polar push pull molecules like HB194, MD353, the aldehyde substituted triphenylamine, and the methoxy substituted triphenylamine in the calculation. Leaving aside the merocyanines, which are known to form crystalline or semicrystalline aggregates leading to considerably lower disorder parameters, the average disorder of the ionization potentials decreases to 148 mev but is still situated on the high end side of the experimentally deduced energy range. This comparably large degree of disorder is also due to the large values obtained for traditional semiconductors [32] like DIP (348 mev) and triphenylamine based compounds. [88] Therefore, it seems reasonable to conclude that especially polaronic transport levels in the vicinity of interfaces in amorphous thin films are subject to a considerable amount of disorder. In view of the recently highlighted influence of long range order and charge delocalization on the efficiency of exciton dissociation at organic heterojunctions, [17,89,90] this result suggests potential efficiency limits arising from low charge mobilities in the realm of the interface. From Figure 7 (upper panel), it becomes furthermore evident that a correlation between the disorder of excitation energies and the disorder of ionization potentials exists. Surprisingly, in contrast to the above given state energy disorders, those molecules with the largest polarizability (eg, the squaraine, diketopyrrolopyrrole, or tri(biphenyl 4 yl)amine (TBA)) generally show rather small disorders in their excitonic and polaronic states (see Figure 7 and Table 1). This implies that compared with absolute state energies, other molecular properties decisively influence state energy differences, ie, the relevant polaronic and excitonic transport levels. To further gain insight, Figure 8 decomposes the disorder for excitation energies (EE disorder) and ionization potentials (IP disorder) into contributions arising from the delocalization across a dimer and monomeric interactions within the dimer (estimated by gas phase dimer calculations, indicated as QM disorder [delocalization, dimer interaction] ) and from electrostatics of the dimer with its surrounding (deduced from dimer calculations in a point charge potential, indicated as electrostatic contribution ). We note that since identical force field parameters were used for the ground and excited state, no additional energy contributions to the excitonic disorder result from the QM/MM calculation. Dimer specific force field parameters were used for ionized dimers. The electrostatic and QM contribution do not necessarily add up to the total disorder of ionization potentials in Figure 8. The origin of disorder of the excitonic states is discussed first. For all molecules, except for the 3 push pull dyes (HB194, TAA, and TAM), the total disorder for excitation energies almost coincides with the QM disorder, ie, results due to delocalization effects and interactions between both monomers of the dimer (gray vs ruby colored bars in Figure 8, right hand side). The strong effects result because the excitation energies strongly depend on the precise dimer arrangements. In some dimer orientations, the monomer excitations couple strongly, causing a large splitting of the dimer excitations. In other orientations, both monomers barely couple in the excited state, and resulting excitation energies are

10 10 of 13 BRÜCKNER ET AL. FIGURE 8 Decomposition of the disorder for excitation energies (EE disorder) and for ionization potentials (IP disorder) into electrostatic interactions with the surroundings and QM disorder. The latter comprises effects arising from delocalization across the dimer and interactions within the dimers not considerably shifted compared to the monomer excitation. With regard to the influence of electrostatic interactions on the EE disorder (checkered bars in Figure 8, right hand side), the electron densities of molecules like anthracene or DIP do not significantly change upon electronic excitation. Electrostatic interactions of the respective ground states with the environment are very similar to interactions of the corresponding excited states with the environment. In contrast, the 3 push pull molecules (HB194, TAA, and TAM) have a significantly larger dipole moment in the excited state than in the ground state (Table 2). Therefore, excited dimers embedded in a point charge field interact differently with their environment compared with the corresponding ground state dimers. This explains the enhanced influence of electrostatics on the disorder parameter of these molecules. While the influence of electrostatics on excitonic states is limited to the 3 push pull molecules, electrostatic interactions dominate the energetic spread of ionization potentials (IP disorder) for most molecules (checkered bars in Figure 8, left hand side). The contributions of electrostatics to the total disorder are especially large for the merocyanines, DIP, and the substituted triphenylamines TAA and TAM. Polaronic delocalization (QM disorder Figure 8, left hand side) also plays TABLE 2 Dipole moment changes upon electronic excitation calculated as relaxed properties on the SCS CC2 [79,80] /cc pvdz [70] level of theory for the optimized geometries, respectively. For the sake of completeness, the corresponding values for MD353 are given although this compound has a rather small excited state dipole moment, which stands in contrast to experimental measurements 25,a Ground state dipole moment, D Excited state dipole moment, D HB TAA TAM MD a Corresponding investigations are under way. a considerable role and contributes in average 90 mev to the total disorder. To further analyze the role of delocalization, the lower panel in Figure 7 correlates the QM contributions to the disorder of exciton and polaron transport levels, respectively. Interestingly, in contrast to the total disorder (upper panel, Figure 7), excitonic, and polaronic disorder parameters resulting solely from delocalization and intermolecular interactions do not correlate well (R 2 value: 26%) although the underlying dimers are identical. This is

