Thiophene-Based Double Helices: Radical Cations with SOMO-HOMO Energy Level Inversion

Abstract

We report relatively persistent, open-shell thiophene-based double helices, radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈. Closed-shell neutral double helices, 1-TMS₁₂ and 2-TMS₈, have nearly identical first oxidation potentials, E^+/0 ≈ +1.33 V, corresponding to reversible oxidation to their radical cations. The radical cations are generated, using tungsten hexachloride in dichloromethane (DCM) as an oxidant, E^+/0 ≈ +1.56 V. EPR spectra consist of a relatively sharp singlet peak with an unusually low g-value of 2.001 – 2.002, thus suggesting exclusive delocalization of spin density over π-conjugated system consisting of carbon atoms only. DFT computations confirm these findings, as only negligible fraction of spin density is found on sulfur and silicon atoms and the spin density is delocalized over a single tetrathiophene moiety. For radical cation, 1^•+-TMS₁₂, energy level of the singly occupied molecular orbital (SOMO) lies below the four highest occupied molecular orbitals (HOMOs), thus indicating the SOMO-HOMO inversion (SHI) and therefore, violating the Aufbau principle. 1^•+-TMS₁₂ has a half-life of the order of only 5 min at room temperature. EPR peak intensity of 2^•+-TMS₈, which does not show SHI, is practically unchanged over at least 2 h.

Graphical Abstract

Radical cations of thiophene-based double helical π-systems possess their spin densities near exclusively delocalized over the carbon atoms and the SOMO energy levels below the HOMO energy levels.

INTRODUCTION

There are a few organic radicals with an electronic energy structure defined as SOMO-HOMO level inversion that formally violates the Aufbau principle, that is the energy level of singly occupied molecular orbital (SOMO) is below the level of the highest occupied molecular orbital (HOMO).(1,2) Of particular importance for photochemistry are the photostable radicals that also display SOMO-HOMO inversion, e.g., PTM-3NCz (Fig. 1).(2–5) This empirical observation of photostability also applies to thermal stability (or persistence) of radicals characterized by SOMO-HOMO inversion (vide infra). Excellent quantum yields of luminescence are observed in some of the recently reported radicals derived from electron-poor chlorinated triarylmethyl radicals π-conjugated with electron-rich carbazole-based non-alternant π-systems.(3,6–11) It was shown that such radicals may provide viable building block for near infra-red organic light emitting diodes (OLEDs).(3,6,9,11) Refinement of such radical-based red-colored OLEDs provided an excellent maximum external quantum efficiency (EQE_max) of up to 27%, thus adding a practical aspect (Fig. 1).(6,11)

Figure 1.

Examples of experimentally studied radicals showing SOMO-HOMO inversion (SHI), near degeneracy (SHND), and luminescent chlorinated triarylmethyl radicals with SHI or without (SH).

All radicals with the SOMO-HOMO inversion studied to date are associated with spin densities on relatively electronegative atoms, such as oxygens, nitrogens, or chlorines, and the radicals are connected through σ-bonds, π-conjugated, or cross-conjugated to an electron rich π-system (Fig. 1).(2–5,12–22)

In this work, we disclose a new case of the SOMO-HOMO inversion in the thiophene-based double helical radical cations, in which the spin density is primarily delocalized over carbon atoms. The observed inversions in thiophene-based double helices are unexpected, because the related radical cation of thiophene-based thia[7]helicene (Fig. 2) does not show the SOMO-HOMO inversion.(21,23,24)

Figure 2.

Thia[7]helicene radical cation and thiophene-based double helices – precursors to the corresponding radical cations. X-ray structure of 1-TMS₁₂ illustrates double helical character of the studied compounds.(28)

The thiophene-based double helix is a fascinating one-dimensional (1-D) carbon–sulfur structure which may be viewed as a π-conjugated double helical ladder oligomer. Such oligomers have potential to possess very high racemization barriers and strong chirooptical properties. Molecules, oligomers, and polymers that emit circularly polarized luminescence have great potential for advanced technology applications, such as three-dimensional displays, and information storage. We wish to pay tribute to Professor Ed Clennan for his important contributions to the field of π-conjugated, helical luminescent materials by designing and synthesizing viologen-based helicenes that have enhanced luminescence lifetimes and are effective electron transfer sensitizers. (25–27)

Our studies are based on the report in which we described synthesis and characterization of thiophene-based double helical oligomers, 1-TMS₁₂, 2-TMS₈, and 3-TMS₆ (Fig. 2).(28) These oligomers were based on α,β-cyclooctatetrathiophene (α,β-COTh) and β,β-cyclooctatetrathiophene (β,β-COTh) moieties sequentially connected in an alternating fashion. We were able to resolve TMS-deprotected oligomer 3-H₆ and demonstrate its extraordinarily strong chirooptical properties and to determine, experimentally and computationally, its large barrier for racemization. (28)

We generate and study radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈, using voltammetry and EPR spectroscopy. Computationally, we study radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈ and employ their analogues 1^•+-H₁₂ and 2^•+-H₈ as model compounds. In addition, we investigate computationally the corresponding diradical dications, as well as the barriers for racemization in oligomer 2-H₈.

