p-Carborane Conjugation in Radical Anions of Cage–Cage and Cage

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

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p‑Carborane Conjugation in Radical Anions of Cage−Cage and Cage−Phenyl Compounds Andrew R. Cook,*,† Michal Valásě k,‡ Alison M. Funston,†,§ Pavel Poliakov,† Josef Michl,⊥,‡ and John R. Miller† †

Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973, United States Institute of Organic Chemistry and Biochemistry, ASCR, Prague 6 16610, Czech Republic § School of Chemistry, Monash University, Clayton, Victoria 3800, Australia ⊥ Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, United States ‡

S Supporting Information *

ABSTRACT: Optical electron transfer (intervalence) transitions in radical anions of p-carborane oligomers attest to delocalization of electrons between two p-carboranes cages or a p-carborane and a phenyl ring. Oligomers of the 12 vertex p-carborane (C2B10H12) cage, [12], with up to 3 cages were synthesized, as well as pcarboranes with one or two trimethylsilylphenyl groups, [6], attached to the carbon termini. Pulse radiolysis in tetrahydrofuran produced radical anions, determined redox potentials by equilibria and measured their absorption spectra. Density functional theory computations provided critical insight into the optical electron transfer bands and electron delocalization. One case, [6−12−6], showed both Robin−Day class II and III transitions. The class III transition resulted from a fully delocalized excess electron across both benzene rings and the central p-carborane, with an electronic coupling Hab = 0.46 eV between the cage and either benzene. This unprecedented finding shows that p-carborane bridges are not simply electron withdrawing insulators. In other cases with more than ∼1/2 of the excess electron localized on a [12], large cage distortions were triggered, producing a partially open cage with a nido-like structure. This resulted in class II transitions with similar Hab but massive reorganization energies. The computations also predicted delocalization in radical cations, but complexities in cation formation allowed only tentative experimental support of the predictions. The results with anions provide clear evidence for carborane conjugation that might be exploited in molecular wire materials, which are classically composed of all π-conjugated molecules.

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INTRODUCTION closo-Carborane cage compounds are intriguing molecules with high symmetry and multicenter delocalized bonding. Broad interest in these materials has resulted in many publications, including comprehensive reviews1−4 and books5,6 exploring their diverse chemistry as well as their impact as substituents in larger molecules. They can be constituents of molecular rods and “tinkertoys” and even “nanocars”.7−14 The unusual bonding patterns and geometries of carborane cages have led chemists to incorporate them, along with aryl π-electron containing groups, into a variety of small molecules and conjugated polymers, where they confer unusual properties.15−21 They may find medical applications22 and form ionic crystals and liquids, rods, nanostructures, and monolayers.13,23−33 These carboranes resemble ordinary saturated hydrocarbons in that they have very large band gaps between the highest occupied and lowest unoccupied orbitals. This is particularly true for para-carboranes, as exemplified by the more than 11 eV difference between the gas phase ionization potential (10.17 eV34,35) and the electron affinity (−1.1 eV36) of the 12-vertex para closo-carborane, p-C2B10H12. While this © XXXX American Chemical Society

wide band gap might suggest that carborane cage compounds are similar to σ-bonded saturated systems, they are known to have 3 center/2 electron bonds, and many results support the notion that they are three-dimensionally aromatic.2,37,38 Less is known about the properties of dimeric or trimeric cages;10,31 such rods might be expected to be excellent axially symmetric electronic insulators. In this work, we report both radical anions and radical cations of 12-vertex p-carboranes in solution. The anions were formed via the attachment of electrons to closo-carboranes with a [2n+2] electron configuration, using pulse radiolysis. With this approach, we investigated two series of the resultant [2n +3] p-carboranes depicted in Chart 1. Optical spectra are reported for radical anions of these molecules, and redox potentials were determined by pulse radiolysis. Computations find that some anions retain a closo structure; others distort to a nido-like structure, with significant impact on Received: November 3, 2017 Revised: December 13, 2017 Published: December 14, 2017 A

