Theory-Driven Insight into the Crystal Packing of Trialkylsilylethynyl

Article pubs.acs.org/cm

Theory-Driven Insight into the Crystal Packing of Trialkylsilylethynyl Pentacenes Karl J. Thorley, Tristan W. Finn, Karol Jarolimek, John E. Anthony, and Chad Risko* Department of Chemistry & Center for Applied Energy Research, University of Kentucky, Lexington, Kentucky 40506-0055, United States S Supporting Information *

ABSTRACT: The functionalization of oligoacenes and similar π-conjugated chromophores with trialkylsilylethynyl groups has proven to be a versatile means to enhance solubility and solution processability and engineer solid-state packing arrangements to produce organic semiconductors that demonstrate outstanding charge-carrier transport characteristics. While a general, empirical-based geometric model has been developed and implemented to direct the solid-state packing arrangements of these molecular materials, there exist numerous examples where the model falters. Here, we employ electronic structure methods to probe the noncovalent, intermolecular interactions of two closely related systems that result in two very different crystal packing configurations: triisopropylsilylethynyl (TIPS) pentacene and its triethylsilylethynyl (TES) analog. The quantum-chemical evaluation details how the slightly larger electron density contained within the volume of the TIPS moiety with respect to TES is in part responsible for the solid-state packing variations. We also make use of periodic density functional theory (DFT) methods to develop in silico polymorphs of these systems and explore the electronic characteristics of varied packing arrangements. The results suggest that TES pentacene, if processed correctly, could be developed into a material with improved charge-carrier transport characteristics when compared to its native form. Overall, the theory-driven insight developed in this work lays an important foundation to build a more robust crystal engineering paradigm for these technologically relevant organic semiconductors.

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INTRODUCTION For organic semiconductors, molecular packing in the solid state is critical to material performance.1 Though the field of organic electronics has undergone continued growth due to a number of favorable material attributes, for example, the ability to tune material electrical and optical properties via the enormous toolbox provided by organic synthesis, the inherent mechanical flexibility of organic materials, and the capability to solution or vacuum deposit thin-film active layers and manipulate morphologies at relatively low temperatures, to name but a few, established protocols to direct solid-state molecular packing remain rare. A simple illustration as to why this packing is so important was elegantly exhibited by Brédas and co-workers2 when they demonstrated how small translations in cofacial sexithiophene pairs can lead to dramatic changes in the magnitudes of the intermolecular electronic couplings, with the important caveat that large spatial overlap of the sexithiophenes does not necessitate large electronic couplings, that is, it is the degree of wave function overlap that is key. When an organic semiconductor is deposited from solution, the resulting thin films generally range from being amorphous to polycrystalline, with recent work demonstrating the ability to inkjet print single crystals;3 that is, the variability in the degree of molecular order in these films is tremendous. Hence, materials studies can lead to contrasting insight as to how to synthetically control solid-state molecular packing. Single crystals of organic semiconductors provide distinctive systems © 2016 American Chemical Society

to investigate how molecular structure, including the chemical composition, atomic arrangements, and larger molecular architecture, can be tuned to precisely direct molecular packing. As such, crystal engineering, and in particular the use of solubilizing alkyl side chains to guide the molecular packing of electronically active polycyclic aromatic hydrocarbon (PAH) chromophores, is a highly active field.4−24 Of particular interest to this work are trialkylsilylethynyl (TAS)-functionalized acenes. The TAS groups, generally substituted along the long axis of the acene chromophore, lead to increased chemical stability against attack from molecular oxygen,25 prevent acene dimerization under photoexcitation,26 and render acenes soluble in common organic solvents, allowing for the solution processing of thin films.27 From a materials design standpoint with a view toward controlling molecular packing in the solid state, perhaps the biggest advantage that these side groups enable is the ability to direct molecular packing by changing the length or branching of the alkyl groups appended to the silicon atom.27 Molecules in the oligoacene series prefer to pack in herringbone packing configurations, where the hydrogen atoms along the long axis of one acene point directly at the so-called π-face of the neighboring molecule.28 The addition of the TAS groups, Special Issue: Computational Design of Functional Materials Received: October 3, 2016 Revised: November 18, 2016 Published: November 21, 2016 2502

DOI: 10.1021/acs.chemmater.6b04211 Chem. Mater. 2017, 29, 2502−2512

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Chemistry of Materials

Figure 1. Chemical structures of TIPS Pn and TES Pn (top row) along with representations of the respective brickwork and slipped-stack packing arrangements. The radii of the spheres containing the TAS moieties, derived from B3LYP-D3/6-31G(d) optimizations of TIPS Pn and TES Pn (rDFT) and extracted from the respective crystal structures (rcry), are provided for reference.