MATERIALS AND METHODS

General Procedures:

Standard techniques for synthesis under inert atmosphere (argon or nitrogen) used custom-made Schlenk glassware, custom-made double-manifold high-vacuum lines, argon-filled Vacuum Atmospheres and MBraun gloveboxes, and nitrogen- or argon-filled glovebags. Chromatographic separations were carried out using normal-phase silica gel. Dichloromethane (DCM) was obtained from commercial solvent purification system (LC Technology Solutions), then distilled from calcium hydride under nitrogen, and stored in the absence of light in a Schlenk vessel on a vacuum line. Dibutyl phthalate (DBP) was obtained from commercial sources; prior to use, it was dried over calcium hydride (CaH₂), and then distilled under vacuum (~10 mTorr).

High-resolution MALDI MS spectra were obtained on a 15-Tesla FT-MS instrument equipped with solarix XR MALDI source.

Electrochemistry:

Cyclic and square wave voltammetric data for racemic double helices 1-TMS₁₂ and 2-TMS₈, using ferrocene as a reference, were obtained according to the following procedure.(21,29,30) The double helix 1-TMS₁₂ (1.49 mg, 0.81 μmol) or 2-TMS₈ (1.61 mg, 1.31 μmol) was evacuated in Schlenk vessel at 60 °C overnight and then filled with argon. Supporting electrolyte solution was prepared as follows: tetrabutylammonium hexafluorophosphate (116.9 or 155.7 mg) was loaded into a Schlenk vessel in an argon-filled glovebox and then placed on vacuum line and evacuated at 60 °C overnight; subsequently, DCM (~3 or ~4 mL) was added by vacuum transfer to form a homogeneous solution. The ferrocene (~0.8 or ~1.0 mg) was weighted to a small vial in argon-filled glovebox and then kept in the antechamber. All these items, including the electrochemical cell in the Schlenk vessel, which was thoroughly evacuated for many days, were placed in the Ar-filled glovebag. (The supply gas was a commercial ultra-high purity argon, certified to contain <1 ppm of O₂ and <1 ppm of H₂O.) The supporting electrolyte solution (~2.4 mL) was transferred to the electrochemical cell and a set of background data was obtained using cyclic and square wave voltammograms, with potential increments of 2–3 mV. Then, a solution of double helix in supporting electrolyte (~0.3 mL) was added and a series of cyclic and square wave voltammograms was recorded. After that, a small amount (2 or 6 drops) of solution of ferrocene (0.8 mg Cp₂Fe in ~0.2 mL supporting electrolyte or 1.0 mg Cp₂Fe in ~0.5 mL supporting electrolyte) was added to the cell, to provide reference potentials (+0.46 V vs. SCE for Cp₂Fe/Cp₂Fe⁺ in DCM).(31) Cyclic and square wave voltammograms were obtained. Commercial potentiostat/galvanostat was used. Three electrodes, quasi-reference (Ag-wire), counter (Pt-foil), and working (100-μm Pt-disk), were employed.

Radical cations:

EPR spectra were obtained using Bruker CW EPR spectrometer (X-band EMXplus). For temperature control (400–95 K), EPR spectrometer was equipped with custom-made nitrogen flow system. Temperatures were calibrated using an additional thermocouple inserted to the EPR tube containing solvent.(22,32,33) DPPH powder (g = 2.0037) was used as a g-value reference. EPR spectra were simulated using EasySpin.(34)

Quantitative EPR spectroscopy for radicals in solutions was carried out using TEMPONE in the identical solvent, as a reference.(22,30,35). Typically, the solvent was thoroughly dried DCM. At each temperature, the radical-containing EPR tube was directly transferred from liquid nitrogen (or dry ice bath) to the cavity and measured. Then, the reference EPR tube was directly transferred from liquid nitrogen (or dry ice bath) to the cavity and measured. The sample and the reference were alternately measured 2 or 3 times. Spin concentrations were reported as percent of S = ½ spin, based upon concentration of radical precursor, 1-TMS₁₂ or 2-TMS₈; e.g., 50% (n = 3), where n is the number of independent measurements.

Radical cations:

1^•+-TMS₁₂ and 2^•+-TMS₈ were generated by chemical oxidation of the corresponding neutral compounds, using tungsten hexachloride (WCl₆) in DCM as an oxidant, E^+/0 ≈ +1.56 V vs SCE.(31) Some attempts were made using silver tetrafluoroborate (AgBF₄) in DCM, E^+/0 ≈ +1.11 V vs SCE (31), to generate 1^•+-TMS₁₂ but the resulting solution showed low spin concentrations.