DOI: 10.1021/acs.jpca.7b10885 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Chart 1. Structures of p-Carborane Species Investigated in This Work

small differences in the reported values below, well within total error. Radiolytic doses of 15−28 Gy were employed. For the radical anion of the carborane dimer, the extinction coefficient was determined relative to that of benzophenone−• reported by Pedersen.49 The temperature was 22 ± 1 °C unless otherwise indicated. Calculations. Many of the species in this study have negative gas phase vertical and adiabatic electron affinities (EAs). Accurate computation of such temporary anion state energies is difficult, as the added electron is often artificially bound in small basis sets, and incorrectly extended outside the molecule with larger ones. While there are multiple sophisticated approaches to this problem,50−53 the current work examines solvated ions and adiabatic EAs and reduction potentials. Determination of gas phase EAs was not required, and methods used herein are straightforward and for our purpose gave reasonably accurate solvated EAs, as described in results below. Calculations were carried out using Gaussian 09.54 The effect of solvation was included in all calculations using the polarizable continuum model (IEFPCM).55,56 Geometries were optimized for all species using the B3LYP hybrid functional and 6-31g* basis set with solvation and checked to ensure they are local minima without imaginary vibrational frequencies. To help avoid finding local minima, multiple starting geometries were often optimized to find a global minimum. Final energies were calculated at the optimized geometry using B3LYP/D95* with solvation. Computed EAs and IPs in solution are differences in enthalpy with solvation free energies. Errors in not using differences in free energy are small, and are expected cancel each other to a large degree. Previous work found for a variety of small molecules, the accuracy of calculations of gas phase negative electron affinities was improved by the use of diffuse functions.57−59 For some carborane anions and small molecules used in this study, we found that diffuse functions resulted in unrealistic singlyoccupied molecular orbitals (SOMOs) where much of the electron density is external to the molecules in the most diffuse orbital in the basis set. Similar behavior was noted by Szarka59 when more than one diffuse function was added. This can be addressed by stabilization calculations.60 While adding solvent can help contain the electron density, it does not always do so. Examples are in Table S1. Szarka also noted the deleterious effect diffuse functions have on calculations of EA in σ-bonded molecules, where EA is large and negative. Similar problems may occur in the 3 center/2e− bonded structures of carboranes. Electron affinities in THF reported herein are thus made without the use of diffuse functions, and may be subject to a systematic error. Omission of diffuse functions in all cases changed computed solvated EA by less than 3% for carborane containing compounds; larger differences were found for small molecules inversely proportional to their size.

their spectroscopy. In all cases, results point to strong conjugation between the icosahedral p-carborane cages that rivals that of π-electron systems.

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EXPERIMENTAL AND COMPUTATIONAL DETAILS Samples. The synthesis and characterization of compounds used in this study are detailed in Supporting Information, Section S0. Solutions were prepared immediately prior to use either under vacuum or in an argon environment and sealed under argon with Teflon vacuum stoppers. Tetrahydrofuran (THF) was dried in a commercial purifier (VAC), and 1,2dichloroethane (DCE) was dried over molecular sieves. Pulse Radiolysis. This work was carried out at the Brookhaven National Laboratory Laser-Electron Accelerator Facility (LEAF).39,40 Briefly, an electron pulse (≤120 ps duration) was focused into a quartz cell with an optical path length of 20 mm containing the solution of interest. During irradiation, samples were exposed to as little UV light as possible to avoid photodecomposition, although no evidence of this occurring was found within the time frames monitored. Transient absorption signals were recorded using a pulsed Xe lamp, photodiodes (EG&G FND-100Q, ≤1000 nm, 1 ns rise time; GPD GAP-500L, 1000−1650 nm, 2 ns; or a Sensors Unlimited SU500, 1500−2500 nm, 8 ns) and a transient digitizer (Tektronix TDS-680B, or LeCroy 8420A). Wavelengths were selected using either 40 or 10 nm bandpass interference filters. Data were analyzed and reaction rate constants were determined in a scheme that accounted for geminate and homogeneous recombination41 using Igor Pro software (Wavemetrics). Where not stated, uncertainties are 15%. Molar extinction coefficients of the radical anions were calculated relative to the electron absorption in water, using G(e−THF) = 0.6042−45 where G is the radiation chemical yield (molecules produced per 100 eV absorbed). The total dose per pulse was determined before each series of experiments by measuring the absorbance of the solvated electron in water, using ε(700 nm, e−aq)46 = 18 500 M−1 cm−1 and G(e−aq, 10 ns) = 2.97,47 and was corrected for the difference in electron density of THF compared to that of water. A recent publication gives ε(715 nm, e−aq) = 19 700 M−1 cm−1,48 that would give

