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Probing Charge Delocalization in Solid State Polychromophoric Cation Radicals Using X-ray Crystallography and DFT Calculations Lena V. Ivanova, Denan Wang, Sergey V. Lindeman, Maxim V. Ivanov, and Rajendra Rathore J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02184 • Publication Date (Web): 13 Apr 2018 Downloaded from http://pubs.acs.org on April 14, 2018

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The Journal of Physical Chemistry

Probing Charge Delocalization in Solid State Polychromophoric Cation Radicals Using X-ray Crystallography and DFT Calculations Lena V. Ivanova,* Denan Wang, Sergey Lindeman, Maxim V. Ivanov* and Rajendra Rathore† Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881

ABSTRACT. Assessing the charge delocalization in polychromophoric assemblies is a critical step towards designing novel charge transfer materials.

Triptycene-based materials are

particularly attractive, owing to their unique packing arrangement in the solid state. Here, we systematically probe, both experimentally (with X-ray crystallography) and theoretically (using Density Functional Theory, DFT), the extent of cationic charge (i.e., hole) delocalization in a set of triptycene derivatives with one, two and three electron-rich 1,2-dimethoxybenzenoid (veratrole) rings. We demonstrate that the amount of charge at each veratrole can be deduced from experiment by analysis of the oxidation-induced bond length changes in comparison with a model compound containing one veratrole ring as a reference. In contrast, DFT calculations provide not only oxidation-induced structural reorganization, but also the charge distribution with the aid of natural population analysis. A comparative analysis shows that both experiment and theory are of equal efficacy in quantifying the extent of hole distribution in polychromophoric cation radicals, despite issues of packing, solvent molecules and counter ions

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that are present in the crystals. Therefore, combining X-ray crystallographic data with insight from DFT calculations can provide a detailed understanding of the hole distribution in polychromophoric cation radicals, in turn allowing an informed design of the next-generation charge-transport materials based on triptycene and other polychromophoric scaffolds.

INTRODUCTION Developing a quantitative understanding of how a hole or cationic charge is delocalized in polychromophoric molecules and assemblies is a critical step towards designing new and improved functional materials for long-range charge transport to improve the efficiency of modern photovoltaic devices.1-3 Triptycene (Figure 1, left) and its derivatives3-7 represent an important class of potential charge-transfer materials owing to their unique packing arrangement in the solid state, where a single charge can be effectively delocalized intramolecularly among three circularly-arrayed phenylenes (Figure 1, middle).8 The close cofacial packing, where the benzenoids of triptycenes make intermolecular sandwich-like contacts with other triptycene molecules, produces a 2D-array, which, in turn, is well-suited for effective long-range charge transfer (Figure 1, right).

Figure 1. Structures of parent triptycene (T), its hexamethoxy derivative (HMT) and the packing of [HMT+•SbCl6-] crystal structure.

Blue shading represents intra-molecular hole

delocalization in isolated HMT+• and a combination of intra- and inter-molecular hole delocalization in [HMT+•SbCl6-] via close sandwich-like contacts between HMT molecules.


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Our continuing exploration of triptycene derivatives6,8 raises a question as to whether the three benzenoid rings need be electronically equivalent for optimal hole delocalization. In order to address this question, herein we carefully examine the redox/optical properties and X-ray crystal structures of both neutral and cation radicals of three triptycene derivatives containing one, two and three electron-rich 1,2-dimethoxybenzenoid (veratrole) rings, i.e. DMT, TMT, and HMT, respectively, together with a monochromophoric model compound M (Figure 2). O

O

O

O

O

HMT

O

O

O

O

TMT

O

O

O

DMT

O

O

M

Figure 2. Structures and naming scheme of the triptycenes and monochromophoric model compound (M) utilized in this study. Note that the three benzenoid rings in various triptycene derivatives are rigidly held at an angle of ~120o. The extent of hole delocalization in polychromophoric cation radicals can be inferred qualitatively from the appearance of inter-valence transitions in the electronic spectra of their cation radicals, and by the lowering of their oxidation potentials in comparison with model compounds.3,9 The quantification of the hole delocalization among multiple chromophores in such cation radicals necessitates a determination of oxidation-induced bond length changes, by analysis of the X-ray crystal structures of the corresponding neutral molecules and their cation radicals.10-13 The reliability of crystallographic electronic structures for discerning the extent of hole distribution, however, suffers from uncertainties associated with crystallographic precision of a given structure, packing forces, presence of solvent molecules, and the presence/position of the counter ions in the X-ray lattice.14-17

