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Virtual Screening for High Carrier Mobility in Organic Semiconductors Christoph Schober, Karsten Reuter, and Harald Oberhofer J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01657 • Publication Date (Web): 23 Sep 2016 Downloaded from http://pubs.acs.org on September 26, 2016

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The Journal of Physical Chemistry Letters

Virtual Screening for High Carrier Mobility in Organic Semiconductors Christoph Schober, Karsten Reuter, and Harald Oberhofer∗ Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universiät M¨ unchen, Lichtenbergstr. 4, D-85747 Garching, Germany E-mail: [email protected]

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Electronic devices with components chiefly made from organic semiconductors raise great expectations, thanks to their novel material properties and favorable economic footprint. 1–6 Substantial experimental and theoretical resources have correspondingly been allocated to understand and identify organic semiconductors that are suitable for everyday application. 7–9 One of the key figures of merit for this is the mobility of charge carriers, which determines the efficiency of charge transport through the material and thus its applicability as light emitter, transistor or solar cell. Unfortunately, this intrinsic material property is difficult to access experimentally. Measured mobilities depend heavily on the employed device architecture 10,11 or device fabrication process, 12–14 and orders of magnitude improvements in carrier mobility have been reported for the same material simply by optimizing these factors. 15–17 While this highlights the relevance and prospects of an eventual device optimization, the limited access to the intrinsic mobility prevents the identification of suitable candidate materials for which such optimization efforts are to be initiated. In this situation highthroughput virtual screening approaches promise an intriguing and increasingly employed alternative. 18,19 These approaches assess the fitness of a (ideally huge) number of candidate materials by calculating computationally undemanding key quantities. The lower the computational cost to determine such descriptor(s), the more materials can be screened. The more representative the descriptor(s) for the actual figure of merit, the higher the likelihood to identify promising candidates. As the quantitative calculation of explicit charge transfer rates in real organic semiconductors is still demanding, 20 prominent descriptors for the mobility of charge carriers 21,22 are the transfer integral Hab and the reorganization energy λ. 23 Roughly speaking, the former mostly reflects the quantum mechanical overlap of the frontier orbitals involved in the charge transport, while the latter quantity accounts for the response of all other charges in the systems to the local change in charge state. While both quantities are intuitively understood in the context of hopping type transport, they are also meaningful descriptors beyond this regime. 24 The electronic coupling, for example, directly enters the tight-binding description of the carrier effective mass in the band-transport pic-

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ture 25,26 and λ can—albeit more indirectly—be viewed as a measure of the electron/phonon coupling strength 27 which e.g. plays a role in the relaxation time approximation of the band transport mobility. 28 Finally, another factor potentially influencing transport properties in organic semiconductors is the degree of disorder present in the system, 29 leading for example to a variation in site energies of localised charges on inequivalent sites. However, this effect is mostly of importance in amorphous systems, 17,30 and can thus for the sake of brevity be omitted for the crystalline semiconductors considered here (see supporting information for an analysis of site energy variations). In a pioneering screening study, Sokolov et al. 24 employed λ to assess the suitability of seven modifications to the well-known dinaphtho-thienothiophene (DNTT) organic semiconductor. 31 The choice for the reorganization energy was thereby not arbitrary, but motivated by the fact that λ can with some limitations be reduced to a single molecule property due to the comparatively low contribution of the external reorganisation energy. 32–34 This allows to screen candidate materials without the prerequisite of having to know their crystal structure. In comparison, the transfer integral Hab is solely defined in condensed phases and therefore requires knowledge about the crystal environment of the system. Moreover, prediction of charge transfer necessitates the determination of charge carrier percolation pathways with large couplings, 35 which is only possible given a full knowledge of the crystal geometry. Employing Hab in a virtual screening approach of unknown materials would therefore have to include a crystal structure prediction routine, which in itself is a huge and computationally generally involved challenge. 36,37 Of course, this disadvantage does not apply to already synthesized and structurally characterized materials. The Cambridge Structural Database (CSD) 38 alone contains for instance about 750.000 molecular crystal structures (CSD Summary Statistic, 16. February 2015), the by far largest part of which has never been investigated for a suitability in organic electronic devices. In this work we correspondingly devise a computational protocol to screen this compound library with a twofold objective. On the one hand, computing Hab and λ for

