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Non-Covalent Intermolecular Interactions in Organic Electronic Materials: Implications for the Molecular Packing vs. Electronic Properties of Acenes Christopher Sutton, Chad Risko, and Jean-Luc Bredas Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b03266 • Publication Date (Web): 30 Oct 2015 Downloaded from http://pubs.acs.org on November 6, 2015

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Chemistry of Materials

Non-Covalent Intermolecular Interactions in Organic Electronic Materials: Implications for the Molecular Packing vs. Electronic Properties of Acenes

Christopher Sutton,1,# Chad Risko,2,* and Jean-Luc Brédas3,*

1

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics Georgia Institute of Technology Atlanta, Georgia 30332-0400 2

Department of Chemistry & Center for Applied Energy Research University of Kentucky Lexington, Kentucky 40506-0055 3

Solar and Photovoltaics Engineering Research Center Division of Physical Science and Engineering King Abdullah University of Science and Technology Thuwal 23955-6900, Kingdom of Saudi Arabia

#

New address: Theory Department, Fritz Haber Institute of the Max Planck Society, Berlin 14195, Germany * Corresponding authors: [email protected]; [email protected]

ACS Paragon Plus Environment


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Abstract Non-covalent intermolecular interactions, which can be tuned through the toolbox of synthetic chemistry, determine not only the molecular packing but also the resulting electronic, optical, and mechanical properties of materials derived from π-conjugated molecules, oligomers, and polymers. Here, we provide an overview of the theoretical underpinnings of non-covalent intermolecular interactions and briefly discuss the computational chemistry approaches used to understand the magnitude of these interactions. These methodologies are then exploited to illustrate how non-covalent intermolecular interactions impact important electronic properties – such as the electronic coupling between adjacent molecules, a key parameter for charge-carrier transport – through a comparison between the prototype organic semiconductor pentacene with a series of N-substituted heteropentacenes. Incorporating an understanding of these interactions into the design of organic semiconductors can assist in developing novel materials systems from this fascinating molecular class.

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I. Introduction Materials derived from organic π-conjugated molecules and polymers have generated extensive academic and industrial interest as the active components in electronic and photonic devices ranging from field-effect transistors to solar cells, light-emitting diodes, and all-optical switches.1-20 To date, organic light-emitting diode displays have delivered the most significant commercial impact through their incorporation in digital cameras, smart phones, tablets, and televisions. Importantly, exploiting the toolbox of organic synthesis brings forward the potential to create materials with well-defined electronic, redox, optical, and mechanical properties, which in turn would allow for innovative materials designs within a broad application space. In most applications, the efficiency of the organic active layer is dependent on the ability of the organic material to transport charges, whether they are holes or electrons. Charge-carrier transport is intimately connected to both molecular – e.g., chemical composition and molecular architecture – and material factors – including material purity, solid-state packing configuration, and crystal grain boundaries to name but a few; the latter are critically dependent on the material deposition protocol (e.g., solution or vacuum processing), interactions with substrates, and/or annealing procedures. Understanding the full spectrum of the material structure-processingproperty profile and the impact on charge-carrier transport is a key component in the development of new generations of organic electronic devices.21-33 The relationships among molecular structure, processing, and charge-carrier transport can be exemplified by molecules within the oligoacene family. Highly-purified, vacuum-deposited single crystals of rubrene – a tetraphenyl-substituted tetracene – can lead to hole mobilities as high as 40 cm2V-1s-1,34-36 which are among the largest intrinsic charge-carrier mobilities reported

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for π-conjugated molecular materials.34,