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RESULTS The structures of the closo 12-vertex p-carboranes investigated in this work are shown in Chart 1. These structures may be grouped into unfunctionalized p-carborane oligomers ([12], [12−12], and [12−12−12]) and p-carborane monomers and dimers which have been functionalized on the carbon atoms with an aromatic p-trimethylsilylphenyl group ([12−6], [6− 12−6], and [6−12−12−6]). The terminal trimethylsilyl groups were introduced to improve solubility of the materials. B

DOI: 10.1021/acs.jpca.7b10885 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Attachment of Electrons to Form Radical Anions of Carboranes. To produce radical anions of the carboranes, pulses of high energy electrons ionize condensed media making solvent radical cations (RH+•) and secondary electrons that quickly become solvated to form solvated electrons, e−s (eq 1). In THF, the solvent radical cations RH+• transfer a proton to a neighboring solvent molecule in less than ∼1 ps61 (eq 2), creating a largely unreactive radical R• and a solvated proton (RH2+). RH → RH+•+e−s +•

•

(1)

RH +RH → R +RH 2 carborane +e

− s

instead be due to a large reorganization energy yielding a very slow attachment rate. While e−s was not observed to react with [12], it reacted at or near diffusion-controlled rates with the [12−12] dimer, the [12−12−12] trimer, and molecules in which [12] is functionalized with p-trimethylsilylphenyl substituents. Those carboranes were also observed to participate in electron transfer reactions with aromatic molecules and their radical anions. The VIS−NIR spectra of the [2n+3] carborane radical anions are shown in Figure 1. The spectra of [12−12]−• and [12−12− 12]−• each have only a broad, single weak absorption band in the visible region (Emax = 2.41, 2.49 eV) and no absorption in the NIR, 900−2150 nm. The addition of p-trimethylsilylphenyl groups leads to a red shift of the absorption bands. The absorption maximum of [12−6]−• is 1.46 eV, while for the symmetric [6−12−6]−• and [6−12−12−6]−•, the very broad bands have maxima near 1.0 and 1.1 eV, respectively. For [6− 12−6]−•, a new strong, sharp band occurs at 0.65 eV. Reduction Potentials of Carboranes Determined by Electron Transfer with Donors and Acceptors. Pulse radiolysis can measure electron transfer equilibria to determine redox potentials in the absence of salts in a wide variety of media by observation of equilibria with molecules with known potentials.70−74 Such measurements in Table 1 find that reduction of the four molecules [12−12], [12−12−12], [6− 12−6], and [6−12−12−6] occurs at similar potentials, while that of [12−6] is 0.2 V more negative.66−69,75 Data in Figure 2 shows that the reduction potential for the carborane dimer [12−12] is similar to that for phenanthrene, but a thermodynamic potential was not obtained because an equilibrium was not observed for electron transfer with any molecule. For electron transfer to and from molecules with reduction potentials near −2.99 V, the electron transfer was so slow that the equilibrium constants could not be discerned. To estimate the reduction potential, rates of several electron transfer reactions with both electron donors and acceptors were measured; these are plotted in Figure 2 against their reduction potentials. Example kinetic traces are shown in Figure S2. Curves passing through the data plot electron transfer rate as a function of ΔE0. The reduction potential of [12−12] was adjusted to obtain optimal agreement with both sets of observed rate constants. Equations used to calculate electron transfer rate as a function of ΔG°, with a diffusion-controlled limit, are given in Section S3. The data shown in Figure 2 do not produce a true redox potential by actual observation of equilibria, but bracket the potential between −3.15 V vs Fc+/0 (biphenyl) and −2.87 (pterphenyl). Phenanthrene, −3.02 V vs Fc+/0, sits in the middle with a reduction potential close to that estimated for [12− 12]−•. Rates and the application of electron transfer theory (Section S3) refine the potential to −2.99 ± 0.08 V vs Fc+/0. The slow rates with molecules near this potential imply a large reorganization energy in accord with computed results described below. The fitted curves in Figure 2 utilized an internal reorganization energy of 0.6 eV and a low frequency (solvent) reorganization energy of 0.5 eV. The fit provides an estimate of 2 × 107 M−1 s−1 for the rate constant of the selfexchange reaction of [12−12]−• in THF solution. The carborane trimer [12−12−12] accepts electrons from phenanthrene anions with a rate constant of (8.5 ± 2) × 108 M−1 s−1. The equilibrium constant for this reaction yields a free energy change of 52 ± 30 meV, indicating a potential slightly less negative than that for the reduction of [12−12].