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rise to a vast number of Hab calculations, which we efficiently handle on the level of fragmentorbital density-functional theory (DFT) 39,40 using the FHI-aims package 41 and organizing the computation tasks and workflows within the Fireworks-framework. 42 All compounds exhibiting at least one transfer integral that exceeds a minimal threshold value of 50 meV are subsequently recalculated with improved computational accuracy. If the minimum Hab value is confirmed, the reorganization energy of the system is calculated. This calculation relies on a QM/MM embedding scheme to account for differences between gas-phase and solid state structures, which can severely bias the predicted reorganization energies. 32 With further details provided in the SI, we thus arrive at an extensive (Hab , λ) descriptor database comprising a total of 10214 systems. Figure 2 depicts the 2D histogram of this database, together with the respective 1D distributions for both Hab and λ. Here we thereby concentrate on the maximum Hab value obtained for each crystal, viewing the largest coupling as performance critical for the system, while in the subsequent detailed analysis we also take percolation pathways into account. Ideal candidate systems promising a high intrinsic carrier mobility will exhibit a low reorganization energy λ and a large electronic coupling Hab . With increasing molecular size it is expected for Hab and λ to decrease due to the increasing delocalization of the wave function, 43 which is indeed confirmed for our dataset (see Fig. S5). A low reorganization energy of a system is therefore very likely to be nullified by a low transfer integral, while a large value of the transfer integral becomes meaningless if the associated reorganization energy is too high. The latter is less likely to occur due to the more favorable distribution of the reorganization energies with a clear maximum around 200 meV. The almost exponential decay of the Hab distribution instead shows that a low reorganization energy is very likely connected with a low transfer integral, rendering a virtual screening for low λs alone a less suitable approach to identify promising organic semiconductor materials. To identify the most promising candidates, we thus need to look for outliers to this trend, highlighting the need for an inclusive study as presented here.

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Table 1: Selected compounds identified in Fig. 2 as promising p-type organic semiconductors. Compiled are the appealing (Hab , λ)-descriptor values, the crystal space group, as well as the low number of steps required to synthesize each compound from commercially available chemicals according to the information provided in the CSD database.

chem. formula Hab / meV λ / meV space group synthesis steps

S1

S2

S3

S4

C8 H9 NS2 190 169 P -1 0

C16 H12 Cl2 131 152 P 21/a 0

C22 H14 O2 120 167 P 21 21 21 1

C20 H14 Br2 85 121 P 21/n 3

however, also many more compounds in this area that exhibit similarly, if not even more promising descriptor values and that have apparently not yet been considered for an application in organic electronics. Deferring a more in depth exploration of this data to a forthcoming publication we present in Fig. 2 and Table 1 a small selection of corresponding materials. This selection has been based on the unique meta-data available for every compound in the CSD database, 38 like the ease of synthesis from commercially available chemicals, straightforward crystallization, or good stability. All selected structures also show at least one continuous percolation pathway with Hab values above 50 meV (see SI for details). Beyond such immediate leads, we nevertheless expect even larger insight and prospects from a subsequent mining of the generated large descriptor database. Analysis of trends and correlations, e.g. between crystal structure, percolation pathways, chemical backbone, type of functionalization, closest end-to-end distance in the crystal packaging, will clearly accelerate the theoretical design and discovery of future high mobility organic semiconductors. Computational Methods All DFT calculations were performed with the FHI-aims package. 41,45 Electronic wave functions were expanded in a tier-2 numeric atomic orbital (NAO) basis and tight integration grids, if not indicated otherwise. Total energies, electronic couplings and forces are calculated using the Becke exchange functional in combination with the 8


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correlation functional by Lee, Yang, and Parr (BLYP). 46,47 Scalar relativistic effects were considered on the level of the zero-order regular approximation (ZORA). Electronic coupling Hab : After constructing the nearest neighbour dimers using an inhouse code we compute electronic couplings for each dimer using the fragment molecular orbital approach (FO-DFT) 39 with the H 2n−1 @D+ A Reorganisation energy λ: A non-periodic QM/MM embedding scheme with a shell of neighbouring molecules is used to mimic the solid state environment during the geometry optimisation of a single (central) molecule. Following an ONIOM-scheme, 48 the MM-forces of the central molecule are subtracted from the full MM region. All atomic positions in the neighbour cell are constrained, and only the coordinates of the central molecule are allowed to change. In the MM calculations using the ”Universal Force Field” (UFF) 49 and the Qeq charge equilibration scheme 50 within the LAMMPS 51 framework, only the two-body interactions are considered. Ackknowledgement The authors gratefully acknowledge support from the Solar Technologies Go Hybrid initiative of the State of Bavaria and the Leibniz Supercomputing Centre for the use of the SuperMUC high performance computing facility. Supporting Information Available Detailed computational methods. Selection criteria and additional statistics for the presented dataset. Details and percolation pathways of suggested structures S1-S4.

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