The Importance of Electronic Dimensionality in Multi-Orbital Radical Conductors.

The exceptional performance of oxobenzene-bridged bis-1,2,3-dithiazolyls 6 as single component neutral radical conductors arises from the presence of a low-lying  -LUMO, which reduces the potential barrier to charge transport and increases the kinetic stabilization energy of the metallic state. As part of ongoing efforts to modify the solid state structures and transport properties of these so-called multi-orbital materials we report the preparation and characterization of the acetoxy, methoxy and thiomethyl derivatives 6 (R = OAc, OMe, SMe). The crystal structures are based on ribbon-like arrays of radicals laced together by SꞏꞏꞏN  and SꞏꞏꞏO  secondary bonding interactions. The steric and electronic effects of the exocyclic ligands varies, affording 1D  - stacked radicals for R = OAc, 1D cofacial dimer  -stacks for R = SMe, and a pseudo 2D brick-wall arrangement for R = OMe. Variable temperature magnetic and conductivity measurements reveal strong antiferromagnetic interactions and Mott insulating behavior for the two radical-based structures (R = OAc, OMe), with lower room temperature conductivities (  RT ~ 10 -4 and ~10 -3 S cm -1 respectively) and higher thermal activation energies ( E act = 0.24 and 0.21 eV respectively) than found for the ideal 2D brick-wall structure of 6 (R = F), where  RT ~ 10 -2 S cm -1 and E act = 0.10 eV. The performance of R = OMe, OAc relative to R = F is consistent with the results of DFT band electronic structure calculations, which indicate a lower kinetic stabilization energy of the putative metallic state arising from their reduced electronic dimensionality.