+

→ carborane

(2) ‐•

(3)

Solvated electrons react with the carborane solutes to form the radical anions of the carboranes (eq 3). Under our experimental conditions, solvated electrons are the only species that generate radical anions of the solutes. Rate constants for the reaction of e−s with the carborane species investigated are summarized in Table 1. The solvated electron did not react Table 1. Reaction Rate Constants for Reaction of e−s in THF with p-Carboranes and Reduction Potentials Determined by Pulse Radiolysis (PR) sample

k3 (1010 M−1 s−1)

PR Eoreda (V)

[12] [12−12] [12−12−12] [12−6] [6−12−6] [6−12−12−6]

−b 5.1 ± 0.9 5.4 ± 0.8 10 ± 1.5 9.5 ± 1.5c 8.2 ± 1.5c

−d −2.99 −2.97 −3.18 −2.96 −2.98

a

Determined by pulse radiolysis equilibria in THF and reported with respect to Fc+/0, uncertainties ±0.02 V, not including uncertainties in potentials of the reference molecule, phenanthrene (−3.02 V vs Fc+/0).66 Streitweiser’s potentials vs Hg pool were corrected to Fc+/0 in THF using the potential of anthracene measured by Shalev and Evans,67 giving −3.15 for biphenyl. Measurements of Meerholz and Heinze68 vs SCE were corrected through biphenyl, yielding −2.87 for p-terphenyl and −3.82 for benzene vs Fc+/0.69 For [12−6], the potential was referenced to biphenyl.66 bNo reaction with solvated electrons was observed, k3 < 1 × 108 M−1 s−1. cThese two rate constants were determined by competition with phenanthrene; k(e−s + phen) was determined to be 6.8 × 1010 M−1 s−1. Direct determination was less accurate due to overlap of the spectra of the anions with that of e−s. dReduction was not observed, possibly indicating Eored < −3.8 V or reaction rate exceptionally slow, 0.01 are considered. Results for lowest energy distorted geometry. cOptical electron transfer class, defined in the Discussion. b

F

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Table 4. Electron Transfer Parameters from Absorption Bands of Radical Anions in Figure 1 (All Energies are in eV) molecule

Emax = λa

ε (M−1cm−1)b

ΔE1/2c

Habd

rab (Å)e

λ (ω)f

[12−12] [12−12−12] [6−12−6] lg [6−12−6] hg [12−6] [6−12−12−6]