In an alternative procedure [NO][SbF₆] in dibutylphthalate (DBP) was used as an oxidant (E^+/0 = +1.46 V in DCM and +1.27 V in acetonitrile),(31) followed by quenching with bis(pentamethylcyclopentadienyl)iron(II) (Cp*₂Fe).(22) Partially deprotected product, 1-TMS₈, was isolated in 72% yield, as described in the Supporting Information (Figures S6 – S8, Supporting Information). Notably, under similar conditions, oxidation of 2-TMS₈, followed by quenching with Cp*₂Fe, gave starting material 2-TMS₈ in 66% isolated yield (Figures S9 – S11, Supporting Information).

Oxidation of 1-TMS₁₂ with WCl₆ was carried out as outlined in the following two procedures.

Procedure A: radical cation kept at room temperature.

1-TMS₁₂ (0.47 mg, 0.255 μmol) in a small amount of DCM was transferred into a custom-made 4-mm O.D. EPR tube, equipped with a high-vacuum Kontes stopcock. Subsequently, the solvent was evaporated on the vacuum line (p = 1 mTorr) at room temperature overnight. DCM (0.28 mL) was added by vacuum transfer to give a transparent solution. Subsequently, the solution was cooled to −78 °C, and the oxidant WCl₆ in DCM (70 μL, 0.9 equiv, 0.00337 mmol/mL) was added under argon gas flow to produce 0.66 mM solution. The color of the reaction mixture changed from colorless to dark blue. The reaction mixture was mixed with stir bar at −78 °C and gently degassed. After 0.5 h at −78 °C, EPR spectra at 195 K showed a singlet peak and the signal intensity did not change for at least 100 min. Using TEMPONE in DCM as reference, spin concentration of the sample was determined to be 53 % (n = 3) at 195 K. Then, EPR spectra were obtained at 117 K; broadened singlet peak was observed in the |Δm_S| = 1 region and no half-field (|Δm_S| = 2) signal could be detected. Subsequently, EPR spectra were obtained at 293 K to check stability at room temperature. Somewhat broadened singlet peak was found and the EPR signal almost disappeared after 30 min. Color of the sample changed from dark blue to light blue, and finally light yellow.

The light-yellow solution was transferred to a vial and evaporated by nitrogen gas flow to give white solid (0.51 mg). ¹H NMR (400 MHz, CDCl₃) and HR MALDI mass spectra show that the product contains a moderate amount of recovered starting material 1-TMS₁₂ and mainly the mixture of partially TMS-deprotected derivatives, including mono-deprotected 1-TMS₁₁ and isomers of di-deprotected 1-TMS₁₀ (FiguresS12 – S18, Supporting Information).

Procedure B: radical cation kept at T ≤ 195 K.

1-TMS₁₂ (0.49 mg, 0.266 μmol) and DCM (0.273 mL) were used to prepare a transparent solution, as described in Procedure A. The solution was cooled to −78 °C, and the oxidant WCl₆ in DCM (75 μL, 1.1 equiv, 0.00405 mmol/mL) was added under argon gas flow. The color of the reaction mixture immediately changed from colorless to dark blue. The reaction mixture was mixed with stir bar at −78 °C and gently degassed. After 1 hour, EPR spectra were obtained at 117 K and 195 K; singlet peak was observed in all spectra. Spin concentration of the solution was determined to be ~100 % (n = 2) at 195 K, using TEMPONE in dichloromethane as reference.

The EPR tube was attached to the vacuum line and the reaction mixture was quenched by addition of Cp*₂Fe (2.1 mg, ~20 eq) in DCM (0.5 mL) under argon gas flow, while stirred at −78 °C. The initial dark blue solution changed its color to light yellow. After 5 min, the solution was transferred to a vial and evaporated by nitrogen gas flow to give green crude solid, which was purified by PTLC (normal silica gel, pentane/ethyl acetate, 10:1) to obtain a white solid (0.18 mg, 37%). ¹H NMR spectrum (400 MHz, CDCl₃) showed the white solid was starting material 1-TMS₁₂ (Figure S21, Supporting Information); this was confirmed by HR MALDI MS (FiguresS22 and S23, Supporting Information).

Oxidation of 1-TMS₁₂ with AgBF₄.

1-TMS₁₂ (0.36 mg, 0.195 μmol) in a small amount of DCM was transferred into a custom-made 4-mm O.D. EPR tube, equipped with a high-vacuum Kontes stopcock. The solvent was evaporated on the vacuum line (p = 1 mTorr) at room temperature overnight. DCM (~0.1 mL) was added by vacuum transfer to obtain a transparent solution of 1-TMS₁₂. Subsequently, the solution was cooled to −30 °C, and AgBF₄ in DCM (205 μL, 10.0 equiv, 0.0095 mmol/mL) was added under argon gas flow to produce 0.54 mM solution of 1^•+-TMS₁₂ /1-TMS₁₂. The reaction mixture was mixed with stirbar at −30 °C and gently degassed. The reaction mixture remained colorless. After 20 min, EPR spectra were obtained at 295 K; a weak singlet peak was observed. Spin concentration was <1%. After about 0.5 h at 295 K, a small side peak was detected, most likely due to decomposition of 1^•+-TMS₁₂. Data fit for 1^•+-TMS₁₂: S = ½, g = 2.0016, lwpp(Gaussian) = 0.0345 mT, lwpp(Lorentzian) = 0.0271 mT, rmsd = 0.009062.

