Mixed-Valence Cations of Di(carbazol-9-yl ... - ACS Publications

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Mixed-Valence Cations of Di(carbazol-9-yl) Biphenyl, Tetrahydropyrene, and Pyrene Derivatives Bilal R. Kaafarani,*,† Chad Risko,‡ Tarek H. El-Assaad,† Ala’a O. El-Ballouli,† Seth R. Marder,§ and Stephen Barlow*,§ †

Department of Chemistry, American University of Beirut, Beirut 1107-2020, Lebanon Department of Chemistry and Center for Applied Energy Research, University of Kentucky, Lexington, Kentucky 40506-0055, United States § School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States ‡

S Supporting Information *

ABSTRACT: Although bis(diarylamino) mixed-valence radical cations have been quite extensively studied, their bis(carbazolyl) analogues have not, even though the holetransporting properties of species such as of 4,4′-bis(9Hcarbazol-9-yl)-1,1′-biphenyl, CBP, are widely exploited in organic light-emitting diodes. This work reports the generation by chemical oxidation of the radical cations of 4,4′-bis(3,6-ditert-butyl-9H-carbazol-9-yl)-1,1′-biphenyl (a model for the unstable radical cation of CBP), 2,7-bis(3,6-di-tert-butyl-9Hcarbazol-9-yl)-4,5,9,10-tetrahydropyrene, and 2,7-bis(3,6-ditert-butyl-9H-carbazol-9-yl)pyrene. The visible and near-IR spectra of these cations have been compared to those of the corresponding dication spectra, to the spectrum of the 3,6-ditert-butyl-9-(4-(tert-butyl)phenyl)-9H-carbazole radical cation, and to the results of time-dependent density-functional calculations. The biphenyl- and pyrene-bridged species are found to be localized (class-II) mixed-valence compounds, whereas stronger coupling between the redox centers in the tetrahydropyrenebridged radical cation results in a delocalized (class-III) species. For all three radical cations, the electronic couplings are lower than those obtained for delocalized 4,4′-bis(diarylamino)-1,1′-biphenyl radical cations.

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INTRODUCTION

indicates that the oxidation primarily involves the benzidine portion of the molecule. The carbazol-9-yl group can be regarded as a bis(diphenylamino) group planarized by a C−C bond between the 2-positions of the two rings, and bis(carbazol-9-yl) derivatives are also widely investigated as organic semiconductors; for example, bis(carbazol-9-yl) species, notably 4,4′-bis(9H-carbazol-9-yl)-1,1′-biphenyl (CBP, 1a, Chart 1) and 1,3-bis(9H-carbazol-9-yl)benzene (mCP), have been extensively examined as charge-transporting host materials for phosphorescent emitters,8−12 and more recently for emitters exhibiting thermally activated delayed fluorescence,13 in OLEDs. Species such as CBP•+ might be anticipated to differ significantly from TPD•+ due to steric interactions that hinder planarization of the carbazole units with the adjacent rings of the biphenyl bridge. However, we are unaware of any studies

The radical cations of bis(diarylamino) derivatives of various bridging groups are among the more widely explored classes of organic mixed-valence (MV) compound,1,2 probably because considerable synthetic flexibility is possible in these systems and because the cations of bis(triarylamino)biphenyl (N,N,N′,N′tetraarylbenzidine) derivatives, such as N4,N4′-diphenyl- N4,N4′di-m-tolyl-[1,1′-biphenyl]-4,4′-diamine (TPD, Ia, Chart 1) and N4,N4′-di(naphthalen-1-yl)-N4,N4′-diphenyl-[1,1′-biphenyl]4,4′-diamine (α-NPD), are charge-carrying species in prototypical organic hole-transport materials for organic lightemitting diodes (OLEDs). Typical bis(diarylamino)biphenyl radical cations have been assigned to Robin and Day’s class III (symmetrical valence-delocalized MV species)3 based on: characteristics of their NIR absorption bands, an X-ray crystal structure, and vibrational spectroscopy.4−7 DFT and crystallographic data indicate that the oxidation is accompanied by nearplanarization of the biphenyl bridge and by a decrease of the angles between the NC3 planes and the adjoining rings of the biphenyl bridge. Consistent with these geometric changes, DFT © 2016 American Chemical Society

Received: November 11, 2015 Revised: December 24, 2015 Published: February 5, 2016 3156

DOI: 10.1021/acs.jpcc.5b11061 J. Phys. Chem. C 2016, 120, 3156−3166

Article

The Journal of Physical Chemistry C

Chart 1. Structures of Bis(carbazolyl) Derivatives Discussed in This Work (1−3), of Related Bis(diarylamino) Derivatives (I− III), and of Monomeric Model Compounds (4 and IV)

Chart 2. Pairs of Comparable Biphenyl- and Pyrene-Bridged Species That Have Been Converted to Mixed-Valence Species by One-Electron Oxidation (V and VI) or Reduction (VII and VIII)

bis(diarylamino) groups with carbazol-9-yl on the electronic coupling between redox sites, the spectra of the radical cations formed by this family of compounds also allow comparison of the efficacy of biphenyl, tetrahydropyrene, and pyrene bridges in mediating electronic coupling. A few previous reports have involved pyrene-bridged MV species (Chart 2), and the electronic couplings inferred for these species are similar to, or somewhat smaller than, those in their biphenyl analogues,39−43 but tetrahydropyrene has not previously been reported as a bridging moiety in a MV compound. This contribution reports the vis−NIR spectra of 1b•+-3b•+; the spectra are compared to one another, to those of the corresponding dications, to that of a monomeric model, 4b•+, to those of previously reported bis(diarylamino)biphenyl radical cations (particularly Ib-c•+4,7,44), and to TD-DFT calculations for both carbazole and bis(diarylamino) species (including the hypothetical species II•+ and III•+). DFT orbital calculations are used to gain insight into the origins of the experimentally observed trends.