While the extent of hole delocalization in

polychromophoric cation radicals can be obtained from the electronic structure calculations (e.g.,


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DFT), this also has limitations due to the self-interaction error that often causes artificial hole delocalization.18 However, this can be overcome by carefully adjusting the exact Hartree-Fock (HF) exchange in a trained DFT functional.19-21 Indeed, we have recently shown that a B1LYP functional with 40% of HF exchange (i.e., B1LYP-40) reproduces experimental redox and optical properties of a variety of π-conjugated22,23 and π-stacked24,25 systems. In this study, we present a dual complementary approach in which the extent of hole delocalization in polychromophoric cation radicals is assessed (and reproduced) via both X-ray crystallography and DFT calculations for a set of triptycene-based derivatives (HMT, DMT, TMT). We will show that a simultaneous utilization of X-ray crystallography and DFT calculations affords deeper insight into the electronic structures of polychromophoric cation radicals with complex electron-transfer induced bond length changes. As such, the combination of X-ray crystallography and DFT calculations can probe in detail the hole delocalization in polychromophoric cation radicals and, in turn, allow informed design of the next-generation, long-range charge-transport materials based on triptycene and other scaffolds containing multiple aromatic hydrocarbons as chromophores.

EXPERIMENTAL AND COMPUTATIONAL DETAILS Synthesis, Electrochemistry and Electronic Spectroscopy of Cation Radicals. Synthetic details for the preparation of triptycene derivatives DMT and TMT, previously synthesized HMT,6,8 and the model compound M (Figure 1) together with characterization via 1H/13C NMR spectroscopy and X-ray crystallography are compiled in the Section S1 in Supporting Information. The reversible cyclic voltammograms (CVs) of the triptycenes showed a decrease in oxidation potentials with increasing number of electron-rich veratrole rings in the parent


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triptycene core (Figure S6A in the Supporting Information). The triptycene-based cation radicals were generated via quantitative26 redox titration using robust chemical oxidants27 THEO+• and NAP+• in CH2Cl2 (Figures S8-S9 in the Supporting Information). Electronic absorption spectra of DMT+•, TMT+•, and HMT+• revealed characteristic intervalence transition signifying the extensive hole delocalization (Figure S6B in the Supporting Information).6,8 Isolation of the triptycene cation radicals was carried out by chemical oxidation using [NO+ SbCl6-]. A solution of the triptycene derivatives and [NO+SbCl6-] in CH2Cl2 was stirred under an argon atmosphere at 0 °C. The resulting solution was layered with the solvent and stored in a refrigerator at -10 °C for two days, yielding single crystals suitable for X-ray crystallography. Computational and Experimental Methodologies to Assess Hole Delocalization. Accurate description of the electronic structure of the cation radicals of polycyclic aromatic hydrocarbons (PAH) is challenging for density functional theory (DFT) due to the self-interaction error (SIE).28 An important consequence of the SIE is the artificial stabilization of the delocalized states in open-shell oxidized/reduced systems, which can lead to incorrect description of redox and optical properties.29-31 The SIE can be partially reduced by addition of a fixed amount of the exact Hartree−Fock (HF) exchange term into the exchange functional, as implemented in hybrid density functionals,19,32 or by a distance-dependent HF exchange term, as implemented in longrange corrected hybrid functionals.33-35 As such, the extent of hole delocalization/stabilization is very sensitive to the amount of the Hartree-Fock exchange, which in many popular density functionals can be either insufficient or excessive.20,36 In recent studies, the amount of HartreeFock exchange term in a standard density functional was fine-tuned to reproduce experimental description of the electronic structures of several selected mixed-valence compounds19-21 and poly-p-phenylene wires.23