35, 37-41

From the structure-property perspective, while

tetracene packs in the edge-to-face herringbone arrangement, the ‘bulky’ phenyl substituents in rubrene disrupt this assembly. This chemical structure-driven modification of molecular packing leads in rubrene to extensive co-facial-like overlap of the tetracene backbones among neighboring molecules along a stacking direction. Such a packing, fortuitously, results in considerable overlap of the frontier π molecular orbitals along the molecular stacks, which, in turn, produces large intermolecular electronic couplings (~100 meV) responsible for the high measured hole mobilities.42, 43 From a materials design standpoint, such “π-π interactions” along molecular stacks are often deemed crucial for large charge-carrier mobilities. Unfortunately, attempts to date to process rubrene from solution or to use chemical substitution to improve on the charge-carrier transport parameters have resulted in limited success,43-46 with the chemical modifications often leading to substantial distortions in both the crystalline molecular structure and packing (see below). Situations such as this – and the countless single-crystal and amorphous systems in the literature that show similar patterns of small and large charge-carrier mobilities as a function of simple chemical substitutions or variations in the processing protocol – bring into question whether we currently have the ability to control materials properties through chemistry. While there are numerous molecular and materials design principles proposed to lead to organic materials with efficient charge-carrier transport for a variety of device applications, the majority of new materials are derived in an ad hoc fashion. Here, our goal is to consider molecular design criteria from the standpoint of a quantum-chemical view of the non-covalent intermolecular interactions, i.e., from a consideration of the exchange repulsion, dispersion, electrostatics, and induction terms (which will be introduced in detail below). These interactions need to be

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understood, manipulated, and balanced (Figure 1) to engender energetically favorable molecular packing configurations and large intermolecular electronic couplings. We note that processing considerations, e.g., vacuum deposition vs. solution deposition, and interactions at materials interfaces are not considered here, though they can have considerable impact on molecular packing and order. It is our hope that by incorporating such a quantum-chemical point-of-view, the toolbox of the synthetic chemist can be better developed through more precise, direct molecular engineering protocols.

Figure 1. Illustration of the quantum-chemical basis for molecular material design considering the exchange repulsion, dispersion, electrostatic, and induction intermolecular interactions: The repulsive exchange energy is balanced by the attractive dispersion, electrostatic, and induction components.

We begin by introducing in Section II definitions of the various non-covalent interactions, which are not typically considered in terms of material design, although they provide the quantummechanical basis for understanding energetically favorable packing motifs. This is followed in

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Section III by a brief description of the relevant computational methodologies (we note that the reader less interested in the theoretical aspects can safely simply glance over this Section). We then move in Section IV to a discussion of a few molecular design principles that have been employed in the development of molecular-based organic electronic materials. Finally, Section V provides a comparison between pentacene and a series of N-substituted heteropentacenes to demonstrate the relationship between intermolecular electronic coupling and the repulsive intermolecular interactions due to electron density overlap. At this stage, it is useful to consider what is meant by “π-π interactions”. Discussions concerned with the packing (or stacking) of π-conjugated molecular / polymer-based materials often suggest a driving or stabilizing force in the context of somewhat nebulous definitions of π-π interactions. As discussed below, while there are clear physical definitions of exchange-repulsion, electrostatic, induction, and dispersion interactions coming from the electronic structure community, there remains a lack of a clear designation for such π-π interactions. In fact, there is much candid and important debate in the literature as to: (i) whether there exist stabilizing forces due to π-π interactions that drive particular intermolecular configurations; (ii) whether such effects come into play for larger π-conjugated structures as opposed to smaller (e.g., benzene) systems; and (iii) what role chemistry (e.g., through heteroatom substitution in the conjugated system or peripheral substitution with electron donating/withdrawing moieties or alkyl chains) may play in governing these interactions.47-59 Here, our intent is not to contribute directly to this debate, but rather to underline that there are precise physical definitions, in terms of the intermolecular forces driving preferred packing configurations, that can provide a refined basis for the discussion of molecular packing. Our focus will be on electronic interactions, i.e., those interactions stemming from the overlap of π-orbitals on neighboring molecules and leading to the

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intermolecular electronic couplings (or band dispersions in crystalline systems) that determine charge-carrier transport.