involving characterization of such cations, or indeed any reports of the MV characteristics of bis(carbazol-9-yl) derivatives.14−18 In part, the absence of reports of carbazole MV compounds can be attributed to the reactivity through the carbazole 3,6positions of the radical ions of both simple monomeric carbazoles16−27 and bis(carbazol-9-yl) species, such as CBP (1a) and related compounds 2a and 3a (Chart 1),7,28−32 as reflected, for example, in the irreversibility of their electrochemical oxidations. Although simple monomeric triarylamines without 4,4′,4″-substituents, such as Ph3N, also undergo irreversible oxidation,33 the radical cations of various bis(diarylamino) species without para-substituents can be persistent, presumably due to delocalization of spin density away from the terminal aryl positions, by delocalization either between the two amines (as in Ia•+ and other class-III bis(diarylamino)biphenyl cations4,5,7,34) or into the bridge (as in the class-II 2,5-bis((E)-4-(diphenylamino)styryl)terephthalonitrile cation35). However, the persistence of both triarylamine and carbazole radical cations can be significantly increased by blocking the reactive positions; for example, the radical cations of 1,3,6,8-tetra-tert-butyl-9H-carbazole36 and 3,6dibromo-9-(4-bromophenyl)-9H-carbazole (4a, Chart 1)37 have been characterized by ESR and vis−NIR spectroscopy, respectively. In the recently reported compounds 1b−3b (Chart 1)32,38 the reactive carbazole 3,6-positions are blocked by tert-butyl groups, resulting in reversible electrochemistry.32 As well as offering the possibility of probing the extent of delocalization in CBP•+-like species and quantifying the effect of replacing

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EXPERIMENTAL DETAILS General. Compounds 1b−3b were synthesized as previously described.32 Oxidants [N(4-C6H4Br)]3]•+[SbCl6]− and SbCl5 (1.0 M in CH2Cl2) were obtained from Sigma-Aldrich; oxidations with the former were carried out by addition of the oxidant to a solution containing excess carbazole derivative, while the latter was diluted to ca. 0.02 M and added dropwise to solutions of known concentrations of carbazole derivatives. All oxidation reactions were carried out under nitrogen using 3157


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Table 1. Redox Potentials (vs FeCp2+/0 in CH2Cl2/0.1 M Bu4NPF6) and Mono- and Dication Absorption Maxima (in CH2Cl2a) for Bis(carbazolyl) Derivatives and Related Species ν̅max/103 cm−1 (εmax/103 M−1 cm−1) +/0

compd

E1/2 /V

1b 2b 3b 4b Ib6,7 IV66

+0.71 +0.60 +0.72 +0.70 +0.25 +0.33

E1/2

2+/+

/V

ΔE1/2/V

+0.75 +0.74 +0.80

0.04 0.14 0.08

+0.55

0.30

monocation 12.3 21.3 12.4 12.4 20.7 14.8

(16), 5.0 (8.3) (25), 4.5 (33) (16), 4.6 (7.4) (13), ca. 7.0 (0.3) (30.1), 6.8 (32.6) (ca. 33b)

dication 12.0 (36) 9.3 (56) 12.0 (35) 12.8 (64.0)

a

Data from 1b−4b obtained using SbCl5; data for Ib and IV obtained in CH2Cl2/0.1 M nBu4NPF6. bAbsorptivity not reported in ref 66 but assumed to be similar to that reported for other triarylamine radical cations in the same study.

and in particular DFT, given the known issues related to the lack of electron correlation in Hartree−Fock and the multielectron self-interaction error in DFT.50−54 The choice of the B3LYP functional in this work was motivated, in part, by the possibility of making direct comparisons to our previous work on the MV characteristics of bis(diarylamino) species.34,35,55−61 Low-lying excited states for both the neutral and radical-cation electronic states were evaluated via time-dependent DFT (TD-DFT) using the same level of theory. All calculations were carried out with the Gaussian09 (Revision A.02) software suite.62