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In this context, we introduced a customized version of B1LYP37 functional with 40% of HF exchange term (i.e., B1LYP-40)23 where amount of HF was empirically adjusted to accurately reproduce oxidation potentials and the cation radical excitation energies of poly-p-phenylenes. Remarkably, it was shown in multiple studies that B1LYP-40/6-31G(d) performs exceptionally well in reproducing the experimental redox/optoelectronic properties of a variety of poly-pphenylene-based wires,22,38,39 other PAHs40,41 and π-stacked assemblies23-25 that were not included in the original training set. In a recent study,42 we also showed on several selected PAHs that time-dependent DFT paired with B1LYP-40 functional provides excitation energies and orbitals involved in the excitation that are consistent with those obtained using a highly reliable43 EOMIP-CCSD method. Therefore, in this manuscript we performed electronic structure calculations of triptycene derivatives and their model compound at neutral and cation radical states using B1LYP-40/6-31G(d) level of theory; to account for the solvent effects we utilized polarizable continuum model (PCM)44 with dichloromethane parameters. It has been shown on multiple examples that X-ray crystallography can be effectively used to establish the oxidation states of an aromatic hydrocarbon, that is, dication (+2 e-), cation radical (+1 e-) or dimer cation radical (i.e., each unit bears 0.5 e-) via analysis of the oxidation-induced bond length changes.10-13 For example, Car-O bond is known to undergo a significant contraction (~5 pm) upon oxidation and therefore has often served as an indicator of the amount of the charge on the respective aromatic unit. Building upon these works, herein we assess the extent of hole delocalization in DMT+•, TMT+•, and HMT+• with the aid of detailed cumulative analysis10 of the multiple oxidation-induced bond length changes in each veratrole using precise X-ray crystal structures of the triptycene derivatives and the model compound M at neutral and cation radical states. To that end, we will correlate the oxidation-induced bond length changes in each


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veratrole unit of the triptycene derivative against the corresponding bond length changes in the model compound M/M+• using linear regression analysis. It is expected that the slope of the linear trend will reflect the fraction of the charge localized at each veratrole of the triptycene derivative with respect to that localized in the aromatic moiety of the model M+•. The hole distribution so obtained from X-ray crystallography was then compared with the distribution obtained from the electronic structure calculations. Considering computational approaches to quantify the extent of hole delocalization, in addition to oxidation-induced bond length changes, DFT calculations also provide a direct access to the charge distribution, e.g. via natural population analysis (NPA).45 For example, NPA of electron density in M+• shows that 0.84 e- is localized at its aromatic moiety, while the remaining 0.16 eis located at the alkyl framework. Oxidation of a π-conjugated system is often accompanied by the structural reorganization in the form of the bond length changes and is often attributed to the polaron formation.46,47 A visual inspection of the HOMO of M shows that the oxidation-induced bond length changes follow the nodal structure of the orbital: C-C bonds at the regions of the bonding lobes undergo elongation (e.g., bonds a, d and b), while the bonds at the regions of the anti-bonding lobes undergo bond contraction (e.g., bonds f, c and e). Importantly, upon M→M+• transformation the bond length changes obtained from calculations follow a linear correlation (the slope of 0.97) with the bond length changes obtained from X-ray crystallography (Figure 3).


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Figure 3. Left: Isovalue plots of HOMO (0.03 au) of M and spin densities (0.003 au) of M+•. Value of the NPA charge (0.84 e-) at the benzenoid moiety is shown. Right: Correlation plot of the oxidation-induced bond length changes in M→M+• transformation obtained by X-ray crystallography and DFT calculations. RESULTS AND DISCUSSION Hexamethoxytriptycene cation radical (HMT+•). The packing diagram of [HMT+•SbCl6-] crystal structure reveals that all three veratrole rings of each HMT+• molecule are intimately involved in the formation of dimeric π-stacked contacts with the veratrole rings of neighboring HMT+• molecules (with a center to center distance of 3.3-3.4 Å) (Figure 4A), suggesting that effective hole delocalization in the crystal lattice can occur both intra- and inter-molecularly. The oxidation-induced bond length changes from the analysis of X-ray structures of neutral HMT and [HMT+•SbCl6-] showed a similar structural reorganization in each veratrole ring, with bond length changes that are smaller by a factor of roughly three than those observed in the oxidation of M (Figure 4B). A correlation plot between bond length changes (averaged over three units) in HMT+• against those in M+• showed a scattered but linear correlation, with a slope of nearly 0.33 (Figure 4B). More importantly, a nearly identical correlation plot is obtained from the bond length changes determined by DFT calculations, with a similar scatter (Figure 4B). This


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clearly suggests that the hole delocalization in HMT+•, determined by X-ray crystallography and almost evenly distributed among the three veratrole rings, can be accurately reproduced by DFT calculations (Figure 4B and 4C).