Introduction
Design strategies for conductive materials based on the use of neutral radicals as molecular building blocks can be traced back to the ideas of Haddon, 1 who applied Hubbard theory 2 to a model one-dimensional (1D) lattice composed of molecular radicals (Figure 1), each with one unpaired electron.Charge transport in such a system can be understood in terms of the competition between (i) the onsite Coulomb repulsion barrier U for charge transfer in the Mott insulating 3 state, which may be approximated in terms of the screened ionization energy (IP) and electron affinity (EA) of the radical, and (ii) the kinetic stabilization energy Ek of the metallic state (Figure 1).The latter is a function of the hopping integral tij for charge migration between adjacent sites (i,j) and the related electronic bandwidth W = 4|tij|. 4For a constant density of states, 5 the insulating and metallic states are degenerate when U = W.In organic solids, however, intermolecular interactions are notoriously weak, yielding small hopping integrals tij and narrow energy bands.Under these circumstances, when W < U, the unpaired electrons are trapped on the radicals, and a Mott insulating state prevails.Recognizing this energetic imbalance, Haddon proposed the use of the non-alternant hydrocarbon phenalenyl 1 (Chart 1) as a prototypal building block for a radical-based conductor (and superconductor), 1 reasoning that the Coulomb barrier U should be minimal since the unpaired electron occupies a purely non-bonding singly occupied molecular orbital (SOMO).In short, his approach was to accept the intrinsically low bandwidth W of organic (carbon-based) materials and to reduce the value of U to the point that U < W.Many variations on the phenalenyl framework have since been examined but, in the absence of steric blockage, dimerization through localized C-C -bonds or cofacial -interactions is hard to avoid. 6,7,8Moreover, estimates of U based on electrochemical data are relatively large.Its magnitude can be lowered by resonance effects, as in 2, 9 in which spin density is partitioned between two phenalenyls, and even greater reductions are observed in spiro-conjugated internal salts such as 3. 10,11 Some of these latter materials show impressively high, albeit activated conductivity, and resonating valence bond ground states have been proposed.10c Chart 1 In contrast to work focused on purely carbon-based frameworks, our efforts towards the development of neutral radical conductors have been directed towards the use of heavy atom heterocycles, specifically those containing open shell thiazyl (SN) and selenazyl (SeN) units. 12,13st as in conductive radical-ion salts of donors such as tetrathiafulvalene, 14 where the presence of sulfur and/or its heavier congener selenium imparts both softness (a lower U) and increased orbital overlap (a larger tij and W), the introduction of heavy heteroatoms into molecular radicals can improve their performance as conductors.However, many of the materials studied early on, notably those based on the dithiadiazolyl framework 4, showed (in the absence of steric protection) 15 a strong tendency to associate in the solid state, resulting in insulating or weakly semiconducting behavior. 16Metallic conductivity could be achieved by p-type doping, 17 but the challenge of improving charge transport without doping required greater spin delocalization to lower U. Synthetic efforts to this end eventually afforded N-alkylated pyridine-bridged bisdithiazolyls 5, 18,19 in which not only was U markedly reduced but dimerization was also suppressed.While the conductivity of materials based on this resonance stabilized framework remained activated, with charge gaps ΔC (= U -W) near 0.5 eV, replacement of sulfur by its heavier congener selenium 20 reduced ΔC to the point that "bad metal" behavior (Eact ~ 0) could be achieved at pressures P < 10 GPa. 21In addition, the selenium-based variants displayed strong isotropic and anisotropic magnetic exchange interactions, 22 affording magnetically ordered phases with high ordering temperatures and large coercive fields. 23,24 with phenalenyls, the charge transport in bisdithiazolyls 5 is well described in terms of the single-orbital Hubbard model shown in Figure 1; the magnitude of U and W depend only on the distribution of the radical SOMO, which dictates the values of IP, EA and intermolecular hopping integral tij.Replacement of the N-alkylpyridine bridge in 5 by an oxobenzene ring affords the seemingly similar framework 6. 25 However, while the ground state electronic structures of bisdithiazolyls 5 and 6 are comparable, the values of U in 6 (estimated from electrochemical data) 25 are significantly smaller than those in 5. 18,19a,b The difference arises from the interaction of the low-lying *-acceptor orbital of the carbonyl group with the -manifold of the radical, 26,27 which leads to a lowering of the LUMO of 6 relative to that of 5.The presence of this low-lying virtual orbital in 6 (Figure 2) creates a multi-orbital effect 28 that opens up the electronic and magnetic degrees of freedom available to the unpaired electron and destabilizes the Mott insulating state.In effect, the Coulomb barrier to charge transport is lowered from U to U = U -V +   K, where  is the SOMO-LUMO gap, V represents the repulsion between electrons in different orbitals and K is the electron exchange term, the sign of which depends upon the spin state (triplet or openshell singlet) afforded by electron transfer.Density functional theory (DFT) calculations on 6 (R = H) suggest a triplet ground state, 29a with the corresponding value of U′ being ∼ 0.2 eV lower than U, in accord with electrochemical measurements.At the same time kinetic stabilization of the metallic state Ek is increased as the Fermi level εF in the metallic state is lowered (from εF = ε0) as electrons are redistributed between the SOMO and LUMO bands.26a,29 The resulting shift in the chemical potential  = ε0 -εF, combined with the dispersion term εdis = εF -εave, affords Ek = εdis + .The first term εdis is analogous to the dispersion stabilization in a single-orbital system (W/4 in Figure 1), but the chemical potential shift  is a purely "multi-orbital" phenomenon.In contrast to single-orbital radicals like 4 30 and 5 18 , where U is largely independent of nature of the exocyclic ligand(s), as the SOMO is nodal at the sites of substitution, the exocyclic ligand R in multi-orbital radicals 6 plays an important electronic role since, while the SOMO remains nodal at the site of substitution, the LUMO is not.To a first approximation its orbital energy 1 is raised (or lowered) depending on the -electron releasing (or accepting) power of the basal R-group.As a result the SOMO-LUMO separation  and hence the value of U is not only small but tunable, 27 so that charge transport can be improved by substituent effects.Bad metal behavior has been induced in several radicals 6 (R = H, F, Ph, NO2) at pressures ranging from 3-12 GPa.25d,29 From a solid state perspective the crystal structures of oxobenzene-bridged bisdithiazolyls are strongly influenced by intermolecular N/Oꞏꞏꞏ S′ secondary bonding interactions (SBIs) 31 (Figure 3a) that generate planar or near-planar ribbon-like arrays (Figure 3b) of radicals which can assemble in a variety of ways, to produce superimposed -stacks, alternating ABABAB -stacks, slipped -stacks and brick-wall (R = F) architectures (Figure 3c-f).The dimensionality of the electronic structures arising from these packing motifs varies considerably, ranging from almost purely 1D (R = Ph, NO2) 25a,27 to quasi-1D (R = Cl, H) 25c,e and 2D (R = F).25d Of these, the 2D brick-wall pattern found for R = F provides the most effective kinetic stabilization of the metallic state; as such this material represents the "gold standard" for a neutral radical conductor.The small residual charge gap in this material (~0.1 eV) found at ambient pressure can be closed at 3 GPa, and further pressurization to 6 GPa affords a Fermi liquid state.29b This latter finding, which represents the first observation of truly metallic behavior in a neutral radical conductor, has provided an incentive for continued exploration of multi-orbital radicals of this type, with the view of identifying specific structural motifs, notably the much sought-after 32 2D brick-wall packing pattern.With this goal in mind we have prepared the acetoxy, methoxy and thiomethyl derivatives 6 (R = OAc, OMe and SMe).As will be shown, these three radicals possess very different structures, ranging from 1D radical -stacks for R = OAc to 1D dimer -stacks for SMe and a seemingly 2D brick-wall architecture for R = OMe.Here we report details of these structures and the associated electronic and magnetic properties.The results are interpreted in the light of DFT band structure calculations, which provide insight into the electronic dimensionality of these materials.