however, often leads to situations where the chromophore πfaces overlap spatially, which can (but not necessarily) induce considerable intermolecular electronic couplings among the chromophores. On the basis of the synthesis and crystal-structure analyses of myriad TAS-substituted acenes, Anthony and Parkin derived a geometric model to predict crystal packing based on the radii of TAS ellipsoids (often considered as the symmetric spherical ellipsoid) and lengths of the acene long axes.27 In short, if the length of the chromophore long axis is roughly twice the length of the TAS diameter, then the model would predict that the TAS acene packs in a layered brickwork pattern that permits a two-dimensional (2D) charge-carrier transport pathway; if the TAS group diameter is smaller than this characteristic size, however, then the chromophore packs in a slipped-stack structure that enables a one-dimensional (1D) charge-carrier transport pathway (Figure 1). In field-effect transistors (FETs), materials with the characteristic 2D charge-carrier transport pathway tend to yield superior thin films and charge-carrier mobilities when compared to 1D slipped-stack materials; it is thought that the improved active material performance of the former structure arises in part from the higher quality films provided by materials with layered structures, along with the ability of charge carriers to avoid defects and trapping sites through diffusion along multiple pathways. As an example, triisopropylsilylethynyl (TIPS) groups appended to the central ring of pentacene (Pn) afford the brickwork structure, and the large and repeatable charge-carrier mobilities from solution processed TIPS Pn films have made this one of the most widely studied materials in the field.29−32 While there now exist countless theoretical studies that aim to predict the charge-carrier transport characteristics of crystalline materials, there are fewer studies that attempt to detail the connections among molecular structure, including both chemical composition and molecular architecture, noncovalent intermolecular interactions, solid-state packing, and the charge-carrier mobilities of crystalline organic semiconductors.33−37 In general, crystal structure predictions remain elusive38−41 and are particularly difficult for most

organic semiconductor materials where there is a significant dependence on dispersion as the main stabilizing force for the low-energy (thermodynamically driven) solid-state packing configurations. A variety of electronic-structure methods, across both wave function and density functional theories, and energy decomposition and interaction analysis techniques have been developed and applied to understand the noncovalent interactions among π-conjugated molecules, with particular focus on the so-called “π−π interactions”.34,36,37,42−66 However, the ability to make use of this information to engineer solidstate packing is still in its infancy. In the meantime, synthetic chemists have undertaken prominent efforts to use alkyl side chains to direct molecular packing. Even though the work remains highly Edisonian, the roles that the alkyl side chains play in determining the packing configurations of organic semiconductors have been established to be tremendous.33,67−73 However, a fundamental understanding of the interplay among intermolecular interactions arising from the many-component molecular systems that ultimately define solid-state molecular packing remains scarce. With an eye toward formulating chemical insight into the interplay of the alkyl and π-conjugated moieties in determining the solid-state packing configurations of organic semiconductors, we embark on a study of two TAS acenes: TIPS Pn and triethylsilylethynyl (TES) Pn. When considered in isolation, the TIPS and TES groups when appended to the acene core have nearly identical radii (rDFT), as measured from the silicon atom to the hydrogen atom on an alkyl chain that lies furthest from the silicon (optimized geometry at the at the B3LYP-D3/631G(d) level of theory): 3.89 Å for TIPS and 3.88 Å for TES (Figure 1). As noted above, TIPS Pn packs in the technologically desirable brickwork pattern, while TES Pn packs in the slipped-stack configuration: TIPS Pn is a benchmark material as an organic semiconductor in FET, while TES Pn shows poor FET performance. While the abovementioned geometric (or space-filling) model would predict that these two materials should pack in a similar fashion, this is definitely not the case. Hence, there is a need to understand the essential differences in these molecular materials, and the 2503


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any errors introduced by AFLOW reshaping the unit cell. Effective masses were calculated using the finite difference method code developed by Fonari and Sutton.94 Second derivatives were calculated on a 5 × 5 × 5 grid with a step size of 0.019 1/Å (0.01 1/rBohr). The cohesive energy density was determined by subtracting the energy of the molecule in the condensed phase from the energy of the molecule in the gas phase. To obtain the energy of an isolated TAS acene molecule for these calculations, the geometry of each individual molecule was optimized using Gaussian 09 (revision A.02)95 with the B3LYP and a 6-31G(d,p) basis set.79,80 Self-consistent calculations, using the PBE-D2 functional and plane-wave basis described above, were then carried out on these isolated molecules in sufficiently large unit cells such that no significant intermolecular interactions were present: 20 × 30 × 30 Å3 for TES Pn, 35 × 30 × 20 Å3 for TIPS Pn, and 35 × 30 × 20 Å3 for TMS DBC.

various impacts that such minor chemical variations have on solid-state packing arrangements, to improve the model to refine the crystal engineering paradigm.