Figure 4. (A) Packing of [HMT+•SbCl6-] crystal structure illustrating layers of HMT+ and SbCl6– counteranions. (B) Correlation plots between oxidation-induced bond length changes in HMT/HMT+• and M/M+• obtained by X-ray crystallography (left, red) and DFT (right, blue). Error bars correspond to standard deviation of the bond length changes (σ(M) = 0.56 pm, σ(HMT) = 1.21 pm). Note that the bond length changes are based on the averages of equivalent bonds. (C) Isovalue (0.003 au) spin-density plots of HMT+• and fraction of the NPA charge at each benzenoid moiety. Tetramethoxytriptycene cation radical (TMT+•). The [TMT+•SbCl6-] crystal structure (Figure 5A) contains arrays of TMT+• molecules, in which both veratrole rings form dimeric π-stacked contacts with the corresponding rings of the neighboring TMT+• molecules. The unsubstituted phenylene ring is not involved in any dimeric contacts in the crystal lattice (Figure 5A). Analysis of the TMT and [TMT+•SbCl6-] crystal structures showed that oxidation produces bond


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length changes in the veratrole units (a and b) that are roughly half of those observed in the oxidation of M (Figure 5B). Indeed, correlation plots between bond length changes in both a and b units of TMT+• against those in M+• show a linear dependence with slopes of ~0.5 (Figure 5B), suggesting that the hole is evenly delocalized amongst two veratrole rings.

Figure 5. (A) Packing of [TMT+•SbCl6-] crystal structures illustrating layers of TMT+• and SbCl6– counteranions. (B) Correlation plots between oxidation-induced bond length changes in TMT/TMT+• and M/M+• obtained by X-ray crystallography and DFT. Error bars correspond to standard deviation of the bond length changes (σ(M) = 0.56 pm, σ(TMT) = 0.88 pm). Note that the bond length changes are based on the averages of equivalent bonds. (C) Isovalue (0.003 au) spin-density plots of TMT+• with indicated fractions of the NPA charge on each benzenoid moiety.


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Surprisingly, a similar analysis of the bond length changes in TMT+• obtained from DFT calculations predicts an uneven hole distribution (~0.7/0.3 for units a/b, see Figure 5B and 5C). Such a disparity between the hole delocalization obtained by crystallography and DFT calculations usually arises when the mechanism of hole delocalization lies at the borderline between two regimes (static delocalization/dynamic hopping or class III/II in Robin-Day classification), where the hole distribution is sensitive to minor changes in electronic coupling and/or structural reorganization.9,48,49 Indeed, the charge distribution in TMT+• was found to be very sensitive to the amount of Hartree Fock (HF) exchange: decreasing the HF contribution from 40% to 35% results in even hole delocalization over both veratrole rings (see Figure S12 in the Supporting Information). Dimethoxytriptycene cation radical (DMT+•). In the crystal structure [TMT+•SbCl6-], the hole is delocalized over two veratrole rings, while the unsubstituted phenylene is largely uninvolved. Therefore, one may assume that in case of DMT+•, the hole will be largely localized onto a single veratrole, due to the large energy difference between the electron-rich veratrole and unsubstituted phenylene rings. Surprisingly, repeated attempts to produce the crystals of [DMT+•SbCl6-] with isolated molecules of DMT+• met with failure. Instead, [DMT+• SbCl6-] cocrystallizes with neutral DMT producing a dimer cation radical (i.e. [DMT+• SbCl6-] + DMT → [2DMT+• SbCl6-]). Examination of the packing diagram (Figure 6A) showed that a pair of veratrole rings from adjacent DMT molecules forms sandwich-like contacts with an interplanar separation distance of 3.4 Å, while the unsubstituted phenylenes are only involved in CH-π contacts.