II. Description of the relevant non-covalent interactions The nature and strength of intermolecular interactions in condensed phases are important in many aspects of the design and processing of π-conjugated molecules/polymers. Here, we provide rigorous definitions of non-covalent interactions and begin with the main repulsive interaction, the exchange interaction, which needs to be overcome to facilitate tight molecular packing. This destabilizing non-covalent force arises as a consequence of the Pauli exclusion principle (i.e., no two electrons [fermions] can occupy the same quantum state)60, 61 and leads to the energetic exponential wall of the interaction potential at small inter-atomic/molecular separation. Exchange repulsion physically limits atom/molecule proximity so that electrons avoid significant overlap (and is the main reason as to why matter has volume).62-64 We further discuss this effect for stacked π-conjugated molecules with large intermolecular electronic couplings, as there is necessarily a large molecular orbital overlap that results in a large electron repulsion. To some extent, chemistry can be used to overcome this repulsive interaction in organic materials, mostly through the exploitation of dispersion, electrostatic, and induction interactions. Dispersion is usually the dominant attractive force in the interaction of nonpolar molecules and results from interactions between instantaneous charge fluctuations (induced dipoles) in the electron density. Interactions among induced dipoles give rise to the dependence of the

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dispersion energy that forms the attractive part of an interatomic potential (such as the potential of bound diatomic noble gases). Electrostatic interactions result from interactions among the permanent multipoles on each molecule, e.g., dipole-dipole, quadrupole-quadrupole, dipole-quadrupole, or (in the presence of an excess charge on one of the molecules) monopole-dipole or monopole-quadrupole interactions. It is important to note that, although the interactions among the permanent multipoles are the determining contributions to the electrostatic energy at large intermolecular distances, the picture becomes more complex at short intermolecular distances (< 4 Å). This is a consequence of the so-called charge penetration phenomenon, by which the electrons of one molecule “penetrate” into the other molecule and are then able to experience significant attraction from the nuclei of the latter, which in turn contributes to counter-act the repulsive electron-electron interactions.55, 65 We stress that the plane-to-plane distances found in systems with high charge-carrier mobility range typically from 3.3 to 3.8 Å; thus, significant charge penetration effects should be present. The smallest (in magnitude) non-covalent interaction in π-conjugated materials tends to be induction (or polarization), which can be understood in terms of the electronic relaxation (the distortion of the charge distribution) of one molecule in response to the presence of another; it corresponds to the interaction that arises from induced electrostatic moments on one molecule in the presence of permanent (such as dipole or quadrupole) moments of the second molecule. The relative importance of the non-covalent terms depends on the specific nature of the system of interest, and multiple terms can play an important role in the stabilization of a given intermolecular interaction: Exemplary cases include halogenated compounds or hydrogen-

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bonded complexes, where strong dipolar interactions are involved; here, the electrostatic terms become large and can sometimes dominate. However, in many π-conjugated organic crystals it is dispersion and exchange repulsion that are generally the largest energy terms.

III. Computational approaches to evaluate non-covalent interactions The evaluation of non-covalent intermolecular interactions through electronic-structure theories has been extensively reviewed elsewhere,66-74 and we only highlight a few relevant points here. First, it must be noted that the study of non-covalent interactions remains a difficult task because of the necessity of highly accurate methods to describe the small forces that arise from electron correlation effects over various length scales.75 Typically the use of high-level ab initio wavefunction methods, such as coupled-cluster with single, double, and perturbative triple electron excitations (CCSD(T))76 in combination with a large basis set, is required to capture these correlation effects.49,

77-80

However, the computational costs for these methods still

preclude their application to systems much beyond the size of the benzene dimer.81,

82

An

alternative approach is to use second-order Møller–Plesset perturbation theory (MP2), though it is known to overestimate interaction energies, especially for dispersive π-interactions.83 However, MP2 methods, when paired with an appropriate basis set, can lead to a fortuitous error cancellation for aromatic systems and, as a result, provide reasonable descriptions for the strength of intermolecular interactions.84, 85 Density functional theory (DFT) has proven to be a quantum-chemical workhorse for large πconjugated systems, providing a reasonable trade-off between accuracy and computational efficiency. However, standard density functionals employ a (semi)local exchange-correlation