Results and Discussion
Synthesis The starting point for the methoxy-and acetoxy-substituted radicals 6 (R = OMe, OAc) is the recently reported benzoquinone-bridged bisdithiazole zwitterion 7 (Scheme 1), 33 the framework of which is readily assembled by a double Herz condensation 34 of 2,6-diamino-1,4dihydroxybenzene 8 (as its hydrochloride salt) with sulfur monochloride.The resulting salt [7][HCl] can be converted to the more soluble triflate salt by metathesis with trimethylsilyl triflate (TMSOTf).Subsequent deprotonation with Proton-Sponge yields neutral 7 which, upon methylation with methyl triflate (MeOTf) affords the methoxy-substituted bisdithiazolylium salt   The new radicals have also been examined using cyclic voltammetry (CV), to establish half-wave potentials for the (-1/0) and (0/+1) couples and the corresponding cell potential Ecell = E½(0/+1) -E½(-1/0), which provides insight into the effective Coulomb barrier U.A summary of potentials so obtained is provided in Table 1, along with corresponding data for related radicals 6 (R = Cl, F, H, NO2) for comparison; relevant CV scans are illustrated in Figure S2.The (0/+1) wave is reversible in all cases, and the observed variation in E½(0/+1) broadly speaking reflects the electron-withdrawing power of the ligand.With the exception of R = NO2, SMe, the (-1/0) wave is irreversible, and for these non-ideal systems Ecell is estimated as the differences in the two cathodic peak potentials, that is, Epc(0/+1) -Epc(-1/0).As discussed earlier, 27,29b the changes in Epc(-1/0) and Ecell can be related the extent of -interactions of the ligand R with the b1 LUMO of the radical (Figure 2).Overall, the Ecell values for the R = OAc, OMe, SMe are all slightly smaller than that of R = F, suggesting that, to a first approximation, the values of U should also be smaller.).e Ecell estimated as Epc(0/+1) -Epc(-1/0).