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COMPUTATIONAL METHODS

We focused on a number of aspects to determine how the different components that make up the TAS Pn scheme direct the crystal packing. Potential energy surfaces (PES) describing intercomponent interactions among TAS groups, isolated from the acene cores, as a function of geometric arrangements in the solid state were determined. Given the large three-dimensional (3D) space needed to map PES for the TAS interactions, the number of atoms, and flexibility of the TAS groups, the semiempirical PM7 level of theory,74 which includes dispersion correction terms, as implemented in the MOPAC software suite was used.75 At each point along the PES, the geometries of the alkyl groups were fully optimized, with the ethynyl groups locked in a particular configuration. PES to describe the interactions among the Pn cores, with the geometries restricted by the space-filling considerations of the TAS groups as described below, were determined via density functional theory (DFT) calculations using the B3LYP functional76,77 in combination with the D3 dispersion correction of Grimme78 and a 6-31G(d) basis set.79,80 These calculations were carried out with the NWChem package81 using a supermolecule approach, where the dimer interaction energy is given by the total energy of the dimer minus the total energies of the constituent isolated monomers. The isolated Pn geometry used in these calculations was optimized at the B3LYP/6-31G(d) level. Likewise, as we will discuss, there exist intermolecular interactions among the Pn chromophores and alkyl side chains in certain TAS Pn crystals. Models to examine these interactions were treated at the same level of theory. In select cases, the magnitudes of the intermolecular noncovalent interaction energies were determined with symmetry adapted perturbation theory (SAPT)82 using the jun-cc-pVDZ83,84 basis set, as implemented in the Psi4 package.85 We made use of the SAPT0 approximation,86,87 which neglects the intramolecular correlation; results arising from the SAPT0/jun-cc-pVDZ calculations will be referred to throughout as SAPT0. Periodic DFT was used to determine the electronic band-structures, effective masses, and cohesive energy densities for a number of TES Pn, TIPS Pn, and 7,14-bis((trimethylsilyl)ethynyl)dibenzo[b,def ]chrysene (TMS DBC)19 solid-state packing arrangements. These calculations were carried out with the VASP88 software suite using PAW potentials (v.52)89,90 and the GGA-PBE functional.91 The kinetic energy cutoff was set to 520 eV. Gaussian smearing with a width of 0.05 eV was employed. van der Waals interactions were modeled with the DFT-D2 functional by Grimme.92 Preliminary geometries for in silico polymorphs, solid-state packing arrangements created in the computer that have yet to be experimentally realized (as described below), were created by modifying the experimentally derived polymorphs of TIPS Pn and TES Pn. The in silico brickwork polymorph of TES Pn was created by modifying the side groups of TIPS Pn (from isopropyl to ethyl) while retaining the original brickwork packing of TIPS Pn; similarly, the in silico slipped-stack polymorph of TIPS Pn was created by modifying the side groups of TES Pn (from ethyl to isopropyl) while retaining the original slippedstack packing of TES Pn. Crystals of TMS DBC in both the brickwork and slipped-stack packing arrangements have been grown, and those structures were used in the evaluations herein.19 The Brillouin zone was sampled with a 2 × 2 × 2 Monkhorst−Pack grid for the slipped-stack configurations of all crystals and also for the brickwork configuration of TES Pn. Grids were reduced to 2 × 1 × 2 and 2 × 2 × 1 for the brickwork configurations of TIPS Pn and TMS DBC, respectively. Gas-phase calculations were performed at the Γpoint only. Atomic positions, cells shapes, and cell volumes were relaxed until the forces were smaller than 0.01 eV/Å. The AFLOW software (version 31024) was used to both order the unit cell vectors and obtain a standardized path in the reciprocal space.93 All periodic structures were then further relaxed with a fixed unit cell to account for