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Figure 6. (A) Packing of [2DMT+•SbCl6-] crystal structures with SbCl6– counteranions between the layers. (B) Correlation plots between oxidation-induced bond length changes in DMT/DMT+1/2• and M/M+• obtained by X-ray crystallography (left, red) and DFT (right, blue). Error bars correspond to standard deviation of the bond length changes (σ(M) = 0.56 pm, σ(HMT) = 0.40 pm). Note that the bond length changes are based on the averages of equivalent bonds. (C) Isovalue (0.003 au) spin density plot of DMT+• and the fraction of the NPA charge at benzenoid moiety. Comparison of the oxidation-induced bond length changes of the veratrole unit in [2DMT+• SbCl6-] crystal structure with those found in the M→M+• transformation showed that each veratrole ring bears ~0.5 charge, as indicated by ~0.5 slope in the linear fit in Figure 6B. Noteworthy, DFT calculations of a single DMT+• in solution showed that the structural reorganization of the veratrole unit is similar to that of M+•, as indicated by a nearly 1:1 correlation in the linear fit (Figure 6B and 6C). This suggests that in solution the hole is largely localized on a single veratrole in DMT+•. In attempt to reproduce the dimer cation radical formation, we performed optimization of the dimer cation radical (DMT)2+•, which however converged to a structure where hole is mostly localized on a single unit (Figure S16 in the


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Supporting Information), suggesting that the formation of the dimer cation radicals in the [2DMT+• SbCl6-] crystal structure is induced by the favorable packing arrangement. Cumulative analysis of the bond length changes: DFT vs X-ray Crystallography. The examples shown above clearly demonstrate that both DFT and X-ray crystallography can serve as tools to quantify amount of the charge residing at a single chromophore of the polychromophoric assembly. The validity of estimating the amount of charge on a given unit in the solid state of various triptycene cation radicals (from Figure 4-6) is further demonstrated by a collective plot, where the magnitudes of these bond contraction/elongations in aryl groups depend linearly on the amount of the cationic charge (approximated as slopes from linear fits in in Figures 4B-6B) at the veratrole unit, i.e., the larger the charge, the larger the magnitude of the bond length change (Figure 7A).

Figure 7. (A) Correlation between charge on the veratrole unit in M, DMT, TMT (TMTa and TMTb) and HMT obtained from X-ray analysis (charge is approximated as a slope from linear regression analysis in Figures 4B-6B) and bond length changes (i.e., ΔR = RCR-RN, where R is the length of bonds a, d and f). (B) Correlation between NPA charge on the veratrole unit in M,


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DMT, TMT (TMTa and TMTb) and HMT and bond length changes (i.e., ΔR = RCR-RN, where R is length of bonds a, b, c, d, e and f) calculated at B1LYP40/6-31G(d)+PCM(CH2Cl2). On the other hand, DFT calculations also provide NPA charges on each veratrole ring in M+•, DMT+•, TMT+• and HMT+•. A plot of the bond length change (i.e., ΔR = RCR-RN) for individual bonds (a–f) against NPA charge for these structures in Figure 4-6, showed a clear linear correlation for each bond and an uncanny similarity with the experimental plot (compare Figure 7A and 7B). It is noteworthy that the magnitude of these bond length changes varies for different bonds. For example, aromatic bonds b and c and single bond e are mainly insensitive to the presence of charge, while CAr-O bond f and aromatic bonds d and a display a high sensitivity to charge. This observation is consistent with the fact that the electron density of HOMO at the bonds a and d is higher than that at bonds b, c and e (see Figure 3). Trends between structural reorganization and charge distribution obtained by the electronic structure calculations (where solvents effects are accounted for implicitly via polarizable continuum model) correspond to the idealized case, as opposed to X-ray crystallography, where the molecular structure of the molecule is impacted by packing, the presence of the explicit solvent molecules and counter ions, and is measured with finite precision. Nevertheless, despite the presence of the scatter in the plots between bond length changes taken from the X-ray structures and charges on the veratrole rings, obtained from X-ray linear fit analysis, there is a clear correspondence to the plots obtained from DFT calculations (Figure 7).