2.49 2.41 0.65h 1.0 1.49 1.1

3270 2570 28 000 7000 15 000 5370

1.07 1.14 0.23 1.5 0.59 1.34

0.48 0.43 0.33h 0.42 0.49 0.38

4.0 4.0 10.3 5.0 4.8 4.8

4.0 4.6 0.19 8.0 1.2 6.0

a The observed band maximum, which gives one measure of reorganization energy. bObserved molar decadic absorption (extinction) coefficient at the band maximum, ±15%. cFull width at half-maximum points on the experimental spectra. Extrapolations were made on the high-energy sides of [12−12] and [12−12−12] and on the low-energy side of [6−12−6] h using the Gaussian fits (Figure 1). dElectronic coupling deduced from spectra using the Mulliken−Hush expression, eq 4. eDistance between the cage centers in angstroms. fReorganization energy deduced from the bandwidth, using eq 5. gThe low (l) and high (h) energy bands for [6−12−6]. hEmax = 2Hab for the low energy band of the anion of [6−12−6] provides an estimate for Hab (0.33 eV) and an upper limit for λ, as for class III Hab > λ. For comparison, eq 4 gives Hab = 0.13 eV, which is small likely due to a narrowed class III band.

termini. Ghirotti92 and Indelli93 reported slow electron and energy transfer respectively in dimetal complexes bridged by linkers containing p-carborane, concluding that electronic coupling was weak in both cases. The former utilized a phenyl-carborane-phenyl bridge connected to bipyridine coordinating units on the metals, much like [6−12−6] in the current study. In radical cations of rhenium complexes bridged by an ethynl−carborane−ethynyl unit, utilizing either 10 or 12 vertex p-carboranes, Fox94 reported spectra consistent with localized class II mixed valence systems (described below), giving electronic coupling between the metal centers of 260 and 140 cm−1 respectively. These couplings over 12.5−12.3 Å are larger than those reported in organic molecules across saturated hydrocarbon bridges,95 but are quite small compared to couplings through π-conjugated bridges,96−98 reinforcing the picture that carboranes are like alkanes. Contrary to that conclusion, diffusion-controlled electron capture, optical spectra, DFT electronic structure computations, and even the redox potentials of all molecules larger than a single carborane cage in the current study paint a very different picture, as explored below. For example, an electron attached to [12−12] experiences strong electronic interactions between the two cages. This carborane conjugation tends to delocalize excess electrons beyond a single cage, and works to a limited degree between two or three carborane cages and to a greater extent between a carborane cage and a benzene nucleus. The present results in fact provide clear evidence of unprecedented full delocalization through a carborane in the radical anion [6−12−6]−•, and do not preclude it in [6−12− 12−6]−•. In [12−12]−• and [12−12−12]−•, electronic coupling is still large but with geometric distortions leading to only partial charge localization, giving rise to class II charge transfer transitions. Radical cations of carboranes with benzene substituents are predicted by calculations to be delocalized like their anion counterparts but with slightly smaller couplings. The experimental spectra are more difficult to interpret because some types solvent holes are captured, while others seem not to be. We show below that the behavior of the present carborane radical ions can be understood in the substantial framework of knowledge on mixed-valence compounds. It is useful to start this discussion with a brief review mixed-valence chemistry and spectroscopy, particularly for organic radical ions. Optical Electron Transfer, OET, (Mixed-Valence) Interpretation of Spectra. OET bands are best known in molecules containing two interacting metal atoms having two

different valences, joined by a bridge, which is usually a ligand for the two metals. In class III mixed-valence compounds, strong electronic mixing completely delocalizes electrons between the two metal centers.96−103 The electronic coupling between the two centers is described by the two-center oneelectron exchange matrix element (transfer integral) Hab. In other cases, electrons may be completely (class I, no OET band) or partly (class II, charge transfer OET band) localized. Organic radical ions carrying two redox centers show fully analogous behavior.96,100,102,103 We propose that the present molecules are well-described by the same paradigm. Whether inorganic or organic, mixed-valence molecules possess new optical absorption bands, often called intervalence, or OET transitions. Both names are imprecise for completely delocalized (class III) cases. Properties of the intervalence absorption bands depend on Hab and the total reorganization energy λ = λv + λs as follows:96−103 1. For delocalized charges (class III), the intervalence transition energy Emax = 2Hab, so the position of the band depends only on Hab. The OET band is strong, occurring between symmetric and antisymmetric combinations of molecular orbitals over both sites. It therefore involves very little redistribution of charge and is often sharp. 2. For partly localized (class II) most (or in class I, all) of the charge resides on one group. The bands are broad, structureless, and often Gaussian in shape with Emax = λ. Although their positions, Emax, are almost independent of Hab, their intensities are smaller than in the delocalized case and increase with increasing Hab. Hab can be estimated for weakly coupled systems, 2Hab < λ, from the integrated intensity of the band using the Mulliken− Hush expression:99,104−108 Hab = 2.06 × 10−2