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RESULTS AND DISCUSSION Even though one can consider TAS Pn to be simply composed of two components, the PES that can be explored during the assembly of the constituent molecules to form the solid-state packing arrangements are quite complex. Here we aim to break down these interactions to build insight into essential features that need to be understood to enhance the crystal engineering guidelines for the solid-state packing of these systems and investigate how these interactions impact the characteristics of the crystal. We begin by describing in more detail features of the TIPS Pn and TES Pn crystals to showcase the intermolecular interactions that arise in each crystal. We then explore interactions among the various components that make up the TAS acenes: TAS−TAS, Pn−Pn, where the spatial regions that are covered are restricted by treating the TAS groups as rigid, space-filling objects, and the TAS alkyl chains interacting with the acene moiety, a motif found in some TAS Pn crystals. Finally, characteristics of the full solid-state structure are determined including an evaluation of the potential that TIPS Pn and TES Pn could take on the slipped-stack and brickwork polymorphs, respectively. Features of TIPS-Pn and TES-Pn Crystal Structures. In both TIPS Pn and TES Pn, stacks of Pn chromophores, where charge-carrier transport takes place, are in general separated from each other by the “greasy” alkyl side chains of the TAS moieties. This suggests that there are two main intermolecular interactions that need to be accounted for when considering molecular design for crystal engineering: TAS−TAS and Pn− Pn. This is definitely the case for the brickwork configuration of TIPS Pn, where discrete Pn layers are clearly isolated by the alkylsilyl groups. Two Pn interactions can be differentiated, with one having more Pn−Pn spatial overlap than the other (Figure 2). On the other hand, the slipped-stack arrangement of TES Pn presents only one Pn−Pn stacking arrangement. In lieu of a secondary Pn−Pn interaction, an ethyl chain from a neighboring layer interacts with a portion of the Pn surface to stabilize the molecular packing arrangement. These interactions among the TES and Pn groups lead to less clearly defined boundaries among the Pn and TES layers. Hence, in the discussion that follows, we consider each of the TAS−TAS, Pn−Pn, and TAS−Pn interactions that arises in the solid state. The variations in TAS Pn packing have been previously discussed in the context of how much physical space the alkyl groups take up in comparison to the length of the Pn.27,96 However, even in the solid state (as with the DFT-optimized structures), the volume variations among the TES and TIPS groups are not significant, as the spherical radii defined by the distance between the silicon atom and the furthest hydrogen 2504


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Figure 2. Depictions of the slipped-stack (top) and brickwork (bottom) packing structures. Molecules of the same color belong to the main Pn−Pn stack, considered as that with the most spatial overlap. Other intrastack interactions (red to blue) consist of TAS−Pn contacts (slipped stack) or secondary Pn−Pn stacks (brickwork). Interstack interactions (e.g., red-to-yellow) between alkyl chains separate the Pn−Pn stacks from one another.

atom on any alkyl chain (rcry) are 3.73 and 3.72 Å for the TES and TIPS groups, respectively. What do differ, however, are the electron and spatial densities of the alkyl groups. By counting only the silicon, carbon, and hydrogen atoms in the triethylsilyl and triisopropylsilyl groups and assuming the volume of a sphere based on rDFT, the “electron density” of TES is 0.26 e−/ Å3, while that for TIPS is 0.36 e−/Å3. As described below, this additional (28%) electron density in the TIPS groups dictates to a large extent the observed variations in the solid-state packing behavior of these systems through a combination of larger exchange repulsion and dispersion interactions, the two noncovalent interactions expected to play the most significant roles in these systems,97 when compared to TES. Moreover, the extra free volume of the TES groups allows for interdigitation among the ethyl chains between neighboring TES moieties in the solid state, a feature not present in the TIPS Pn crystals, and a higher degree of compressibility. These features, as discussed below, lead to smaller silicon−silicon distances among the molecules that make up the main stack in TES Pn crystal structures when compared to TIPS Pn. TAS−TAS Interactions. There are two main TAS−TAS contacts in the crystal structures: those occurring for (i) TAS acenes that make up the same Pn stack (intrastack contacts), with the TAS groups pointing in the same direction, and (ii) among TAS acenes in different stacks (interstack contacts), where the TAS groups point in opposing directions (see Figure 2). Interactions in both alignments were modeled starting from three arrangements so as to not limit the TAS group rotamers. In each case, the interacting moieties included the trialkylsilyl group appended to an ethynyl unit, Figure 3. During the development of the PES at the PM7 level of theory (Figure 3 and Supporting Information), the silicon−silicon distances and broader TAS orientations were kept fixed, while all atoms in the alkyl chains were allowed full freedom to relax. As discussed above, the TES and TIPS groups have very similar physical size, though the electron density packed into those volumes differs. This difference is manifested in the PES by the fact that TIPS appears bigger in terms of its dispersive potential size, that is, the length at which stabilizing interactions engage between interacting groups; for example, the

Figure 3. PM7 interactions energies as a function of silicon−silicon distance for TES (green) and TIPS (red). Here, the PES are generated as a function of x and y displacement. Vertical lines depict estimated TAS diameters. For the intrastack contacts, the diameter for TES is 5.8 Å and for TIPS is 6.7 Å, while the interstack contact diameters are 5.6 Å for TES and 6.5 Å for TIPS.