Oxidation of 2-TMS₈ with WCl₆.

Procedure A: oxidation at T = 195 K.

2-TMS₈ (0.60 mg, 0.488 μmol) in a small amount of DCM was transferred into a custom-made 4-mm O.D. EPR tube, equipped with a high-vacuum Kontes stopcock. The solvent was evaporated under vacuum at room temperature overnight. DCM (0.212 mL) was added by vacuum transfer to give a transparent solution. The solution was cooled to −78 °C, and the oxidant WCl₆ in DCM (190 μL, 1.2 equiv, 0.00302 mmol/mL) was added under argon gas flow. Color of the reaction mixture changed from colorless to dark green. The reaction mixture was mixed with stir bar at −78 °C and gently degassed, to produce 1.21 mM solution. The sample was kept at −78 °C for about 1 h before the EPR spectra were obtained at 195 K. Sharp singlet peak was found and the peak intensity did not change for at least 170 min at 195 K. EPR spectra at 117 K provided a broad singlet peak in the |Δm_S| = 1 region; no half-field (|Δm_S| = 2) signal could be detected. EPR spectra were obtained again at 195 K to check the sample integrity. After the temperature of the cavity was set to 293 K, a broad singlet peak spectrum was recorded and the peak intensity did not change for at least 150 min. Spin concentration of the sample was determined to be 67 % (n = 3) at 195 K and 38 % (n = 3) at 293 K, using TEMPONE in DCM as reference.

The EPR tube was attached to the vacuum line and the reaction mixture was quenched at room temperature by addition of Cp*₂Fe (1.6 mg, ~10 eq) in DCM (0.5 mL) under argon gas flow. The initial dark green solution changed its color to light yellow. The solution was transferred to a vial after 5 min and the solvent was evaporated by nitrogen gas flow to give green crude solid. The crude solid was purified by PTLC using 1 % ethyl acetate in pentane as eluent to give 2-TMS₈ (0.45 mg, 75%) (Figure S25, Supporting Information)

Procedure B: oxidation at room temperature.

2-TMS₈ (0.48 mg, 0.39 μmol) and DCM (~0.2 mL) were used to prepare a transparent solution, as described in Procedure A. WCl₆ in DCM (110 μL, 1.0 equiv, 0.00362 mmol/mL) was added under argon gas flow at room temperature. The color of the reaction mixture changed from colorless to dark green. The reaction mixture was mixed with stir bar at room temperature and gently degassed, to produce 1.20 mM solution. After 20 min at rt, broad singlet EPR spectra were obtained at 293 K. Position of sample tubes in the EPR cavity was adjusted to optimize the Q-value at 293 K (Q-value: 800–900). Spin concentration of the sample was determined to be 41% (n = 3) at 293 K, using TEMPONE in DCM as reference.

The EPR tube was attached to the vacuum line, and the stirred reaction mixture was quenched at room temperature by addition of Cp*₂Fe (1.3 mg, 10 eq) in DCM (0.5 mL) under argon gas flow. The initial dark green solution changed to light yellow. The solution was transferred to a vial after 5 min and the solvent was evaporated by nitrogen gas flow to give green crude solid. The crude solid was purified by PTLC using 15 % benzene in pentane as eluent to give 2-TMS₈ (0.40 mg, 83%) (Figure S26, Supporting Information).

Computational details:

All geometry optimizations for 1-H₁₂, 2-H₈, and their radical cations and diradical dications were carried out at the UB3LYP/6-31G(d,p) level of theory, in the gas phase, using Gaussian 09 or 16.(36,37) All geometry optimizations for 1-TMS₁₂, 2-TMS₈, and their radical cations and diradical dications were carried out at the UB3LYP/6-31G(d) level of theory, in the gas phase, using Gaussian 09 or 16.(36,37) Geometry optimizations of radical cations of 1-H₁₂, 2-H₈, 1-TMS₁₂, 2-TMS₈ were also carried out employing Head-Gordon’s long-range corrected hybrid functional ωB97xD;(38) Gaussian 16 default solvent model for water, that is polarizable continuum model employing the integral equation formalism (IEF PCM), was used. All computations in Gaussian 09 were carried out with keyword int=(grid=ultrafine), which is default in Gaussian 16. All stationary points on the potential energy surface (PES) were characterized by vibrational frequency calculations; transition states, which possessed one imaginary frequency, were further characterized by intrinsic reaction coordinate (IRC) computations. Where needed, IRC calculations used the alternative local quadratic approximation (LQA) approach.