Emax εmax ΔE1/2 rab

(4)

where Emax is the energy at the maximum (peak) of the CT band, εmax is the molar extinction coefficient at the maximum, ΔE1/2 is the full width at half max for the CT band, and rab is the distance of electron transfer in angstroms. This description provides good approximate values of Hab when the OET transition moves charge between two redox sites or their symmetrized combinations but is less accurate when transitions occur largely to the bridge between them.99,103,109 The wellknown99 expression for the width (fwhm) G

DOI: 10.1021/acs.jpca.7b10885 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A ΔE1/2 = 2[4 ln(2)λ(ω)RT ]1/2

Given that the excess electron is substantially localized to one carborane cage in [12−12]−•, it is logical to expect similar localization in [12−12−12]−•. Indeed, its absorption spectrum and redox potential are very similar to those of [12−12]−•. The intensities present puzzles which can be understood as discussed in Section S12. For [12−6] −• , the structureless, moderately intense absorption band can be understood as a borderline class II/ III OET transition99 (see Section S12). This is supported by the difference in reduction potential of distorted [12] vs [6], leading to partial localization and smaller reorganization energy than other class II transitions like those in [12−12]−• and [12− 12−12]−•.99 Delocalized Radical Anions. For [6−12−6]−•, the narrow low energy absorption band (Emax = 0.65 eV, Figure 1) is characteristic of a delocalized electron class III OET transition. DFT calculations in results found the lowest energy geometry did not exhibit the large distortions present in the oligomeric carboranes or [6−12]−•, giving a nearly ideal lowest energy absorption between symmetric and antisymmetric delocalized orbitals over the entire molecule (Table S11). Such delocalization can be understood if the difference between the reduction potentials of [6] and undistorted [12] is less than the reorganization energy. Figure 4 concludes the reduction potential of distorted [12] (AD) is −3.24 V vs Fc+/0, but that for the nearly symmetric [12]−• (AS) is indeed quite close to −3.74 V measured for [6]. In this description, the carborane does not act like a high energy bridge producing coupling only through superexchange, but rather [6−12−6]−• requires a three-state description. Brunschwig99 gave the analytic solution to the adiabatic 3 state donor(D)−bridge(B)−acceptor(A) system halfway between the donor and acceptor:

(5)