intermolecular interaction energy reaches −1 kcal/mol at a silicon−silicon distance of 10 Å for TIPS, while it is not until 9 Å that this interaction energy is reached for TES. Further, contour maps reveal that the areas (or, rather volume, as the x and z axes in the laboratory frame of the model are effectively the same) with interaction energies larger than −4 kcal/mol (see the purple regions in Figure S2 in the Supporting Information) are quite expansive for TIPS when compared to those of TES. Likewise, the additional electron density in the TIPS groups affords larger exchange-repulsion energies. Thus, TIPS arrives at the potential minimum at a larger displacement, and experiences an earlier onset of the repulsive wall, when compared to TES. These discussions are supported by SAPT0 calculations (see Supporting Information), which show that dispersion is the major stabilizing force in TAS interactions, and that both the dispersion and exchange energies are stronger for TIPS when compared to TES at the same molecular displacement. At distances under 6 Å, the TES groups have stronger interaction energies due to the lower degree of exchange repulsion. From Figure 3, we observe that the interaction radius, half of the silicon−silicon distance at the potential minimum (somewhat analogous to the van der Waals radius for atoms) of TES is 2.88 Å, while for TIPS it is 3.35 Å. These are both substantially smaller than the estimates made from simply measuring the furthest silicon−alkyl-hydrogen distances, as the alkyl groups reorganize to best fill the available space and 2505


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the main stacking (z-axis) direction between 3 and 4 Å were considered, as these are ranges that are typically found in organic semiconductor crystals. Note that the pentacene molecules remain parallel to one another throughout the PES modeling, and no slip is taken into account along the molecular short axis (y axis). Within these confines, Pn dimers were generated, and the TAS groups were neglected so as to focus on the strength of the Pn−Pn interactions, determined the B3LYP-D3/6-31G(d) level of theory. With this model, we can directly gauge how the Pn groups interact with one another given the spatial constraints. While the TAS groups in large part will dictate how the Pn will align, there remains some flexibility to the final Pn−Pn configurations that are driven by the nature and strength of the Pn-Pn interactions. For Pn−Pn dimers representing the slipped-stack packing configuration, PES were determined for center-of-mass distances that range from 5−9 Å in increments of 0.1 Å (see Supporting Information for PES). Figure 4 shows the interaction energies of the PES minima plotted against R. As R increases, the interaction energy at the PES minimum becomes weaker, as expected. The vertical (z axis) displacement at the minima shows a total variation of less than ±0.1 Å, with a median value of 3.56 Å. This distance is on average larger than that observed in the experimental crystal structures, as not all (compression) forces expected in the solid state are taken into account (i.e., the dimer is treated in the gas phase), though the results do agree with similar theoretical studies.66 When R is approximately 7 Å, the pentacenes can pack slightly closer together in the z direction, and with stronger Eint, than neighboring R values. This is likely due to localized differences in electron density and accompanying variations in exchange energy, as observed with other studies of acene interactions.66 A trimer model was used to determine interaction energies in Pn−Pn brickwork packing arrangements. This molecule was placed at a fixed distance from the top pentacene in the original dimer, with the relative in-plane displacement taken from the TIPS Pn crystal structure. When compared to the slipped-stack arrangement, the variation in the vertical separation at the energetic minimum for each R is decreased, and the interaction energies at these minima are fairly consistent across the values of R investigated (Figure 4). As R increases, the molecular overlap of the main stack is once again decreased, but the overlap in the secondary stack increases at the same time. Similar to the slipped-stack results, there is a tendency toward closer packings with stronger interaction energies at R ≈7 Å. By taking these results in combination with the interaction radii from the TAS−TAS PES, space filling from TES (R = 5.8 Å) should result in stronger Pn−Pn interactions in a dimer when compared to TIPS (R = 6.7 Å), with the Pn−Pn interaction energies being −14.00 and −12.87 kcal/mol, respectively. This trend is reversed when the third molecule is introduced, but the difference between the two values is very small (only 0.4 kcal/mol). While the Pn−Pn interactions are individually stronger than the TAS−TAS interactions, the differences in Pn−Pn interaction energy due to space filling alignments can be easily overcome by interactions involving the solubilizing TAS groups, which showcases the vital role that the TAS groups play in directing TAS acene solid-state packing. TAS−Pn Interactions. We finally consider interactions between TAS and Pn. The slipped-stack configuration of TES Pn does not show the second backbone-stacking interaction found in brickwork TIPS Pn but rather an alkyl group from a molecule in a different Pn stack interacts with the chromophore