For diradical dications, the broken-symmetry approach was applied for open-shell singlet calculations and spin contamination errors were corrected by approximate spin-projection method (Eq. 1).(39–41)

$$\Delta E_{\text{ST}}=\Delta E_{\text{U}}\left[<{S^2}_{\text{T}}>/\left(<{S^2}_{\text{T}}>–<{S^2}_{\text{BS}}>\right)\right]$$ (1)

In eq. 1, the calculated energy difference (ΔE_U) between the triplet and broken-symmetry (BS) singlet states is modified by the mean values of S² operator, to provide corrected values of singlet-triplet energy gaps (ΔE_ST). Selected BS singlet wavefunctions (<S²> ≈ 1.0) and radical cation doublet wavefunctions ((<S²> ≈ 0.75) were checked for stability (Gaussian 16 keyword: stable=opt).

Spin density surfaces for radicals were calculated using either UωB97xD or UB3LYP functionals with 6-31G(d,p) or 6-31G(d) basis sets. Cube files were obtained using “medium” setting in Gaussian 16 (or 09), and surfaces were plotted with isodensity of 0.001 or 0.002 electron/Bohr³. MO isodensity plots were obtained by generating individual cube files for each MO in Gaussian 16 utility using “coarse” setting and the surfaces were plotted with isodensity of 0.02 electron/Bohr³.

EPR parameters (g-tensor and ¹H A-tensors) for double helical radical cations, 1^•+-TMS₁₂ and 2^•+-TMS₈, were calculated using the B3LYP density functional (as implemented in ORCA)(42) and 6-31G(d) basis sets. No symmetry constraints were placed on the wave function. Using analogous approach, EPR parameters (D-tensor, g-tensor, and ¹H A-tensor) for triplet states of diradical dications were computed. All calculations used the previously optimized UB3LYP/6-31G(d) geometries (Gaussian 09). Input files were prepared using Gabedit.(43) Quasi-restricted B3LYP density functional was used (“uno” option in ORCA). Calculations of D-tensor employed spin-spin dipolar coupling only.(44) Absolute values of D and E are typically overestimated compared to the experiment,(45–48) though, for recently studied N-centered diradical dication, based on double helicene, good agreement with the experiment was obtained.(22) For g-tensor, origin was set at the center of electronic charge (Ori = −3), and the calculations were carried out using ORCA default (“gTensor 1”) using coupled-perturbed Kohn–Sham (CP-KS) theory.(42)

RESULTS AND DISCUSSION

DFT computations:

We carry out DFT computations on radical cations and diradical dications of the double helices 1-H₁₂, 2-H₈, 1-TMS₁₂, and 2-TMS₈ in the gas phase using UB3LYP functional and either 6-31G(d,p) or 6-31G(d) basis set. In addition, geometries for various states of radical cations were optimized in solvent model for water (or DCM), using UωB97xD functional with either 6-31G(d,p) or 6-31G(d) basis set (Tables 1 and 2).

Table 1.

Summary of DFT geometry optimizations for model double helices 1-H₁₂ and 2-H₈.

Double helix	Species	DFT	Phase	Point group	Statea	E°	E° + ZPVE	<S2>	RMSFb	ΔESTc
1-H12	Neutral	RB3LYP/6-31G(d,p)	Gas	D 2	1 A	−6616.97787175	−6616.495447	0.0000	0.53	-
		RωB97xD/6-31G(d,p)	Water	D 2	1 A	−6616.21053107	−6615.718911	0.0000	0.91	-
	Radical cation	UB3LYP/6-31G(d,p)	Gas	D2	2A*	−6616.74247592	−6616.261193	0.7532	0.15	0.00
				D 2	2B3*	−6616.74216352	−6616.260638	0.7535	0.33	0.35
		UωB97xD/6-31G(d,p)	Gas	C2	2 A*	−6615.93292566	−6615.442195	0.7653	0.48	0.00
				D2	2 A	−6615.91998494	−6615.428891	0.7572	0.14	8.35
			Water	C 2	2A*	−6615.99664378	−6615.506597	0.7656	0.64	0.00
				C 2	2B**	−6615.97029825	−6615.479896	0.7677	0.56	16.76
				D2	2A**	−6615.96920638	−6615.479062	0.7572	0.14	17.28
					2B3*	−6615.96913394	−6615.478994	0.7572	0.35	17.32
	Diradical Dication	UB3LYP/6-31G(d,p)	Gas	D 2	3 B 3	−6616.44085771	−6615.959542	2.0153	0.33	0.00
				D 2	BS	−6616.44085823	−6615.959542	1.0151	0.42	0.00
		UωB97xD/6-31G(d,p)	Water	C 1	3A*	−6615.77515650	−6615.286170	2.0414	0.58	0.00
				C 1	BS*	−6615.77521686	−6615.286236	1.0413	0.60	−0.08
				C2-TSd	3 A	−6615.76006658	−6615.272561	2.0235	1.04	8.54
				C2	BS*	−6615.76332003	−6615.273248	0.8337	0.72	8.11
2-H8	Neutral	RB3LYP/6-31G(d,p)	Gas	D 2	1 A	−4412.11489175	−4411.779383	0.0000	1.34	-
		RωB97xD/6-31G(d,p)	Water	D 2	1 A	−4411.60196359	−4411.260551	0.0000	0.65	-
	Radical cation	UB3LYP/6-31G(d,p)	Gas	D 2	2A*	−4411.86606767	−4411.531986	0.7572	0.28	-
		UωB97xD/6-31G(d,p)	Water	D 2	2A*	−4411.38181132	−4411.043314	0.7646	1.12	0.00
				C 2	2A*	−4411.37638802	−4411.035133	0.7641	1.07	5.13
				D 2	2B3**	−4411.34844245	−4411.007716	0.7560	0.41	22.34
	Diradical Dication	UB3LYP/6-31G(d,p)	Gas	D 2	3B3*	−4411.51561479	−4411.182737	2.0094	0.79	0.00
				D 2	BS*	−4411.51425044	−4411.181289	0.9288	0.39	1.69
2A-H8	Dication	RB3LYP-6-31G(d,p)	Gas	C 2	1 A	−4411.47860564	−4411.142573	0.000	0.58	25.2