for weakly coupled centers is useful for estimation of reorganization energies. Here, we enumerate the manifestations of the coupling between two or more carboranes or between carboranes and benzene rings that we refer to as carborane conjugation. Table 4 summarizes estimates of Hab and λ determined from the radical anion absorption spectra in Figure 1. Paragraphs below describe details of the methods used for the estimates with specific notes of the properties of the radical ions utilizing the language of mixed-valence compounds. Important insights into the natures of the observed transitions from TD-DFT calculations are also discussed. A brief examination of the table tells us that the values of Hab between two neighboring cages are similar and are all near to 0.4 eV. This is a surprisingly large coupling for a moiety that was expected to act as an insulator like a saturated hydrocarbon. Reorganization energies, λ are large, 2.4−4 eV or more for [12−12]−• and [12−12−12]−•, in which the transition takes an electron from one carborane cage to another. These large reorganizations are due to distortions of the carborane cages as described above in the computational section. In contrast, λ is small, 0.19 eV, in the low energy band of [6−12−6]−•, signaling that this transition is different than the others, likely a class III OET band in which the electron is delocalized and does not involve transfer of charge. We now discuss OET bands of individual anions. For brevity, we placed much of the discussion in the Supporting Information, Section S12. Distorted and Localized Radical Anions. The computations found that the chemistry of oligomeric carborane radical anions is dominated by the very large distortions. [12−12]−• is an excellent example, showing a broad and weak absorption band near 2 eV, compared to biphenyl−• that might have been expected to be a good model. Biphenyl−• exhibits a relatively sharp and strong absorption, characteristic of a fully delocalized class III OET band.80 The observed band for [12−12]−• by contrast has an onset at ∼1.3 eV and reaches a maximum at 2.5 eV, with a maximum extinction coefficient of εmax = 3200 M−1 cm−1, smaller by a factor of 4 relative to biphenyl−•, and by a factor of 15 relative to the delocalized anion [6−12−6]−• in Figure 1. These results suggest that unlike in biphenyl−•, the extra electron is not fully delocalized, and [12−12]−• is better characterized as a class II mixed valence compound. This is consistent with computation results above that found the excess electron mostly localizes on the strongly distorted cage and transfers to the other upon excitation. These observations are consistent with [12−12]−• having the strong electronic coupling between the two carborane cages, Hab = 0.48 eV in Table 4, but also a large reorganization energy that localizes the electron mainly to one cage. Such a large change in geometry is also consistent with observed slow reaction of [12−12] in weakly exergonic electron transfer reactions (Figure 2). Table 4 contains two estimates of the reorganization energy, λ, for [12−12]−•. One is 2.49 eV from Emax and another, 4.0 eV, from the width, ΔE1/2. For an OET band in which all the reorganization energy arises from low-energy modes that can be described classically, these two estimates would be expected to yield identical values. The difference may signal involvement of severe, possibly anharmonic, skeletal distortions in [12−12]−•, as indicated by the computations.

(G B − G D) = (ΔGg 2 + 8HDB 2)1/2

(6)

where ΔGg is the difference in energy of the diabatic states of the bridge and donor. In the limit of large coupling and all three diabatic states having the same free energy, Emax = HDB 2 , with HDB = HBA

(7)

For [6−12−6]−•, eq 7 gives H6−12 = 0.46 eV, nearly identical to the value determined for [6−12]−• above. A small error may occur because the diabatic state energy of [12] may be different from that of the two [6]’s by ±0.1 eV, but this is much smaller than H6−12. An expectation for class III bands with 2Hab > λ is that they are narrowed and cut off on the red edge.96,99 This is not obvious in Figure 1, but the band may be distorted by difficult experimental measurements at these long wavelengths and also broadened by variations in the dihedral angles between cages. Still, the band does appear to drop more precipitously on the low-energy side. If the band is narrowed, λ reported in Table 4, determined by eq 5, is a minimum for the reorganization energy. The very broad higher energy band (Emax = 1.0 eV, Figure 1) is likely due to a distorted structure of [6−12−6]−•, suggested by alternate computational methods (Section S13) that give more localization. Nelsen96 made the important observation that near the class II/III border, it was possible to have both delocalized and localized structures in equilibrium. Section S12 concludes that there is an equilibrium, Keq = 0.53, between the delocalized class III and a localized class II structure of [6−12− 6]−•, slightly favoring the class III version, that results a H

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groups across [12], 0.4−0.5 eV.110 Additional tests with different pendant aromatic groups (Table S14), showed that a single [12] provides nearly the same electronic coupling between groups, even when their reduction potential is more than 1.3 eV more favorable than [12]. It seems likely the internal 3D aromaticity of carboranes when compared to saturated spacers is responsible for the effective transfer of coupling. One could imagine constructing molecular electronics with these bridges regulating the transmission of electrons. The axial symmetry of p-carboranes suggests they might rotate relative freely. In π-conjugated molecules such as biphenyl, it is well-known that the coupling is strongly dependent on the dihedral angle between the rings, with a maximum when coplanar, and zero at 90 deg. Is this also true for carboranes? Plots of computed total energy and Hab are given in Figure S15 for different rotations in [6−12−12−6]−•. Results find a small, 45 meV, increase in coupling as the dihedral angle between the 2 central carboranes is changed such that opposing boron atoms become aligned. While coupling is not appreciably changed, steric interference of 5 sets of protons hinders rotation, increasing the total molecule energy by 0.21 eV when opposed. Rotation of [6] relative to [12] results in nearly no loss,