11 BRÜCKNER ET AL. 11 of 13 somewhat surprising because it necessarily implies that the disorder contributed by electrostatic interactions compensates the differences in the disorder parameters arising from the diverging exciton and polaron delocalization. The influence of delocalization is further illustrated in Figure 9, which displays excitation energies and ionization potentials calculated for 20 arbitrarily selected gas phase dimers of MD353 and DIP. Within the supporting information, some selected dimer orientations are quantified in more detail. Their energetic distribution results only from delocalization and intermolecular interactions. It is evident from Figure 9 that variations of the excitation energies do not necessarily parallel corresponding fluctuations of ionization potentials. This results from the different coupling mechanisms of excitation energies (for excitons) and ionization potentials (for charges). The usually dominant long range component to the singlet excitation energy coupling is essentially a dipole dipole interaction of the transition dipole moments, whereas charge couplings depend primarily on orbital overlap. [91] Therefore, a given dimer could allow for a large dipole dipole coupling while simultaneously exhibiting poor orbital overlap. Whereas the resulting ionization potential is only negligibly shifted with respect to the monomer, the dimer's excitation energies considerably split. This leads to the general conclusion that in addition FIGURE 9 Excitation energies (blue bars) and ionization potentials (pink bars) calculated for 20 randomly selected dimers of MD353 (upper panel) and DIP (lower panel) to the frequently addressed morphological dependence of the disorder parameter, [2,12] the latter is also specific for the type of transport, ie, exciton and charge transport may experience different degrees of disorder within the same morphology. 5 CONCLUSION A subtractive QM/MM scheme along with the dimer method at the ωb97x D/cc pvdz//amoeba level of theory was used to calculate the DOS for ground, excited, and cationic state energies and for corresponding transport levels, ie, excitation energies and ionization potentials, in the vicinity of disordered organic organic interfaces. The study comprises various molecular semiconductors acting as p type conductors in heterojunctions with the n type semiconductor fullerene C 60. Computed energy distributions showed Gaussian profiles with a significant amount of disorder. Hence, exciton and charge transport in the vicinity of and across such prototypical interfaces in organic thin films should be disorder limited. [2] The reduced packing density at the interfaces strongly affects the short range [83] van der Waals interactions, which dominate the DOS of ground and excited state energies. However, the van der Waals interactions are rather state independent [85] and cancel for transport determining energy differences like excitation energies and ionization potentials. In contrast, polarization and electrostatic interactions being of rather long range character are less susceptible to the packing density, but they differ for different states. It was shown that ionized state energies depend on the ground state dipole moments of the surrounding molecules. As a consequence, electrostatic interactions with the environment account for a significant amount of disorder of ionization potentials, ie, of the differences between ionized and ground state energies, which is completely in line with the Bässler model derived for amorphous bulk phases. [1] Electrostatic interactions also cause an energetic spread of excitation energies as soon as molecules undergo a change in polarity upon electronic excitation. In addition, exciton and polaron delocalization over dimers profoundly influences the DOS of polaronic states and even dominates the DOS of excitonic states. The strong influence results because the state energies largely differ for different geometrical dimer arrangements. Moreover, because of different coupling mechanisms for excitons and polarons, a given morphology might result in largely disordered polaronic and considerably less disordered excitonic states and vice versa. We therefore conclude that disorder is not only a morphology dependent characteristic but also depends on the kind of transport to be considered (exciton vs polaron).

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