^a”*” Means wave function was checked for stability and it was found stable, while “**” implies that the wave function was unstable; BS = BS singlet = broken-symmetry singlet state.

^bRMSF = Gradient norm ×10⁶ in Cartesian coordinates.

^cΔE_ST in kcal mol⁻¹: corresponds to either singlet-triplet energy gap in dications or relative energies of doublet states for radical cations in water solvent model.

^dFor C₂-TS transition state of triplet (³A) state of diradical dication, 1^2•2+-H₁₂, one imaginary frequency (B, i88.2 cm⁻¹) is found.

Table 2.

Summary of DFT geometry optimizations for double helices 1-TMS₁₂ and 2-TMS₈.

Double helix	Species	DFT	Phase	Point group	Statea	E°	E° + ZPVE	<S2>	RMSFb	ΔESTc
1-TMS12	Neutral	RB3LYP/6-31G(d)	Gas	D 2	1 A	−11521.1041150	−11519.394600	0.0000	1.47	-
	Radical cation	UB3LYP/6-31G(d)	Gas	D 2	2A*	−11520.8844548	−11519.177258	0.7526	0.12	-
		UωB97xD/6-31G(d)	Water	C2-TSd	2A*	−11519.6354095	−11517.908593	0.7658	4.39	0.00
				D 2	2B2**	−11519.6110205	−11517.883634	0.7695	0.05	15.66
				D 2	3B3**	−11519.5995006	-	0.7571	-	-
	Diradical Dication	UB3LYP/6-31G(d)	Gas	D 2	3B3*	−11520.60789350	−11518.900448	2.0151	0.08	0.00
				D 2	BS*	−11520.60789550	−11518.900450	1.0149	0.05	0.00
2-TMS8	Neutral	RB3LYP/6-31G(d)	Gas	D 2	1 A	−7681.51176494	−7680.357925	0.0000	0.16	-
		RωB97xD/6-31G(d,p)	Water	D 2	1 A	−7680.68766701	−7679.520889	0.0000	0.27	-
	Radical cation	UB3LYP/6-31G(d)	Gas	D 2	2A*	−7681.28352013	−7680.131298	0.7585	0.21	-
		UωB97xD/6-31G(d)	DCM	D 2	2A*	−7680.47449531	−7679.309596	0.7681	0.27	-
			Water	D 2	2A*	−7680.47959299	−7679.314678	0.7682	0.18	0.00
				D 2	2B1**	−7680.45670988	−7679.289821	0.7698	0.08	15.60
				D 2	2A**	−7680.43701882	−7679.273042	0.7573	0.23	26.13
	Diradical Dication	UB3LYP/6-31G(d)	Gas	D 2	3B3*	−7680.95227731	−7679.801830	2.0117	0.20	0.00
				D 2	3B1*	−7680.95128457	−7679.800571	2.0218	0.12	0.79
				D 2	BS*	−7680.95439007	−7679.802910	0.6410	7.45	−0.99
2A-TMS8	Dication	RB3LYP/6-31G(d)	Gas	C 2	1 A	−7680.88039117	−7679.726708	0.0000	0.37	47.14

^a”*” Means wave function was checked for stability and it was found stable, while “**” implies that the wave function was unstable; BS = BS singlet = broken-symmetry singlet state.

^bRMSF = Gradient norm ×10⁶ in Cartesian coordinates.

^cΔE_ST in kcal mol⁻¹: corresponds to either singlet-triplet energy gap in dications or relative energies of doublet states for radical cations in water solvent model.

^dFor C₂-TS transition state of doublet (²A) state of radical cation, 1^•+-TMS₁₂, one imaginary frequency (B, i45.4 cm⁻¹) is found; the minimum structure could not be located.

SOMO-HOMO inversions in radical cations.