dry solvents. Vis−NIR spectra were recorded using an Agilent CARY 5000 spectrometer. Electrochemical data for 1b−3b were taken from ref 32; the potentials for 4b and [N(4C6H4Br)]3]•+[SbCl6]− were determined in the same way, i.e., by cyclic voltammetry (50 mV s−1) under nitrogen in deoxygenated 0.1 M Bu4NPF6 in dry CH2Cl2, using a CH Instruments CHI620D potentiostat, a glassy carbon working electrode, a platinum wire counter electrode, a AgCl-coated Ag wire pseudo-reference electrode, and ferrocene as an internal reference. 3,6-Di-tert-butyl-9-(4-(tert-butyl)phenyl)-9H-carbazole 4. A 10 mL microwave tube was charged with 1-bromo-4-tertbutylbenzene (300 mg, 1.41 mmol), 3,6-di-tert-butyl-9Hcarbazole45 (433 mg, 1.55 mmol), and a magnetic stir bar. The tube was sealed and was deoxygenated with nitrogen for 10 min. In a glovebox under nitrogen atmosphere, tris(dibenzylideneacetone)dipalladium(0) (52 mg, 0.056 mmol), tri-tert-butylphosphine (140 mg, 0.48 mmol), sodium tertbutoxide (300 mg, 3.12 mmol), and dry toluene (5 mL) were added. The tube was sealed under nitrogen, and the reaction was conducted in a CEM microwave reactor under power control conditions (power, 180 W; max temp, 175 °C; run time, 60 min; pressure, 120 psi). The reaction mixture was then poured into water (150 mL) and extracted with chloroform (4 × 50 mL); the extracts were washed with water and brine, dried over anhydrous MgSO4, and run through a short bed of silica. The solvent was removed under reduced pressure, and the resulting solid was recrystallized from toluene/ethanol to yield 4b as beige crystals (379 mg, 65%). 1H NMR (500 MHz, CDCl3): δ 8.06 (d, J = 2.0 Hz, 2H), 7.48 (d, J = 8.5 Hz, 2H), 7.38 (d, J = 8.5 Hz, 2H), 7.35 (dd, J = 8.5, 2.0 Hz, 2H), 7.27 (d, J = 8.5 Hz, 2H), 1.39 (s, 18H), 1.34 (s, 9H). 13C{1H} NMR (125 MHz, CDCl3): δ 149.82, 142.52, 139.32, 135.36, 126.55, 126.15, 123.42, 123.15, 116.12, 109.27, 34.72, 34.69, 32.02, 31.43. HRMS-EI (m/z): [M]+ calcd for C30H37N, 411.2926. Found: 411.2935. Anal. Cald. for C30H37N: C, 87.54; H, 9.06; N, 3.40. Found: C, 87.64; H, 9.15; N, 3.50. Quantum-Chemical Studies. The ground states of neutral 1b−4b, Ib, and II−IV and of their radical cations were examined at the density functional theory (DFT) level using the B3LYP hybrid functional46−49 in conjunction with the 631G(d,p) basis set. tert-Butyl groups were truncated to methyl groups to reduce the computational cost; normal-mode analyses were undertaken to ensure that optimized structures were minima on the potential energy surface. The choice of functional has important consequences for how theoretical results should be interpreted. Indeed, there has been considerable recent effort to determine the best way to evaluate MV characteristics through electronic structure calculations,

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RESULTS AND DISCUSSION Electrochemistry. As previously reported, 1b−3b, in contrast to analogues 1a−3a, which lack 3,6-substitution of the carbazolyl moieties, each undergo two successive reversible oxidations;32 the redox potentials are summarized in Table 1, along with that for the single reversible oxidation of the new compound 4b (synthesized as described in the Experimental Details). In each case there is a measurable separation between first and second redox processes, ΔE1/2, indicating that the monocations have reasonable stability with respect to disproportionation (values of Kcomp = = [M+]2/[M2+][M] = exp(FΔE1/2/RT) vary from ca. 101 to 104). Although values of ΔE1/2 are an unreliable measure of electronic coupling in MV species,63 it is worth noting that in the present series 2b exhibits a much larger value of ΔE1/2 than 1b or 3b, and also exhibits a qualitatively different extent of delocalization in its radical cation (vide inf ra).64 The first oxidation potentials are in each case close to the potential we measure under the same conditions for the [N(4C6H4Br)]3]+/0 couple (+0.71 V). Thus, tris(4-bromophenyl)ammoniumyl hexachloroantimonate, which we have previously used for generating the mono- and dications of bis(diarylamino) species,35,55,56,59−61 is sufficiently oxidizing for generating the bis(carbazolyl) radical cations in the presence of excess neutral bis(carbazolyl) compound, but insufficiently oxidizing to generate the corresponding dications. Accordingly, a stronger oxidant, antimony pentachloride, was used for generating the dications.65 Experimental Mono- and Dication Spectra. Each of the carbazole species was oxidized in a stepwise fashion using successive portions of SbCl5 in CH2Cl2.67 Figure 1 compares the experimental spectra of 1b•+−4b•+ and 1b2+−3b2+, as well as showing theoretical monocation absorption spectra derived from vertical transition energies and oscillator strengths from TD-DFT calculations convoluted with a Gaussian broadening (fwhm = 0.3 eV); these TD-DFT spectra are discussed in more detail in the following section. Absorption maxima assigned to 3158


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Figure 1. Experimental vis−NIR spectra of the monocations (blue solid lines) and dications (red broken lines) of 1b−3b, and of the monocation of 4b generated using SbCl5 in CH2Cl2 compared to TD-DFT-calculated spectra of the monocations (transition energies and oscillator strengths indicated by orange bars; spectra, in blue, obtained by applying a Gaussian broadening). Note that the vertical scale varies between the spectra. Note also that the TD-DFT spectra for 1b•+−3b•+ are based on delocalized radical-ion structures. The strong very narrow features in the NIR region of the experimental spectra are due to vibrational overtones of the solvent.