maximize interactions with their neighbors; these results also highlight the larger compressibility of TES. It should be noted that the TAS groups are indeed not spherical, as can be seen in the contour plots (see Supporting Information), but these numbers serve to approximate the size of each group. Similar conclusions are drawn from 3D contour maps and silicon− silicon distance analyses of the interstack contacts, with slightly smaller radii determined for TES (2.80 Å) and TIPS (3.25 Å) when compared to the intrastack interactions. Pn−Pn Interactions. So-called “π-stacking” interactions are often assumed to be the main noncovalent interactions driving molecular packing in materials developed from π-conjugated chromophores. As with the TAS−TAS interactions, however, it is more correct to think of these intermolecular interactions as being largely a balance of repulsive Pauli exchange interactions and attractive dispersion interactions, though at very close distances electrostatic interactions arising from charge penetration can play a significant role.59,66,98−101 Prior studies, many of which have been referenced already, have mapped these interactions with varying molecular alignments including intermolecular separation, short and long axis displacement, and rotation. Here, however, we want to understand the nature and strength of the intermolecular interactions in dimensions constrained by the TAS groups. To do so, we map several Pn− Pn PES in a space that is restricted by what the TAS moieties themselves will allow. For each PES, the center-of-mass distance between the dimer pair is fixed to a single value (denoted R in Figure 4) that equals the diameter of the side group; in essence, by changing R, we are allowing for a comparison across a wide variety of potential TAS groups. The angle (θ) controls the degree of molecule long axis (x axis) slip and stacking height (z axis) at the fixed R. The range of θ was limited such that only Pn pairs with plane-to-plane distances in

Figure 4. (top) Depiction of the geometric parameters used to determine the interaction between two Pn molecules confined to move within the space provided by space-filling (rigid) TAS groups. The Pn centers-of-mass distance are fixed at a distance R, while the angle θ is varied. (bottom) Interaction energies at PES minima for each R value are plotted for Pn slipped-stack dimers (black) and brickwork trimers (red) as determined at the B3LYP-D3/6-31G(d) level of theory. 2506


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Chemistry of Materials in the mode of a C−H···π interaction.102−107 To evaluate this interaction, we make use of a naphthalene model to represent the portion of the Pn that interacts directly with an alkylsilyl group. PES for vertical displacement between the naphthalene and the TAS groups were generated in a similar manner as the TAS−TAS interaction PES. The TAS groups were oriented in three rotamers, and the alkyl groups were allowed to relax using the PM7 semiempirical method; the silicon and alkyne atoms were fixed. From these three optimizations, the lowest energy geometries were used to evaluate the B3LYP-D3/6-31G(d) interaction energies. We find that TIPS interacts more strongly with the naphthalene model at larger distances when compared to TES, but also reaches the repulsive wall at a longer distance. Again, this feature can be traced directly back to the larger electron density in TIPS when compared to TES. Notably, at the silicon−Pn distance taken from the TES Pn crystal structure, the TIPS interactions with the naphthalene model are stronger than that for TES. This result shows that, in this instance, the single pairwise interaction model is not sufficient to describe the reasons behind this interaction in the solid state. As highlighted above, the TAS−TAS interactions will dictate much of the spatial proximity that the molecules can explore. A full picture as to when and why the TAS and Pn groups will come into direct contact in the solid requires information from other interacting bodies. At this stage, we have developed a series of PES for pairwise interactions in TAS Pn structures. The results showcase the sensitive balance among the TAS−TAS, Pn−Pn, and TAS−Pn interactions that determine the favored solid-state packing arrangements in these crystalline materials, a balance that can be greatly altered by modest changes in the molecular chemistry of these fairly large molecules. The results suggest that simple geometric (space filling) models are not substantive enough to adequately describe the packing in these systems. Importantly, the data reveal that quantum-chemical effects arising from TAS group electron density, along with potential chemical variations in the π-conjugated chromophores,36 need to be accounted in the solid-state design model to refine the crystal engineering paradigm. Impact of Packing Configuration on the Solid-State Electronic Characteristics. With the information on the component interactions in hand, we now consider the materials implications for the variations in solid-state packing that are directed by the TAS functionalities. In particular, we are interested in addressing whether or not there may be some advantage to consider variations in processing conditions to alter the crystal structure of TES Pn. As discussed previously, the slipped-stack configuration adopted by TES Pn is not favorable for applications requiring efficient thin-film chargecarrier transport. To address this question, we developed in silico polymorphs where the TES Pn and TIPS Pn are exchanged into the respective packing configurations, TES Pn into the brickwork and TIPS Pn into the slipped-stack arrangements, to determine the energetics and electronic characteristics of these as-of-yet experimentally unrealized structures. Importantly, we note that a similar TAS-substituted chromophore, 7,14-bis((trimethylsilyl)ethynyl)dibenzo[b,def ]chrysene (TMS-DBC),19 has been crystallized in both the slipped-stack and brickwork packing configurations by providing literature precedent for this type of crystal packing variations in the same molecular material.