Crystal Structures
The crystal structures of the oxobenzene-bridged bisdithiazolyls 6 (R = OAc, OMe, SMe) have been determined by single crystal X-ray diffraction; crystal data are listed in Table S1.Selected intramolecular metrics, which are nominal for this class of compound, are provided in Table S2, and ORTEP drawings of the asymmetric units are shown in Figure 5.At the molecular level, the three radicals differ only in the size and polarity of the basal ligand R.
In all cases the ligand is rotated away from the plane of the radical.When R = OMe, the exocyclic C-O(CH3) group generates a torsion angle  = 38.1°with respect to the semiquinone ring, while for R = OAc  = 67.7°.This rotation gives rise to a slight inequality in the intramolecular O2ꞏꞏꞏS2 and O2ꞏꞏꞏS4 contacts, suggesting a slight hypervalent interaction on one side.In the R = SMe derivative there are two molecules in the asymmetric unit.These are aligned in a twisted transcofacial manner and mutually inclined so as to produce interannular SꞏꞏꞏS' distances (Figure 5c) that are just inside the standard Van der Waals separation (3.6 Å) for two sulfur atoms. 36The rotation of the two SMe groups is more extensive ( = 72.1°and 89.9°) and there is little or no bias in the S5(1)ꞏꞏꞏS2(1) and S5(1)ꞏꞏꞏS4(1) contacts, indicating a negligible hypervalent effect.
We discuss the crystal structures of the three radicals starting with that of the acetoxy derivative 6 (R = OAc), which belongs to the orthorhombic space group P212121; it is the simplest to describe and sets the stage for later comparisons.Views of the unit cell and packing are shown in Figure 6.
The characteristic ribbon-like architecture is readily apparent, with neighboring radicals along the y direction laced together by short intermolecular O/NꞏꞏꞏS' SBIs d1,2.The bulky acetyl group plays two roles, serving partly as a structure maker, linking neighboring radical ribbons with intermolecular OꞏꞏꞏS SBIs (d3 and d4), but also as a buffer that separates radicals within the ribbons, so that the ribbons themselves are warped or ruffled away from planarity.A similar effect is observed in the structure of 6 (R = H), 25e where intermolecular face-to-edge or "tilted-T" -arene interactions 37 break up the otherwise planar arrays.In both cases, as a result of ruffling, lateral slippage of the ribbons is not possible, and the radicals are forced to adopt an isolated but uniformly spaced 1D AAAA slipped -stack arrangement with interplanar spacing  = 3.401Å.Crystals of 6 (R = SMe) also belong to the orthorhombic space group P212121 and, when viewed parallel to the a-axis, the unit cell (Figure 7) is reminiscent of that observed for the R = OAc derivative, with ribbons of radicals running along the y direction laced together by short intermolecular O/NꞏꞏꞏS' contacts d1-6.In this case, however, the SMe group does not serve as a structure maker, in that it does not generate close lateral intermolecular contacts.Instead its steric bulk leads not only to ruffling of the ribbons but also the formation of the weakly associated cofacial -dimers shown in Figure 5 and a concomitant doubling of the a axis so as to afford an essentially 1D ABABAB slipped -stack architecture.The crystal structure of 6 (R = OMe) belongs to the monoclinic space group P21/c (Figure 8) and provides a marked contrast to those described above.While a ribbon-like arrangement of radicals linked by intermolecular O/NꞏꞏꞏS' contacts d1,2 is still observed, the relatively small size of the ligand combined with a small torsion angle  is such that ruffling of the ribbons is not observed.
Nonetheless the methoxy groups still play a steric role in partially separating neighboring ribbons, but the resulting close four-center SꞏꞏꞏS' contacts d1,2 suggest a degree of lateral interactions along the y direction.The most striking feature of the structure of 6 (R = OMe) is the resemblance of the layering of the molecular ribbons to afford a brick-wall motif (Figure 3d) similar to that found for 6 (R = F).25d However, closer inspection reveals this similarity is only apparent.The high symmetry space group Cmc21 found for R = F requires that each radical in the xy plane be surrounded by four equivalent neighbors, a crystallographically 2D arrangement associated with a single intermolecular contact 1 (Figure 9a).By contrast, in the lower symmetry structure found for R = OMe the four nearest neighbors fall into two pairs (Figure 9b), one involving sites related by translation (contact 1), the other sites related by c-glides (contact 2).Accordingly, the packing is more akin to that illustrated in Figure 3e, and the resulting electronic structure is perhaps better described as lying between a 1D and 2D system.That being said, the small interlayer spacing ( = 3.189 Å) observed for R = OMe is close that found for R = F ( = 3.151 Å), 25d suggesting comparable interlayer hopping integrals associated with contact 1.However, a more meaningful comparison of the relative merits of the two packing arrangements requires analysis of their band electronic structures, to be described below.Magnetic Susceptibility Measurements Previous work on the magnetic behavior of oxobenzenebridged radicals 6 has revealed a remarkable tendency for strong ferromagnetic exchange interactions driven by Hund's rule coupling. 24,26In many cases (R = F, H, Ph, Cl and IꞏEtCN) 25c,d,e,26b these effects give rise bulk ordering as spin-canted antiferromagnets.However, DC magnetic susceptibility (χ) measurements on 6 (R = OAc, OMe) provide no indication of an FM response let alone magnetic ordering.Instead the results, illustrated in Figure 10a in the form of cooling curve plots of χT versus T over the range 2-300 K and measured using an external field of H = 1 kOe, reveal a strong, featureless antiferromagnetic (AFM) response, with the value of χT at 300 K lying well below that expected (0.375 emu K mol −1 ) for a paramagnetic S = ½ system with a nominal value of g ≈ 2. Perhaps not surprisingly, analogous behavior was observed for the structurally related radical 6 (R = Cl, as its MeCN solvate).In the case of 6 (R = SMe), AFM interactions are much stronger, with χT barely reaching 0.13 emu K mol -1 at 300 K.Moreover, on cooling to near 100 K, χT drops to a near-zero value, indicative of eventual complete association of the radicals into closed-shell singlet state.In accord with the above analysis of the crystal structure of the R = OAc derivative (space group P212121), intermolecular interactions in this material are weak and highly 1D.Total CO dispersion in the lower band is greatest (near 0.34 eV) along the Γ X vector, which corresponds precisely to the -stacking direction, weaker along Γ Y (near 0.21 eV) and virtually negligible along from Γ Z.In the R = OMe derivative (space group P21/c) intermolecular interactions are stronger than for R = OAc.However, in spite of the appealing lamellar 2D-packing pattern its electronic structure remains largely 1D.Dispersion in the lower band along Γ X, which loosely speaking reflects the magnitude of hopping integrals along the slipped -stacks (contact 1, Figure 9b), is significantly larger than along Γ Y, which derives from hopping between radicals related by cglides (contact 2, Figure 9b).By contrast, in the R = F derivative (space group Cmc21) dispersion in both bands is strong along both Γ X and Γ Y, in accord with the perfectly 2D brick-wall architecture illustrated in Figure 9a, whereby hopping integrals in the directions of the four nearest neighbor contacts (1) are all equal by symmetry.
As outlined in the introduction, we have previously demonstrated that the total kinetic stabilization energy of the putative metallic state of a multi-orbital radical Ek can be expressed as the sum of two components (Figure 2), one ( ) arising from a lowering of the Fermi level (F) relative to the Mott state (0) occasioned by electron redistribution between the SOMO and LUMO bands, the other stemming from the dispersion effects, that is, the delocalization of electrons within these bands (εdis), which lowers the average kinetic energy per electron (ave) relative to F. 26a,29 To illustrate the applicability of these concepts to the new radicals (R = OAc, OMe) we have carried out an analogous analysis of their band structures and the resulting density of states (Figure S2).
Derived values of , εdis and Ek are presented in Figure 11d, along with those previously obtained for R = F. 26a,29 Overall, the results reveal the superiority of the 2D radical R = F, for which both the dispersive (εdis) and redistribution () terms are significantly greater than those found for R = OMe and, more particularly R = OAc.In fairness, it is noteworthy that εdis in R = OMe and R = F are comparable, as a result of strong 1D interactions in the former, but with less SOMO-LUMO hybridization in R = OMe,  falls well short of that found in R = F, so that the overall Ek value is significantly lower.With even more weakly interacting 1D -stacks and little SOMO-LUMO mixing, the R = OAc derivative falls short on both counts.