Invariably, global minima for all radical cations correspond to ²A states. In the gas phase, all species, that is neutral, radical cations and diradical dications, possess D₂-symmetric global minima, when using B3LYP functional. Notably, we observe SOMO-HOMO inversions in radical cations. However, the recent literature suggests that, for some radical ions, such as 4-carboxy-TEMPO (Fig. 1), SOMO-HOMO inversions exist in the gas phase but do not exist in polar solvents, such as water, and when using density functionals that account for dispersion.(15–17) We and others found that in π-conjugated radical cations, the SOMO-HOMO inversions tend to persists in polar solvents.(19,21,22) We now study SOMO-HOMO inversions in radical cations using the more reliable, long range- and dispersion-corrected UwB97xD functional,[38] in conjunction with the PCM solvent model for water. We are surprised to discover that at this level of theory radical cation 1^•+-H₁₂ adopts C₂-symmetric global minimum, while 2^•+-H₈ and 2^•+-TMS₈ are D₂-symmetric. Analogous to 1^•+-H₁₂, radical cation 1^•+TMS₁₂ has symmetry-broken structure (Tables 1 and 2). This symmetry-breaking is perhaps most strikingly illustrated by their spin density distribution maps (Fig. 3).

Figure 3.

Spin density distributions for radical cations (²A-states) at the UwB97xD/6-31G(d,p)+ZPVE or UwB97xD/6-31G(d)+ZPVE level of theory, using PCM solvent model for water: A and C, 1^•+-H₁₂ and 1^•+-TMS₁₂ (both C₂-symmetric) and, B and D, 2^•+-H₈ and 2^•+-TMS₈ (both D₂-symmetric). All surfaces were plotted with isodensity of 0.001 electron/Bohr³. E and F: X-ray structures for effectively D₂-symmetric 1-TMS₁₂ and 2-TMS₈ are shown for reference.(28)

For 1^•+-H₁₂, the C₂-symmetric ²A state is more than 17 kcal mol⁻¹ lower in energy than D₂-symmetric ²B₃ state at the UωB97xD/6-31G(d,p)+ZPVE level in water. This is in contrast to the UB3LYP/6-31(d,p)+ZPVE results in the gas phase, where D₂-symmetric the ²A state is only 0.35 kcal mol⁻¹ below the ²B₃ state (Table 1). We note that D₂-symmetric ²A state and C₂-symmetric ²B state at the UωB97xD/6-31G(d,p)+ZPVE level in water have unstable wave functions (Table 1), which give C₂-symmetric ²A state upon complete re-optimization.

In all studied radical cations, spin densities are predominantly delocalized over a single α,β-cyclooctatetrathiophene (α,β-COTh) moiety. Almost no spin density is found in the adjacent β,β-cyclooctatetrathiophene (β,β-COTh) moieties or the other two α,β-COTh moieties of 1^•+-H₁₂ and 1^•+-TMS₁₂. In addition, as shown in Fig. 3, spin densities on the second-row sulfur and silicon atoms are negligible; that is, overwhelming fraction of spin density is delocalized over the carbon atoms, with important implications for their EPR spectra (vide infra).

In C₂-symmetric 1^•+-H₁₂ (and 1^•+-TMS₁₂), the cyclooctatetraene ring bearing the spin density in the α,β-COTh moiety shows lesser extent of bond length alternation, i.e., β,β- and α,α- vs. α,β-linkages in Table 3, compared to the ring of opposite terminal α,β-COTh moiety without spin density. In addition, the bond lengths between the most outer dithiophene β,β-linkages are C3-C7 = 1.443 and C58-C61 = 1.474 Å (Table 3, left column).

Table 3.

Atom numbering scheme for radical cation 1^•+-H₁₂ and the selected bond lengths.

8-memb. ring	Bond lengths (Å)
	β,β	α,α	β,β	α,β	α,β
with spin density	C3–C7 = 1.443	C4–C12 = C8–C9 = 1.433	C10–C11 = 1.457	C3–C4 = C7–C8 = 1.410	C9–C10 = C11–C12 = 1.397
without spin density	C58–C61 = 1.474	C52–C55 = C56–C60 = 1.462	C46–C53 = 1.475	C55–C58 = C60–C61 = 1.375	C45–C52 = C53–C56 = 1.372

We observe the SOMO-HOMO energy inversions of about 13.08 and 4.20 kcal mol^–1, as indicated by the difference of energies of the relevant α orbitals for 1^•+-H₁₂ and 2^•+-H₈ in their lowest energy ²A states at the UωB97xD/6-31G(d,p) level in water solvent model (Figs. 4 and 5). While 1^•+-TMS₁₂ shows analogous inversion (12.83 kcal mol^–1), 2^•+-TMS₈ does not show SOMO-HOMO energy inversion (Figures S1 and S2A, Supporting Information). Also, the inversion is not found in 2^•+-TMS₈, when using less polar solvent, such as DCM – relevant to the experiments (vide infra), and UωB97xD functional (Figure S2B, Supporting Information).