We start with the slipped-stack configuration for TES Pn, whose experimental density is 1.16 g/cm3. When the structure is relaxed at the GGA-PBE-D2 level of theory, the density increases modestly to 1.27 g/cm3; this density will serve as our computational baseline by providing a measure of the variation of the in silico structures (at 0 K and 0 bar) when compared to the experimental crystal structure. The main structural differences between the experimental and DFT-relaxed structure are decreased interstack distances in the DFT-derived structure, which leads to the increased unit cell density. The cohesive energy density, a measure of the stabilization of TES Pn in the slipped-stack packing configuration when compared to the isolated molecule in the gas phase, is 562.24 J/cm3 in the DFT-optimized structure. Substituting TIPS Pn into the slipped-stack configuration and allowing the system to fully relax results in final unit cell density of 1.21 g/cm3. This density is slightly smaller than that for TES Pn, even though there are more atoms in the molecular unit, and results from increased unit cell volume and molecular displacements. The most significant packing changes, when compared to TES Pn, generally occur in the interstack region, as the TIPS Pn molecules move away from each other due to the increased interaction radius of the TIPS groups. In the Pn− Pn stacks, the Pn moieties slip along their long molecular axes to result in a lower degree of spatial overlap (increased molecular displacement) by 0.2 Å. This change has only a minor effect on B3LYP-D3/6-31G(d)-determined pairwise interaction energies (Figure 5). However, only around 40% of the stabilization of the main stacking interaction along the slipped-stack comes from direct Pn−Pn interactions, which showcases the importance of the TAS−TAS contributions.97 The intermolecular displacements defining the stacking interaction between the Pn and TIPS groups decrease along the long axis (x) direction (essentially making up for the smaller Pn−Pn overlap of the main stack) but increase in the y and z directions and result in a net increase in overall molecular spacing. This TAS−Pn interaction is weaker in the TIPS Pn slipped-stack crystal when compared to TES Pn due to a greater overall distance between the molecules (Figure 5), as supported by SAPT0 calculations (see Supporting Information). The cohesive energy density for TIPS Pn in the slippedstack configuration is 421.18 J/cm3. By turning to the brickwork packing configuration, the experimental density of TIPS Pn is 1.10 g/cm3, while DFT relaxation leads to a density to 1.22 g/cm3. Here, again, the increased density in the DFT-relaxed structure arises mostly from changes in the interstack contacts. The cohesive energy density for brickwork TIPS Pn is 487.14 J/cm3. Substituting TES Pn into the brickwork configuration results in an increased density, when compared to TIPS Pn, of 1.26 g/cm3. The molecular spacing, when compared to TIPS Pn, decreases in most directions (Figure 5). Notably, there is increased long-axis overlap (decreased molecular displacement) of the Pn moieties in the main Pn stack. A knock-on effect of this realignment, and in reversal to the overall trend, is that there is increased molecular spacing in the other two intrastack interactions. A combination of the increased silicon−silicon distance and the generally smaller dispersion forces between TES groups leads to a loss of over 5 kcal/mol for each of these intrastack interactions (Figure 5). Fragment interactions (see Supporting Information) show that these differences in the interaction energy come from direct TAS−Pn or TAS−TAS (rather than 2507


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crystals were grown; interestingly, the crystal growth was independent of growth method (e.g., gas-phase or solution).19 Further, solvent-vapor or thermal annealing,108,109 solvent additives,110 deposition procedures that induce nonequilibrium strained packing arrangements,111 for example, the now commonly employed solution-shearing method,10,112 nanoconfinement,14 chemical modifications to the substrate,113 or other processing protocols,114 could provide access to the alternative polymorphs discussed here. The question that arises from this analysis is whether it might be worth the effort to experimentally derive the brickwork (slipped-stack) packing configuration for TES Pn (TIPS Pn). To explore this possibility, we evaluated the band structures and effective masses of TES Pn and TIPS Pn in both the slipped-stack and brickwork polymorphs; the results for TMS DBC have been previously reported.19 Electronic band structures for all in silico polymorphs considered are presented in the Supporting Information. We will focus here on the valence band dispersion and hole effective masses, as these materials are generally considered as hole-transporting semiconductors. For TES Pn, the valence band dispersion in the slipped-stack configuration is 0.452 eV, while in the brickwork configuration it is 0.448 eV. The TES Pn hole effective mass is 0.54 me in the slipped-stacked structure and 0.64 me in the brickwork. These results suggest that there is very minimal change in key (static) parameters often considered for chargecarrier transport when TES Pn is in either polymorph. Hence, there is a strong indication that TES Pn could become an effective organic semiconductor for transistor applications if it could be processed into the device-favorable brickwork polymorph. The same cannot be said, however, for TIPS Pn. Here, the valence band dispersion decreases by 3.8-times when it goes from the preferred brickwork (0.366 eV) to the slippedstack (0.096 eV) polymorph, and the hole effective mass increases by 4.6-times (0.29 me in the brickwork and 1.61 me in the slipped-stack polymorphs).