Summary and Conclusion
Within the language of the single-orbital, single-electron Hubbard model, high conductivity in organic radical-based materials is impeded by the energetic imbalance between the large potential energy cost (U) of site-to-site transfer of an unpaired electron and the limited kinetic stabilization energy (W) afforded by charge delocalization into a half-filled energy band.To break out of the Mott insulating state that this condition imposes, a variety of approaches have been pursued.The use of spin delocalization to lower U, as Haddon originally proposed, 1 and the incorporation of heavy heteroatoms (chemical pressure) to increase W, have both been extensively explored.
Performance can also be improved by moving away from the classical one-orbital, one-electron model, as in mixed-valence spiroconjugated bis-phenalenyls 10,11 and chemically doped radical ion salts, 17 in which the effective Coulomb barrier is significantly reduced as additional channels for charge transport become available.
In oxobenzene-bridged bisdithiazolyl radicals 6 conductivity is enhanced by means of a multiorbital effect, that is, the presence of a low-lying LUMO introduced by mixing of the radical manifold with the -acceptor orbital of the exocyclic carbonyl group.The benefits are two-fold: (i) The Mott state is destabilized by lowering the Coulombic barrier U to charge transport, and (ii) kinetic stabilization of the metallic state Ek, that is, the effective bandwidth, is increased by mixing and hybridization of the SOMO and the LUMO, which lowers the Fermi level relative to that of the Mott state.Together or separately, these two effects lead to a reduction in the charge gap C between the Mott insulating and metallic states.As such these purely organic materials provide an interesting comparison to open-shell (S = ½) Au(III) bis-dithiolate complexes, 38,39 where a multi-orbital effect emerges by virtue of a high-lying HOMO.
In terms of structure/property correlations, the crystal structures of 6 (R = OAc, OMe, SMe), like those of other oxobenzene-bridged radicals, are strongly influenced by intermolecular SꞏꞏꞏO and SꞏꞏꞏN SBIs which generate ribbon-like arrays of radicals.However, the steric and electronic demands of the ligands also play an important role.When R = OAc, the acetyl group causes severe ruffling of the ribbons, but also maintains regularity of the spacing between the layers by means of SBI effects, so as to produce a highly 1D AAAA -stacked architecture.By contrast, when R = SMe, there are no SBI effects, but the steric demands of the ligand leads to the formation of ABABAB dimer -stacks.Finally, in the R = OMe derivative, steric and SBI effects involving the ligand are both minimal, and ribbon ruffling is not observed.Instead, slippage and layering of the ribbons results in a lamellar packing motif which provides an appealing but strong but illusory resemblance to the perfectly 2D brick-wall architecture found for the R = F material.DFT band structure calculations indicate that its electronic structure is better described as being more nearly 1D.The extent of SOMO-LUMO mixing is decreased, and the resulting contributions dis and  to the overall kinetic stabilization energy Ek for R = OMe are significantly smaller than for R = F, leading to a larger charge gap C, notwithstanding the smaller U' suggested by the Ecell measurements.By virtue of the high kinetic stabilization energy of its metallic state, the R = F radical remains the "gold standard" as a neutral radical conductor.29b Investigations of the transport properties of this latter material are ongoing.

