Supplementary Materials for

Extreme Electron-Polaron Spatial Delocalization in π-Conjugated Materials

Jeff Rawson,† Paul J. Angiolillo,‡* Michael J. Therien†*

†Department of Chemistry, Duke University, French Family Science Center, 124 Science Drive, Durham, North Carolina 27708-0346, United States ‡Department of Physics, Saint Joseph’s University, 5600 City Avenue, Philadelphia, Pennsylvania 19131, United States

Additional Figures ...................................................................................................................... 2 Experimental methods ............................................................................................................... 7

General materials: .................................................................................................................... 7 Synthetic details: ...................................................................................................................... 7 Instrumentation: ....................................................................................................................... 9 Spectral processing: ................................................................................................................. 9

Computational methods ........................................................................................................... 10 Molecular structures .............................................................................................................. 10 Time-dependent calculations of electon-polaron states ......................................................... 10 Four-point calculation of internal reorganization energy ...................................................... 10

References ................................................................................................................................. 12

Additional Figures

Figure S1. Electronic absorption spectrum of neutral PZnE2 (black) and the 660-1000 nm-range electronic absorption spectrum of [PZnE2]–• (red) generated by doping with CoCp*2 in THF solvent at 298 K.

Figure S2. ESR spectrum of [PZnE2]–• (black) in THF solvent at 298 K, and fit to the spectrum (red). Fitting parameters: g = 2.0008, proton hyperfine couplings = 0.23 and 0.14 mT, Gaussian line broadening = 0.15 gauss.

Figure S3. Comparison of electron-polaron spectra recorded for [PZnn]–• in THF solvent with TDDFT-calculated transitions determined using either the (blue circles) M11 or (magenta squares) LC-ωPBE functionals.

Figure S4. Full structures of all meso-ethyne-bridged porphyrins studied in this work.

Figure S5. (black structure) PZn2 and (blue structure) [PZn2]–• modeled using the LC-ωPBE functional with range-correction parameter ω = 0.05 and no symmetry constraints. This view is down the ethyne axis to provide a sense of the degree of deviation from coplanarity in this system, and to illustrate the principle displacements required in the relaxation from the neutral species to the electron-polaron state.

Figure S6. Comparison of α-HOMO wavefunctions calculated for [PZnn]−! using (left, black surfaces) M11 functional and (right, white surfaces) ω-PBE functional with ω set to 0.05. All orbitals plotted as 0.007 isodensity surfaces.

Figure S7. Structures of π-conjugated materials whose electron-polaron spatial dimensions have been previously measured; the structure of PZn7 is presented for comparison. Rectangles represent the areas used in calculating the two-dimensional spatial extents of electron polarons. Molecular length scales are denoted above each structure; the calculated areal electron polar delocalization is centrally highlighted.

Experimental methods General materials: All manipulations were carried out under argon previously passed through an O2 scrubbing tower (Schweitzerhall R3-11G catalyst) and a drying tower (Linde 3Å molecular sieves) unless otherwise stated. Air sensitive materials were handled and stored in a Braun 150-M glove box. Standard Schlenk techniques were employed to manipulate air-sensitive solutions, using 10 micron vacuum. THF solvent used for these experiments was freshly distilled from sodium/benzophenone ketyl under argon onto freshly activated molecular sieves and subsequently purged with argon gas for at least two minutes per mL. Synthetic details: Permethylcobaltocene was synthesized by sonicating a THF suspension of the bis(pentamethylcycolpentadienyl)cobalt(III) hexafluorophosphate salt1 over sodium metal for two hours, followed by airfree filtration through celite and solvent removal under vacuum; it was sublimed twice before use. The syntheses of PZnE2, PZn2, PZn3, PZn5, and PZn7 have been reported previously,2, 3 and all presented pristine characterization data before use in this study. An exemplary synthesis of PZn7 is outlined in Figure S8. The syntheses of intermediates closely followed the established procedures.3, 4

Figure S8. Outline of the synthetic approach to PZn7.

Instrumentation: n-Doping experiments were performed in a custom airfree cell (Figure S9) that could be attached to a Schlenk line. Electronic absorption spectra were collected using a Cary 5000 spectrometer. X-band ESR measurements were performed using a Varian E-109 spectrometer; all spectra were collected at 10 mW power and the magnetic field was referenced to 2,2-diphenyl-1-picrylhydrazyl (dpph) and weak pitch standards.

Figure S9. Airfree tandem vis-NIR and ESR cell used for doping of PZnn molecules with CoCp*2.