compound 4b (Figure 1, see below for more discussion of the spectrum of 4b•+) and that of the previously reported related cation 4a•+ (maximum at 820 nm, i.e., ca. 12 200 cm−1, in MeCN),37 suggesting that this is a feature characteristic of localized carbazole radical cations. The low-energy feature

mono- and dications are also given in Table 1. Figure S1 plots the evolution of the spectra of one example, 1b, on oxidation. Two principal features are assigned to 1b•+, the higher energy of which (at 811 nm, i.e., ca. 12 300 cm−1) is very similar to the main feature obtained on oxidation of the model 3159


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Table 2. IVCT Characteristics for Bis(carbazolyl) and Bis(diarylamino) Mixed-Valence Species (DFT and TD-DFT Data in Italics)a compd 1b•+ 2b•+ 3b•+ Ib•+h Ic•+i II•+ III•+

3 −1 νm ̅ ax/10 cm 4.97 [4.84] 4.41 5.51 4.49 [4.32] 6.82 7.61 6.36 8.33 6.49

Δν1̅ /2[obsd]b/ 103 cm−1

Δν1̅ /2[Hush]c/ 103 cm−1

Δν1̅ /2[high]/Δν̅

4.70 2.33 5.05 3.22 3.17

3.39 3.19 3.22 3.97 3.83

1.1 2.0 1.2 1.4 1.4

b

Δν̅1/2[high]/Δν̅

1/2[low]

1/2[Hush]

1.4 0.98 1.7 0.92 0.98

μged/D 8.8 13.0 9.0 12.3 11.7

[14.5] 14.6 [13.6] 13.8 12.8 13.3

VNNe/103 cm−1 0.91 1.20 0.85 1.76 1.56

1.48 1.69 1.24 2.21 2.24 1.81

Vclass‑IIIf/103 cm−1 2.20 3.41 3.18

VKTg/103 cm−1

[2.42] 2.76 [2.16] 3.81

0.62 0.85 0.61 1.61

4.17 3.24

2.04 1.63

a Experimental data in CH2Cl2. Lineshape parameters taken from spectra generated using [N(4-C6H4Br)]3]•+[SbCl6]− as oxidant, since these spectra are slightly less affected by vibrational features at low energy; absorptivity used for estimation of μge taken from spectra generated using SbCl5. DFT and TD-DFT values at the B3LYP/6-31G(d,p) level; computed values given in brackets assume a class-III structure for species that experiment suggests belong to class II. bWidth at half-height and asymmetry of IVCT from experimental spectrum. For 1•+ and 3•+, where parts of the lowenergy portion of the band are obscured by vibrational artifacts or beyond the range of the spectrometer, the width at half-maximum on the lowenergy side of the band was estimated using the width on the high-energy side and the asymmetry determined from the half-widths at 0.7 of the maximum. cFrom eq 1. dEstimated as μge [D] ≈ 0.0954 (1.064 × εmax [M−1 cm−1] × Δν̅1/2[obsd] [cm−1]/ν̅max [cm−1])0.5 (i.e, assuming a Gaussian line shape for each half of the absorption band) or (in italics) from TD-DFT. eEstimated from eq 2 using a common value of R = 9.9 Å from g experimental or (in italics) TD-DFT values of ν̅max and μge. fFrom eq 3 using the experimental or (in italics) TD-DFT values of νm ̅ ax. Obtained using DFT from VKT = 0.5(EHOMO − EHOMO−1) for the neutral molecule. hExperimental data from ref 7 in CH2Cl2/0.1 M Bu4NBF4; DFT and TD-DFT data from this work. iExperimental data from ref 44 in CH2Cl2/0.1 M Bu4NPF6.

(with a maximum at ca. 2010 nm, 4970 cm−1) is assigned to intervalence charge transfer (IVCT). Further oxidation leads to disappearance of the IVCT band but further growth of the higher energy band, with the appearance of a poorly defined shoulder on the low-energy side of this band. This type of behavior, where the spectrum of the MV species has features similar to those of both fully reduced and fully oxidized species plus an IVCT band, is expected for a charge-localized, i.e., classII, MV compound, as described by Robin and Day in their classification of MV species,3 and has been observed for several weakly coupled bis(diarylamino) derivatives.35,44,68 Furthermore, the characteristics of the IVCT band of 1b•+ are consistent with assignment to class II: it is more-or-less symmetrical in shape,67,69 and its width at half-maximum, Δν̅1/2[obsd], is somewhat broader than the limit given by Δν1/2[Hush] = 4 (ln 2)λkBT ̅

(1)

Figure 2. Comparison of the IVCT bandshapes for 1b•+ (red), 2b•+ (black), and 3b•+ (blue) generated in CH2Cl2 using [N(4C6H4Br)]3]•+[SbCl6]−. Dotted lines denote portions of the spectra severely affected by vibrational features (mostly vibrational overtones characteristic of the solvent that are too strongly absorbing to be adequately removed by a baseline correction) that have been deleted to emphasize the underlying shapes of the IVCT bands.