Experimental Section
General Methods and Procedures., 34.58; H, 4.97; N, 11.52.Found C, 34.14; H, 5.05; N, processed with APEX2 software 44 and SADABS. 45The results for R = OAc, OMe were further analyzed using the WANNIER90 code 51 to generate a tight-binding model including the SOMO energy 0, which was obtained after rotation of the resulting Hamiltonian into diagonal form at each site.The resulting density of states are shown in Figure S2, along with values of 0, F and ave, as well as , εdis and Ek derived as described previously.26a,29b Supporting Information.The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/xxx.xxxxx.

Figure 1 .
Figure 1.The single-orbital, single-electron Hubbard model applied to a 1D array of neutral radicals.(a) The Coulomb barrier U (= IP -EA), intersite hopping integral tij and orbital energy 0.(b) The kinetic stabilization energy Ek of the metallic state expressed as the average energy ave (= tij = W/4) of the band electrons relative to 0.Total energies per site of the insulating (EMott/N) and metallic (Emetal/N) states are degenerate when W = U.

Figure 2 .
Figure 2. (a) Frontier orbitals and Coulomb barriers to intersite charge transfer U, U along a 1D chain of multi-orbital oxobenzene-bridged bisdithiazolyl radicals 6 (R = H).U is defined in terms of U (Figure 1), the SOMO-LUMO energy separation Δε, electron repulsion V between electrons in different orbitals on the same site, and electron exchange K.(b) Schematic overlap of energy bands arising from combinations of the SOMO and LUMO, showing contributions to the kinetic stabilization Ek of the metallic state afforded by (i) band dispersion dis = εF -εave, and (ii) electron redistribution  = 0 -F between the two bands.

Figure 4 .
Figure 4. X-band EPR spectra of radicals 6 with (a) R = OAc and (b) R = OMe in DCM and (c) R = SMe in toluene; spectral width = 3.0 mT.

Figure 6 .
Figure 6.(a) Unit cell drawing of 6 (R = OAc), viewed parallel to the a-axis; lateral intermolecular SꞏꞏꞏO′ (blue) and SꞏꞏꞏN′ (green) SBIs d1-4 are shown with dashed lines.(b) Ruffling of molecular ribbons in the y direction.(c) Tipped radical -stacks, with interplanar separation .

Figure 7 .
Figure 7. (a) Unit cell drawing of 6 (R = SMe), viewed parallel to the a-axis; lateral SꞏꞏꞏO′ (blue) and SꞏꞏꞏN′ (green) SBIs are shown with dashed lines.(b) Ruffling of molecular ribbons in the y direction.(c) Slipped -stacks of dimers; SꞏꞏꞏS′ contacts (red) defined in Figure 5.

Figure 8 .
Figure 8.(a) Unit cell drawing of 6 (R = OMe), viewed perpendicular to the planes of the molecular ribbons; lateral SꞏꞏꞏO′ (blue), SꞏꞏꞏN′ (green) SBIs and SꞏꞏꞏS′ (red) contacts d1-4 are shown with dashed lines;  is the mean interplanar separation.(b) Slipped radical -stacks running parallel to the a-axis.

Figure 9 .
Figure 9. (a) Side and (b) top views of layering of ribbons in 6 with R = F and OMe, with alternate layers in green and yellow.For R = F, space group Cmc21, alternate layers are related by Ccentering, and each radical has 4 equivalent neighbors (contact 1).For R = OMe, space group P21/c, neighboring layers are related by c-glides, with two distinct pairs of contacts (1 and 2). 19c

Figure 11 .
Figure 11.Band dispersion diagrams for 6 with (a) R = OAc, (b) R = OMe and (c) R = F, assuming a metallic state, showing frontier crystal orbitals arising from mixtures of the SOMO and LUMO (Figure 2); the Fermi level (εF) is indicated with a red line.(d) Values of the multi-orbital redistribution term Δμ = ε0  εF, the dispersion term εdis = εF  εave and the total kinetic stabilization energy Ek = εdis + Δμ (all in eV).

Table 1 .
Electrochemical potentials a for selected radicals 6.