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functional and, therefore, are incapable of capturing the long-range dispersion effects ( ) that are required to capture the attractive van der Waals interactions of a given system. Recent advances in the development of density functionals have sought to overcome this issue by including an atomic pair-wise correction term for long-range dispersion interactions. For example, the dispersion-corrected DFT methods (DFT-D)66, 86-89 use an energy correction term in the form of an potential for each pair of atoms (we note that by convention distances between electrons are usually denoted with r and those between nuclei/atoms, with R); specifically, these methods make use of an atom-speciﬁc dispersion coefficient ( ) and an exponential damping function to enforce the proper long-range behavior of the correlation energy. Several strategies have been employed to generate the dispersion coefficients, such as the use of an atom-specific term derived from experimental (or computed) atomic polarizabilities and ionization potentials.86-88 Extensions of these models can account for the coordination number of the atom to include information of the bonding environment (e.g., sp3 vs. sp2 carbon atoms), and/or include higher powers in dispersion energy to better describe the short-to-medium dispersive force range (e.g., ).88, 89 The inclusion of an empirical three-body dispersion term has also recently been suggested.67 Alternatively, density-based approaches for determining the term have been developed, such as those based on the electron density of the system scaled to a free-atom reference value,90-92 through the interaction of instantaneous fluctuations in the exchange-hole dipole moment (XDM),93-95 and similar density-dependent corrections to the dispersion energy.96, 97 While a systematic analysis of the accuracy of various DFT methods relative to benchmark databases has been reported,98 we only briefly note here that, in general, the pairwise-based methods tend to overestimate the stability of large complexes that have considerable overlap of

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the π molecular orbitals.99 Further improvements can be obtained by incorporating many-body effects of the relevant chemical environment into the pair-potentials through a self-consistent procedure.100-102 So far, we have only highlighted atom-pair interactions. However, methods have been developed that move beyond these concepts: For instance, the inclusion of non-local correlations based on the adiabatic fluctuation dissipation theorem103-105 (which connects DFT with many-body theory) has allowed the development of new functionals with the random phase approximation,106-114 or including a non-local component directly into the DFT functional (e.g. vdW-DFT).115-118 When considering the interaction energy ( ) between two components, say, molecule A and molecule B forming a complex, an indirect determination comes from the difference of the complex energy ( ) compared with the energies of the isolated subsystems ( and ) at a fixed geometry: = − − Such supermolecular methods, however, do not provide for a decomposition of the interaction energy into the physical components described above. In addition, the application of the supermolecular approach requires the need for very accurate methods capable of calculating extremely small differences in total energies, as the total energy of a system is several orders of magnitude larger than the non-covalent intermolecular interaction energies. Moreover, concern arises due to basis set inconsistency within such calculations, which can lead to the basis-set superposition error (BSSE).119, 120

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Decomposition schemes, alternatively, rely on perturbation theory to determine the interaction energy from a sum of various energy terms. A widely used approach, in particular for studies of small, stacked aromatic systems, is symmetry-adapted perturbation theory (SAPT).121 Notably, recent advances incorporating density-fitting schemes allow efficient wavefunction-based SAPT calculations on large systems.122-124 SAPT calculations decompose the non-covalent interactions into the physically meaningful energetic contributions we described above: exchange repulsion [Eexch], electrostatics [Eelec], induction/polarization [Eind], and London dispersion [Edisp]; the total interaction energy is then the sum of the individual components: Eint = Eexch + Eelec + Eind + Edisp. The so-called SAPT0 approach (where the “0” indicates that intra-monomer electron correlation is neglected) has been shown to give accurate stacking energies for a wide array of non-covalent systems, when combined with an appropriately sized basis set (such as jun-cc-pVDZ);122, 123 in particular, this approach performs well compared to the high-quality benchmark data available for the S22 test set (a database of non-covalent model dimers categorized with regard to the nature of the dominant interactions such as hydrogen-bonded, dispersion, or mixed-character).77, 123, 125

This level of theory, importantly, can provide rigorous insight into the nature of

intermolecular interactions in π-conjugated systems.122, 123, 126 A particular success from SAPT-based studies by Sherrill and co-workers has been the revelation of the importance of charge penetration effects in stacking interactions among π-conjugated molecules with close intermolecular packing distances. While there is substantial orbital overlap in these systems, which should lead to large exchange repulsion, there is also a stabilization from attractive electrostatics that arises due to charge penetration at short intermolecular distances (

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