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Figure 5. Pairwise B3LYP-D3/6-31G(d) interaction energies as a function of silicon−silicon (Si−Si) distance for TES Pn (green) and TIPS Pn (red) molecules in DFT-optimized slipped-stack (top) and brickwork (bottom) packing structures. Solid circles are interstack interactions, and open circles are intrastack interactions, as defined in Figure 2.

CONCLUSIONS Crystal engineering offers a distinctive opportunity to use the foundations of synthetic organic chemistry to direct molecules to pack in beneficial arrangements for a variety of electronic and optoelectronic applications. However, clear molecular design and processing paradigms need to be established to fulfill this promise. The results of this quantum-chemical investigation reveal some of the limitations behind current geometric (space filling) models employed to build TAS acene crystals, though the models remain powerfully simple tools in the arsenal of the materials chemist. Specifically, this work has demonstrated that a balance must be achieved among three critical moiety interactions, TAS−TAS, Pn−Pn, and TAS−Pn, to fully control the molecular packing. Further, it is not just the TAS volume that plays a key role in determining the preferred packing arrangements, but rather it is the electron density contained within the TAS volume, which affects interdigitation, compressibility, and the strength of the TAS-based interactions, that directs a majority of these intercomponent interactions. While the Pn−Pn interactions, often referred to as π−π interactions, do play an important role, the results here show how that they are not the majority player in these systems; for example, though these interactions are the single largest component interactions in the TAS acenes at 40%, the remaining 60% is dictated by the TAS−TAS and (possible) TAS−Pn interactions. We are currently embarking on a theory-

Pn−Pn) interactions. For TES Pn in the brickwork packing configuration, the cohesive energy density is 525.04 J/cm3. On the basis of the changes in geometries and cohesive energy densities, we learn quite a bit about these structures. Notably, the cohesive energy densities are largest for slippedstack TES Pn and brickwork TIPS Pn, that is, the most stable configurations derived experimentally. While there is nothing surprising with this result, the differences in cohesive energy densities forecast an intriguing potential for TES Pn. The difference in the cohesive energy density of the two TES Pn polymorphs is 37.20 J/cm3, while that for TIPS Pn is twice as large at 65.96 J/cm3. Importantly, the difference in the cohesive energies for TMS DBC, the molecular system that has been grown in both the slipped-stack and brickwork structures, is 67.09 J/cm3. That TES Pn (TIPS Pn) shows a smaller difference in the polymorph cohesive energy density compared to TMS DBC suggests that various processing considerations could lead to TES Pn (TIPS Pn) taking on the brickwork (slipped-stack) packing configuration. For instance, the TMSDBC slipped-stack and brickwork polymorphs were derived by controlling the temperature of the substrate on which the 2508


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driven analysis of scores of TAS acene crystals that have been synthesized and combining this information with material processing and device characterization to expand the TAS acene crystal engineering model to allow for more precise materials design for explicit electronic targets. As well as the direct significance to molecular design and crystal engineering of small molecule crystalline materials, this work has larger implications in refining our understanding of the design of oligomeric and polymeric materials for organic electronics that do not necessarily rely on the precise packing arrangements of crystals. Alkyl chain lengths and structure (e.g., linear vs branched) are often chosen with regards to increasing polymer solubility, for instance, but in actuality will have profound effects on polymer chain alignment and packing through dispersion stabilized interactions among the solubilizing groups and between solubilizing groups and the polymer backbones. From a computational standpoint, this work also points to the important role that theoretical materials chemists can play in defining the design paradigms requisite for efficient organic semiconductors beyond just computing the electronic characteristics of isolated molecules and bulk materials.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b04211. Additional data and discussion pertaining to intercomponent and full intermolecular interactions; packing variations in the in silico polymorphs; electronic band structures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

John E. Anthony: 0000-0002-8972-1888 Chad Risko: 0000-0001-9838-5233 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by seed funds from the Center for Applied Energy Research (CAER) at the University of Kentucky and the National Science Foundation (NSF DMR1627428 and CMMI-1255494). C.R. thanks the University of Kentucky Vice President for Research for start-up funds.

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REFERENCES

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