where λ is the reorganization energy of Marcus theory and equal to ν̅max of the IVCT for a class-II species, and it is strongly solvatochromic, with a hypsochromic shift of ca. 1700 cm−1 between CH2Cl2 and 1:1 MeCN/CH2Cl2 (which can be compared to a shift of 2170 cm−1 between CH2Cl2 and MeCN for a class-II bis(diarylamino)tolane57). The experimental spectra of the pyrene-bridged 3b monoand dications are qualitatively and quantitatively similar to their 1b counterparts, as shown in Tables 1 and 2, and in Figures 1 and 2. As noted in the Introduction, previous studies also show similar behavior for biphenyl- and pyrene-bridged MV species. Most comparable to the present study, in that the interactions between the redox sites are primarily mediated by filled bridging orbitals, are the two class-III RuII/RuIII trications formed through one-electron oxidation of biphenyl-bridged V39 and pyrene-bridged VI40 (Chart 2), which show very similar IVCT bands to one another. The delocalized radical anions formed by the bis(dimesitylboryl) species VII42 and VIII43 (Chart 2) also show similar NIR spectra to one another, although that of the pyrene species is somewhat red-shifted. On the other hand, the mono- and dication spectra of tetrahyropyrene-bridged compound 2b (Figure 1) are qualitatively different. First, the IVCT band of 2b•+ is narrower and

considerably less symmetrical than that of 1b•+ and 3b•+ (emphasized in Figure 2 and Table 2); the bandshape resembles that seen for various bis(diarylamino) MV species that have been assigned to the charge-delocalized class III (in some cases with additional support from X-ray crystallography and vibrational spectroscopy),4,6,35,44,56−58,70 where the asymmetric bandshape has been attributed to coupling of the electron-transfer coordinate to symmetric vibrational modes.71−76 Second, the higher energy part of the monocation spectrum does not resemble the spectrum of 4b•+ or that of 2b2+; this type of behavior suggests that 2b•+ is more delocalized than its biphenyl- and pyrene-bridged analogues. Qualitatively similar behavior is seen for class-III bis(diarylamino) MV cations (such as Ib•+, data for which, along with that for a monomeric model, IV•+, are included in Table 1 for comparison6,66) and a few strongly coupled class-II 3160


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Finally, TD-DFT calculations for 4b•+ indicate that the main visible band for this cation arises from several overlapping transitions, the two strongest of which involve excitation from a primarily phenyl-based orbital or a carbazole-localized orbital to the SOMO, which corresponds closely to the HOMO of neutral 4b, which in turn resembles a combination of the HOMO of carbazole and that of the arene substituent (see Figure S3 for details). Presumably, therefore, the experimentally observed strong visible bands of 1b•+ and 3b•+ also have similar origins. The calculations also reproduce the very weak feature observed at much lower energy in the experimental spectrum and indicate that this arises from a transition between orbitals closely corresponding to the HOMO−1 and HOMO of 4b. Presumably similar transitions are also present for 1b•+ and 3b•+, but are dwarfed by the overlapping IVCT bands. Electronic Couplings. The electronic coupling between diabatic states in MV species, V, can be estimated from the transition dipole moment, μge, and absorption maximum, νm ̅ ax, of the IVCT band according to the Hush equation:

bis(diarylamino) species.6,35,44,56 Finally, the IVCT transition is considerably less solvatochromic than that of 1b•+ (the ca. 500 cm−1 blue shift on increasing solvent polarity from CH2Cl2 to 1:1 MeCN/CH2Cl2 can be compared to shifts of ca. 900 cm−1 between CH2Cl2 and MeCN for both benzene- and stilbenebridged class-III bis(diarylamino) MV ions57,70). Overall, these differences strongly suggest that 2b•+ is a class-III MV compound. TD-DFT Monocation Spectra. B3LYP/6-31G(d,p) DFT geometry minimizations (in which tert-butyl substituents were replaced by methyl groups for computational simplicity) afford symmetrical structures for all three bis(carbazolyl) monocations, consistent with the general tendency of semilocal and global-hybrid density functionals to give overdelocalized structures for MV species including bis(diarylamino) derivatives,35,52,54,56,72 a result of the many-electron self-interaction error.53,54,77,78 TD-DFT calculations for the monocations all afford strong transitions at similar energies to the experimentally observed IVCT bands; in each case the calculated transitions correspond to excitations to the singly occupied molecular orbital (SOMO, closely corresponding to the HOMO of the neutral species) from an orbital closely corresponding to the HOMO−1 of the neutral species. In turn, these two orbitals (discussed in more detail below) can be well-approximated as antibonding and bonding combinations of the HOMOs of two carbazole units, the former being destabilized by contributions from filled bridge-localized orbitals, consistent with the description of the low-energy transitions as IVCT bands. The rest of the calculated spectrum of 2b•+ (also shown in Figure 1) is also in agreement with experiment, further supporting assignment of the experimental structure to class III. Specifically, a strong transition is calculated at ca. 23 000 cm−1, close to the complex feature seen at 20 000−22 400 cm−1 in the experimental spectrum, with only weak transitions calculated at energies between the IVCT band and this high-energy band, i.e., with no strong transition at energies close to the strong absorption feature of 4b•+ (ca. 12 000 cm−1). The calculated weak peak at 13 800 cm−1 arises from two transitions, both of which are welldescribed as one-electron excitations from a carbazole-localized orbital to the SOMO. The strong transition at 23 000 cm−1 involves a more complicated admixture of one-electron excitations, some involving the α-spin orbitals and some of the β-spin orbitals. The experimental spectrum of the delocalized Ib•+ cation7 is also well reproduced by the TDDFT calculations (see Figure S2): as for 2b•+ no strong transition is calculated close to that of the monomeric model compound (Figure S2 also gives the calculated spectrum of IV•+) and, consistent with experiment, the calculated IVCT transition energy is considerably higher than that of 2b•+ (Table 2). The calculated spectra for 1b•+ and 3b•+ (based on the symmetric DFT geometries) are qualitatively similar to that for 2b•+. Notably, only relatively weak transitions are calculated at energies between the IVCT and strong features at 22 600− 25 000 cm−1, in contrast to the experimental observation of strong absorptions at comparable energy to that of 4b•+ (see below). In addition the experimental trend in the IVCT transition energies from 1b•+ to 2b•+ to 3b•+ is not reproduced (see Table 2). Thus, comparison of TD-DFT-calculated and experimental spectra is also consistent with our assignment of these two cations to class II.