Spectral processing: Deconvolution of the electronic spectral data from multistep doping experiments was performed using the MCR-ALS toolbox5 running in MatlabTM. All deconvolutions were found to exhibit negligible rotational ambiguity as determined by MCR-BANDS analysis.6 The OriginTM software package was utilized for all spectral analysis and display; this was also used for double integrations of ESR spectral data and the fit of peak-to-peak line widths (∆BP-P) for [PZn2-7]−! to the Norris expression.7 Oscillator strengths of the NIR bands P1 and P2 were determined as described in Lakowicz.8 The ranges used for P1 and P2 are summarized in Table S1 below. Table S1. Energy ranges, in wavenumbers, used for determination of the oscillator strengths for NIR polaron bands P1 and P2. PZn electron polaron P1 range / cm-1 P2 range / cm-1 [PZn2]−! 7893−3225 14514−7893 [PZn3]−! 6146−3333 11161−6146 [PZn5]−! 5800−3225 11500−5800 [PZn7]−! 5184−3225 11136−5184

N

N N

N

Ar

Ar

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N

N N

N

Ar

Ar

Zn

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Co

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Dual spectroscopy on stable reduced species

connect'to'Schlenk'line'

Computational methods Molecular structures All structure optimizations, single-point energy calculations, and time-dependent (TD) calculations were performed using Density Functional Theory (DFT) in the Gaussian09, Rev D.19 software package. The structures of PZnn compounds were simplified by modeling the aryl groups as unsubstituted phenyl rings. For all polaron wavefunction models used in the text, as well as for TDDFT calculations, the structures were further simplified to the D2h point group by restricting the individual porphyrin rings to lie in a single plane. Optimization of PZn2 with no symmetry constraint finds an angle between the neighboring N,N,N,N consensus planes of 26.7°, and for [PZn2]−! this angle is calculated to be 16°. These small deviations in interporphyrin dihedral angles exercise negligible impacts upon the PZnn electronic structures, and the approximation to planarity allows these calculations to serve as useful qualitative models. For the calculations of intramolecular electron-phonon coupling λi models with no symmetry and more realistic interporphyrin plane angles were used (Figure S5). The Becke three-parameter hybrid10 and the Lee-Yang-Parr correlation functional11, 12 (B3LYP) were employed for initial optimizations of the neutral species. All calculations employed tight convergence criteria and the 6-311g basis set13, 14, 15, 16, 17, 18, 19, 20, 21 with two additional d functions (6-311G(2d)) as implemented in Gaussian09. A polarized continuum solvation model (SCRF=IEF-PCM in Gaussian09) with THF as solvent was used for all calculations except for determination of λi. Time-dependent calculations of electron-polaron states Optimizations of the electron polaron states of PZnn were initially performed using the M11 functional22 with the default parameters implemented in Gaussian 09. TDDFT calculations using these structures were found to severely overestimate the energies of the major polaron transitions in the energy range below 1.55 eV (800 nm), with virtually no effect for oligomer lengthening beyond PZn2. Employing the LC-ωPBE23 functional with the range-separation parameter ω set to 0.05 dramatically improved the agreement of the calculated spectra with those observed; for all oligomers transition energies within 0.1 eV of major absorption maxima were calculated using this technique (Figure S3). A comparison of the highest occupied majority-spin orbital (HOMOα, sometimes referred to as SOMO) spatial extents determined using these two functionals, as manifested in their 0.01 isodensity surface plots, reveals that with the M11 functional the polaron wavefunction is essentially localized upon the central porphyrins; in contrast the LC-ωPBE polaron wavefunction extends to the limits of the PZnn frameworks (Figure S6). Thus agreement of the TDDFT-calculated transitions with the observed spectra is correlated with structures that feature highly delocalized HOMOα wavefunctions. Four-point calculation of internal reorganization energy The internal reorganization energies (λi) were calculated following an approach attributed to Nelson et al.24 Neutral PZnn and electron-polarons [PZnn]−! were modeled in the gas phase with no symmetry constraints. Because the ωPBE functional with ω = 0.05 provided an accurate model of [PZnn]−!, this was used for all λi calculations.

Table S2. Calculated total energies used in the estimation of internal reorganization energy λi. PZn2     Hartree  energy   eV  energy   λi  /  eV  E-‐  Q0   PZn2-‐  neutral  geom   -‐6531.63470964   -‐177734.82676338  

 E-‐  Q-‐   PZn2-‐  relaxed   -‐6531.63640677   -‐177734.87294464    E0  Q0   PZn2   -‐6531.56043642   -‐177732.80568619    E0  Q-‐   PZn2  anion  geom   -‐6531.55877410   -‐177732.76045216   0.09141529  

         PZn3          E-‐  Q0   PZn3-‐  neutral  geom   -‐9834.88468126   -‐267620.83349237  

 E-‐  Q-‐   PZn3-‐  relaxed   -‐9834.88635566   -‐267620.87905511    E0  Q0   PZn3   -‐9834.79850214   -‐267618.48843916    E0  Q-‐   PZn3  anion  geom   -‐9834.79694940   -‐267618.44618695   0.08781495  

         PZn5          E-‐  Q0   PZn5-‐  neutral  geom   -‐16441.37081170   -‐447392.47108493  

 E-‐  Q-‐   PZn5-‐  relaxed   -‐16441.37234590   -‐447392.51283264    E0  Q0   PZn5   -‐16441.27462030   -‐447389.85358371    E0  Q-‐   PZn5  anion  geom   -‐16441.27321760   -‐447389.81541430   0.07991712  

C60  wpbe005   Hartree  energy   eV  energy    E-‐  Q0   C60-‐  neutral  geom   -‐2284.48879586   -‐62164.10415233    E-‐  Q-‐   C60-‐  opt   -‐2284.49082507   -‐62164.15936995    E0  Q0   C60  opt   -‐2284.39921378   -‐62161.66649986    E0  Q-‐   C60  anion  geom   -‐2284.39732266   -‐62161.61503987   0.10667761  

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