CONCLUSIONS Given that the density functional is well calibrated, DFT calculations provide quantitative information about the extent of charge delocalization in polychromophoric assemblies, as


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opposed to the qualitative information usually inferred from the experimental data such as electrochemistry and electronic spectroscopy. In this manuscript, we have shown that the amount of the cationic charge on a given chromophore of a polychromophoric assembly can be obtained from X-ray crystallography via a cumulative analysis of the oxidation-induced bond length changes, as has been clearly demonstrated on the example of triptycene derivatives DMT+•, TMT+• and HMT+• and model compound M+•. Importantly, precise experimental data on the oxidation-induced bond length change in polychromophoric assemblies can serve as a valuable reference data in validation/parameterization of the novel density functional theory methods. Finally, such a powerful combination of calculations and experiment to assess the charge delocalization in polychromophoric assemblies is invaluable for the rational design and synthesis of next-generation molecular scaffolds for long-range charge-transport materials.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: Full experimental details for synthesis DMT and TMT, generation of cation radicals DMT+• and TMT+•, X-ray crystallography data and computational details. (PDF) X-ray structural data for DMT, TMT, DMT+•SbCl6- and TMT+•SbCl6- (CIF) Optimized equilibrium structures of triptycene derivatives (TXT)

AUTHOR INFORMATION


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Corresponding Author * E-mail: [email protected] * E-mail: [email protected] †Deceased February 16, 2018 ACKNOWLEDGMENT We thank the NSF (CHE-1508677) and NIH (R01-HL112639-04) for financial support, Prof. Scott Reid for helpful discussions and Dr. Khushabu Thakur for preliminary experiments. The calculations were performed on the high-performance computing cluster Père at Marquette University and XSEDE. REFERENCES (1) Wasielewski, M. R. Self-assembly Strategies for Integrating Light Harvesting and Charge Separation in Artificial Photosynthetic Systems. Acc. Chem. Res. 2009, 42, 1910-1921. (2) Kory, M. J.; Wörle, M.; Weber, T.; Payamyar, P.; van de Poll, S. W.; Dshemuchadse, J.; Trapp, N.; and Schlüter, A. D. Gram-scale Synthesis of Two-dimensional Polymer Crystals and Their Structure Analysis by X-ray Diffraction. Nat. Chem. 2014, 6, 779-784. (3) Navale, T. S.; Thakur, K.; Vyas, V. S.; Wadumethrige, S. H.; Shukla, R.; Lindeman, S. V.; and Rathore, R. Charge Delocalization in Self-assembled Mixed-valence Aromatic Cation Radicals. Langmuir 2012, 28, 71-83. (4) Thomas, S. W.; Joly, G. D.; and Swager, T. M. Chemical Sensors Based on Amplifying Fluorescent Conjugated Polymers. Chem. Rev. 2007, 107, 1339-1386.


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(5) Swager, T. M. Iptycenes in the Design of High Performance Polymers. Acc. Chem. Res. 2008, 41, 1181-1189. (6) Chebny, V. J.; Navale, T. S.; Shukla, R.; Lindeman, S. V.; and Rathore, R. X-ray Structural Characterization of Charge Delocalization Onto the Three Equivalent Benzenoid Rings in Hexamethoxytriptycene Cation Radical. Org. Lett. 2009, 11, 2253-2256. (7) Margulies, E. A.; Shoer, L. E.; Eaton, S. W.; and Wasielewski, M. R. Excimer Formation in Cofacial and Slip-stacked Perylene-3,4:9,10-bis(dicarboximide) Dimers on a Redox-inactive Triptycene Scaffold. Phys. Chem. Chem. Phys. 2014, 16, 23735-23742. (8) Talipov, M. R.; Navale, T. S.; and Rathore, R. The HOMO Nodal Arrangement in Polychromophoric Molecules and Assemblies Controls the Interchromophoric Electronic Coupling. Angew. Chem. Int. Ed. Engl. 2015, 54, 14468-14472. (9) Heckmann, A. and Lambert, C. Organic Mixed-valence Compounds: A Playground for Electrons and Holes. Angew. Chem. Int. Ed. Engl. 2012, 51, 326-392. (10) Ivanov, M.; Wang, D.; Navale, T.; Lindeman, S.; and Rathore, R. From Intramolecular (Circular) in An Isolated Molecule to Intermolecular Hole Delocalization in a Two-Dimensional Solid-State Assembly: The Case of Pillarene. Angew. Chem. Int. Ed. Engl. 2018, 57, 2144-2149. (11) Navale, T. S.; Talipov, M. R.; Shukla, R.; and Rathore, R. Interplay Between Entropy and Enthalpy in (Intramolecular) Cyclophane-Like Folding Versus (Intermolecular) Dimerization of Diarylalkane Cation Radicals J. Phys. Chem. C. 2016, 120, 19558-19565.


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Probing Charge Delocalization in Solid State ... - ACS Publications

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