V=

μge νmax ̅ eR

(2)

where e is the electronic charge and R the diabatic electrontransfer distance, i.e., the distance between redox centers in the absence of electronic coupling. Estimates of V according to this equation, obtained by equating R to the N−N distance (ca. 9.9 Å from crystallographic and computational data for a range of bis(carbazol-9-yl) and bis(diarylamino) derivatives of biphenyl, tetrahydropyrene, and pyrene4,6,7,32,44), are given in Table 2. The estimated values of VNN for 1b+ and 3b+ are lower than for 2b+, consistent with the more delocalized behavior inferred for the latter based on the IVCT line shape and solvatochromism. For class-III systems, such as 2b+, the coupling can also be estimated according to ν̅ V = max 2

(3)

The value obtained in this way for 2b+ is approximately twice that obtained using eq 1 and the N−N distance. Similar discrepancies are found for other delocalized MV compounds, including class-III bis(diarylamino)biphenyl MV species35,56,60 such as Ib+ and Ic+,7,44 for which estimated couplings are also included in Table 2; these discrepancies indicate that the diabatic states should in fact be regarded as somewhat delocalized into the bridging moieties, rather than localized on the nitrogen atoms of the terminal groups. For all three bis(carbazolyl) compounds the electronic couplings are significantly lower than couplings estimated in the same way for bis(diarylamino)biphenyl analogues such as Ib•+ and Ic•+. As noted above, DFT affords symmetrical delocalized structures for all three cations. However, the trend in electronic couplings, Ib•+ ≫ 2b•+ > 1b•+ ≥ 3b•+, indicated by application of either eq 2 or eq 3 to the TD-DFT transition energies and transition dipole moments obtained for these symmetric structures is completely consistent with that obtained from experimental data and eq 2. Application of eq 3 to the TD-DFT data for the analogous bis(diarylamino) species also suggests that the dependence of electronic coupling on the bridging moiety exhibits the same trend as that shown in the carbazole series; i.e., II•+ > Ib•+ > III•+. The same trend is seen by applying eq 2, although the estimated couplings for II•+ and Ib•+ are very similar owing to near-cancellation of a higher 3161


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Figure 3. Selected B3LYP/6-31G(d,p)-calculated molecular orbitals for 1b−3b (with tBu groups replaced by Me) and for end-group (modeled as 3,6,9-trimethyl-9H-carbazole) and bridge (biphenyl, 4,5,9,10-tetrahydropyrene (THP), and pyrene) fragments. Black and red lines denote HOMO and HOMO−1 respectively.

Orbital Origin of the Trends in Coupling. As noted above, trends in electronic coupling in cationic MV species can often be rationalized by examining the energy difference between the HOMO and HOMO−1 of the corresponding neutral species. In the absence of any electronic coupling, these two molecular orbitals would be expected to be degenerate symmetry-adapted combinations of the local HOMOs of the two redox-active groups; this degenerancy will be lifted by interactions with orbitals associated with the bridging groups. This picture is confirmed in the present case by DFT calculations: in each case the HOMO and HOMO−1 are indeed essentially combinations of the local HOMOs of the two carbazole (or diphenylamine) terminal groups, with some bridge contributions, the most significant being contributions that destabilize the HOMO. In the case of 1b and 2b the bridge contributions closely resemble the HOMOs of biphenyl and tetrahydropyrene (THP), respectively. The greater HOMO/ HOMO−1 splitting and greater electronic coupling seen for the latter can be attributed to a stronger mixing of bridge and endgroup orbitals owing to a smaller energetic offset arising from the higher energy HOMO of the THP moiety (Figure 3), which, in turn, can be attributed to the effects of both its greater planarity (the angle between the two aromatic rings in the bridge of 2b is calculated to be 17° and to be reduced to 16° in the cation, whereas a twist of 37° in 1b is reduced to 30° in 1b•+)80 and the inductively electron-donating effect of the CH2CH2 portions of the bridge. The HOMO of pyrene, which is both completely planar and a larger π-system than biphenyl or THP, is higher still in energy so might be expected to give even greater coupling; however, this orbital has nodes in the 2,7-positions that are occupied by the carbazolyl substituents and so it is the HOMO−1 of pyrene, which resembles the

transition energy and lower transition dipole moment for the former; this may be a result of greater delocalization of the adiabatic states into the bridge in the latter case. Finally, the separation between ground and excited states of the MV cation at the symmetric point on the ground-state cation surface is equal to 2V for both class-II and -III species, and so is also approximated by the separation between the vertical first and second ionization energies of the neutral molecule if the geometry of the neutral molecule is similar to that of the above-mentioned symmetrical cation.34 Within the framework of the Koopmans theorem,79 this difference in ionization energies will be given by the difference in the energies of the HOMO and HOMO−1 of the neutral molecule. Indeed values of VKT (also shown in Table 2), obtained from the DFT orbital energies, for the bis(carbazolyl) species show the same trends as those seen in VNN and Vclass‑III and are also smaller than for the corresponding bis(diarylamino) species. The ordering of VKT values within the bis(diarylamino) series is a little different; the pyrene compound III•+ is slightly more strongly coupled by this measure than its biphenyl analogue, Ib•+. This minor discrepancy may arise from the greater twist of the biphenyl moiety present in the neutral species; a similar discrepancy seen in comparing bis(diarylamino) MV species with stilbene and tolane bridges was found to be attributable to differences in bridge planarity between the neutral and monocationic stilbene derivative.56 The observation of similar couplings for biphenyl- and pyrene-bridged species in the present work is consistent with previous comparisons; data for the trications of V39 and VI40 suggest very similar couplings, while application of eq 3 to the delocalized anions of VII42 and VIII43 suggests an effective coupling that is ca. 225 cm−1 lower in the pyrene example. 3162



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HOMOs of biphenyl and THP, that is the main bridge orbital responsible for mediating the carbazole−carbazole coupling (and also the Ru−Ru interaction in VI and related compounds40,81); this orbital is slightly lower in energy than the HOMO of biphenyl, and similar HOMO/HOMO−1 splittings are obtained in 3b and 1b. A qualitatively similar orbital picture is obtained for the bis(diarylamino) species Ib, II, and III (although, as noted above, the splitting in III is marginally larger than that for Ib, whereas that of 3b is slightly smaller than that of 1b). However, in each of the bis(diarylamino) compounds, there are more significant bridge-based destabilizing contributions to the HOMO than in the analogous bis(carbazolyl) species, and also more stabilizing contributions to the HOMO−1 (from the bridge LUMO or, in the case of pyrene, LUMO+1), accounting from the larger splittings and couplings seen in this series (see Figure S4). This pattern cannot be rationalized by considering only the relative energies of the local end-group and bridge orbitals. The planarity of a carbazole might be expected to lead to a stronger N−Ar antibonding interaction and thus destabilize the HOMO relative to that of a diarylamine, but, on the other hand, a bonding interaction between the two aryl groups will stabilize the HOMO. The net effect is that the calculated HOMO for isolated di-p-tolylamine is higher in energy than that of 3,6-dimethylcarbazole and so one would expect less bridge contribution to the HOMO in the bis(diarylamino) series (and more to the HOMO−1) owing to the greater mismatch with the energy of the end-group HOMO. The stronger coupling in the bis(diarylamino) compounds can, therefore, be ascribed largely to greater orbital overlap between the nitrogen pπ orbitals and the orbitals of the bridge, the overlap being limited in the case of carbazole donors by sterically induced twist between the carbazole ring and adjacent bridge ring. Whether a given MV species belongs to class II or III depends not only on the coupling but also on the reorganization energy, i.e., the energy required to change the energy of one diabatic state to that of the other. Some insight into how reorganization energies compare for bis(carbazolyl) and bis(diarylamino) MV compounds can be gained through DFT calculations of the internal reorganization energies for the 4b/4b•+ and IV/IV•+ self-exchange reactions. Similar values are obtained (0.14 and 0.13 eV, respectively, see Table S1 for more details and also for reorganization energies for the self-exchange reactions of the bis(carbazolyl) and bis(diarylamino) MV ions), suggesting that the qualitative differences between the MV behavior of 1b•+/3b•+ and that of their bis(diarylamino) analogues is primarily due to differences in electronic coupling.

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Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b11061. Vis−NIR and TD-DFT spectra, orbitals involved in transitions, partial MO diagram, DFT reorganization energies, and complete citations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS B.R.K. thanks the Petroleum Research Fund of the American Chemical Society (Grant No. 47343-B10) and the Arab Fund Scholarship Program for financial support. C.R. thanks the University of Kentucky Vice President for Research for start-up funds. S.R.M. thanks Georgia Power, a Southern Company, for funding of an Endowed Chair that helped support this work.

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REFERENCES

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CONCLUSION

3,6-Di-tert-butyl substitution of carbazole enables the synthesis of an analogue of CBP that, in contrast to CBP itself, can be oxidized to a MV radical cation that is persistent in solution. The estimated electronic coupling between redox sites in this cation is much lower than that in analogous bis(diarylamino) compounds, resulting in class-II (valence-localized) behavior. Similar behavior is obtained for a pyrene-bridged analogue, but the tetrahydropyrene bridging moiety is sufficiently electronrich to afford a class-III (delocalized) cation. 3163


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potential as the monomeric model compound 4b. The same effect is seen in DFT-calculated ionization energies (see ref 32) and HOMO energies and so is likely not related to the qualitatively different delocalization (DFT affords symmetrical cation structures) but to the more electron-rich character of the tetrahydropyrene bridge (see Figure 3). (65) The spectra of the radical cations obtained using the two different oxidants are very similar to one another. (66) Amthor, S.; Noller, B.; Lambert, C. UV/Vis/NIR Spectral Properties of Triarylamines and their Corresponding Radical Cations. Chem. Phys. 2005, 316, 141−152. (67) The reactions were shown to be chemically reversible by adding traces of water or a drop of hydrazine and regaining the spectrum of the neutral species. (68) Bonvoisin, J.; Launay, J.-P.; Verbouwe, W.; Van der Auweraer, M.; De Schryver, F. C. Organic Mixed Valence Systems. II. TwoCenters and Three-Centers Compounds with Meta Connections around a Central Phenylene Ring. J. Phys. Chem. 1996, 100, 17079− 17082. (69) The IVCT bands of the present compounds are seen at rather low energy relative to many other organic MV species, meaning that the low-energy portions of the bands overlap severely with vibrational features of the solvent and the low-energy tails of 1b•+ and 3b•+ lie outside the range of the spectrometer (190−3300 nm). Therefore, only the approximate bandshape can be obtained. (70) Szeghalmi, A. V.; Erdmann, M.; Engel, V.; Schmitt, M.; Amthor, S.; Kriegisch, V.; Nöll, G.; Stahl, R.; Lambert, C.; Leusser, D.; et al. How Delocalized is N,N,N′,N′-Tetraphenylphenylenediamine Radical Cation? An Experimental and Theoretical Study on the Electronic and Molecular Structure. J. Am. Chem. Soc. 2004, 126, 7834−7845. (71) Coropceanu, V.; Malagoli, M.; André, J. M.; Brédas, J. L. Intervalence Transition in Triarylamine Mixed-Valence Systems: A Time-Dependent Density Functional Theory Study. J. Chem. Phys. 2001, 115, 10409−10416. (72) Coropceanu, V.; Malagoli, M.; André, J. M.; Brédas, J. L. Charge-Transfer Transitions in Triarylamine Mixed-Valence Systems: A Joint Density Functional Theory and Vibronic Coupling Study. J. Am. Chem. Soc. 2002, 124, 10519−10530. (73) Piepho, S. B. Vibronic Coupling Model For The Calculation Of Mixed-Valence Line-Shapes - The Interdependence Of Vibronic And MO Effects. J. Am. Chem. Soc. 1988, 110, 6319−6326. (74) Reimers, J. R.; Hush, N. S. The Effects of Couplings to Symmetric and Antisymmetric Modes and Minor Asymmetry on the Spectral Properties of Mixed-Valence and Related Charge-Transfer Systems. Chem. Phys. 1996, 208, 177−193. (75) Borrás-Almenar, J. J.; Coronado, E.; Ostrovsky, S. M.; Palii, A. V.; Tsukerblat, B. S. Localisation vs. Delocalisation in the Dimeric Mixed-Valence Clusters in the Generalised Vibronic Model. Magnetic Manifestations. Chem. Phys. 1999, 240, 149−161. (76) Bailey, S. E.; Zink, J. I.; Nelsen, S. F. Contributions of Symmetric and Asymmetric Normal Coordinates to the Intervalence Electronic Absorption and Resonance Raman Spectra of a Strongly Coupled p-Phenylenediamine Radical Cation. J. Am. Chem. Soc. 2003, 125, 5939−5947. (77) Perdew, J. P.; Zunger, A. Self-Interaction Correction to DensityFunctional Approximations for Many-Electron Systems. Phys. Rev. B: Condens. Matter Mater. Phys. 1981, 23, 5048−5079. (78) Koch, W.; Holthausen, M. C. A Chemist’s Guide to Density Functional Theory; Wiley & Sons: New York, 2000. (79) Koopmans, T. Ü ber die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen eines Atoms. Physica 1934, 1, 104−113. (80) Since DFT affords an overdelocalized structure for 1b•+, the angle in the actual localized (class-II) cation may be larger than calculated. (81) The LUMO of pyrene also has nodes in the 2,7-position and so it is the LUMO+1 of pyrene that contributes to the LUMO of VIII. However, the orbital picture for VIII is rather more complex than that for the current systems: the LUMO of the neutral species can be 3165


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The Journal of Physical Chemistry C regarded as a combination of boron-based orbitals stabilized by interaction with the pyrene LUMO+1, while the LUMO+1 corresponds to the LUMO of pyrene, but the NIR transition of VIII•− is better described as a transition from a SOMO resembling the neutral LUMO to a SOMO+1 that consists of the other symmetryadapted combination of boron-based orbitals. (82) Kurata, R.; Tanaka, K.; Ito, A. Isolation and Characterization of Persistent Radical Cation and Dication of 2,7-Bis(dianisylamino)pyrene. J. Org. Chem. 2016, 81, 137−145.

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NOTE ADDED IN PROOF The structure and spectra of the mono- and dications of N,N,N',N'-tetrakis(4-methoxyphenyl)pyrene-2,7-diamine (i.e., the analogue of III in which the terminal methyl groups are replaced with methoxy groups) have very recently been reported.82 The monocation is a class-III MV species, and the experimental value of Vclass‑III (2610 cm−1) is smaller than that for its biphenyl-bridged analogue, Ic •+ (3180 cm−1 ), qualitatively consistent with the TD-DFT calculations in the present work (Table 2), which predict smaller Vclass‑III for III•+ than for Ib•+. The frontier orbitals for the neutral pyrene- and biphenyl-bridged diamines were also compared and are similar to those shown for III and Ib, respectively, in the present work (Figure S4).

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