Figure 4.

Orbital maps for the C₂-symmetric double helical structure of model radical cation 1^•+-H₁₂ (²A state) at the UωB97xD/6-31G(d,p) level, using water PCM solvent model. The molecule is oriented exactly as shown in Table 3 and Fig. 3; SOMO largely describes spin density. Positive (red) and negative (blue) contributions are shown at the isodensity level of 0.02 electron/Bohr. Singly occupied α orbital is matched in a nodal pattern (a symmetry) to the lowest unoccupied β orbital to provide the SOMO energy level. Doubly occupied molecular orbitals are identified by matching nodal patterns (a, a, and b symmetry for HOMO, SHOMO, and S2HOMO) and energies (in Hartrees) of the α and β occupied orbitals.

Figure 5.

Orbital maps for the D₂-symmetric double helical structure of model radical cation 2^•+-H₈ (²A state) at the UωB97xD/6-31G(d,p) level, using water PCM solvent model. The molecule is oriented exactly as shown in Fig. 3; SOMO largely describes spin density. Positive (red) and negative (blue) contributions are shown at the isodensity level of 0.02 electron/Bohr. Singly occupied α orbital is matched in a nodal pattern (a symmetry) to the lowest unoccupied β orbital to provide the SOMO energy level. Doubly occupied molecular orbitals are identified by matching nodal patterns (a and b₃ symmetry for HOMO and SHOMO) and energies (in Hartrees) of the α and β occupied orbitals.

Typically, the inversion is associated with improved stability of the radical (vide infra, EPR spectroscopy section),(16–19,21) and a triplet ground state with significant ΔE_ST in the corresponding diradical dication that is formed upon one-electron oxidation radical cation.(13,21,22) For 2^2•2+-H₈, triplet ground state with a significant ΔE_ST is computed and for 2^2•2+-TMS₈, singlet ground state is predicted (Tables 1 and 2); these results correspond to SOMO-HOMO inversion in 2^•+-H₈ and absence of it in 2^•+-TMS₈. Although the magnitude of the SOMO-HOMO inversions in radical cations 1^•+-H₁₂ and 1^•+-TMS₁₂ are much more pronounced than that in 2^•+-H₈, the corresponding diradical dications 1^2•2+-H₁₂ and 1^2•2+-TMS₁₂ have near degenerate triplet and singlet ground states. This suggests the different origins of SOMO-HOMO inversion in 1^•+-H₁₂ and 2^•+-H₈.

It is instructive to compare electronic configurations of the closed-shell 1-H₁₂, 2-H₈, and 2-TMS₈ obtained using B3LYP functional in the gas phase (Fig. 6).

Figure 6.

Near-degeneracy of HOMO and SHOMO in closed-shell D₂-symmetric 1-H₁₂ (gas phase, B3LYP).

Notably, in 1-H₁₂, the HOMO-SHOMO energy gap in the gas phase (B3LYP) is only 0.176 kcal mol⁻¹ and it is smaller than the analogous gap in 2-H₈ and 2-TMS₈ by a factor of about 20 – 50. In water at the ωB97xD/6-31G(d,p) or ωB97xD/6-31G(d) levels of theory, the HOMO-SHOMO energy gap is even smaller in 1-H₁₂ (0.088 kcal mol⁻¹) and the corresponding factors for 2-H₈ and 2-TMS₈ are about 30. This near degeneracy in 1-H₁₂ may be then responsible for symmetry breaking in radical cation 1^•+-H₁₂. For example, in terms of 2^nd order (pseudo) Jahn-Teller distortion, the product of these near degenerate, a- and b₃-symmetric MOs, a × b₃ = b₃, suggests that b₃ (symmetry-breaking) vibrational mode may possess a small or negative force constant in D₂-symmetric radical cation.(49,50) This is an analogous mechanism for symmetry breaking to that proposed for m-phenylene triarylmethyl radical anions, which were derived from dianions with near degenerate HOMO and SHOMO.(51–53) Recent computational analyses of radicals and radical cations, including that of azathia[7]helicene (Fig. 1), suggested, that not only strong electrostatic repulsion among the frontier orbitals and the repulsion between the α and β spin components of the orbitals but also, near degeneracies of HOMO and SHOMO in the closed-shell precursors may be a contributing factor to SOMO-HOMO inversions.(2,22)

Barrier for racemization of double helix 2-H₈: DFT computations.

We carry out DFT computations at the RB3LYP/6-31G(d,p)+ZPVE level of the stationary points at the potential energy surface (PES) for racemization of 2-H₈. We start with locating the first transition state, (MM)-TS1, in which two adjacent terminal di-thiophene moieties are approximately flattened, while the other two di-thiophenes possess chiral axes of M configuration (Table 4, Fig. 7). Interestingly, this transition state as well as its enantiomer, (PP)-TS1, are C₁-symmetric, not C₂-symmetric as we originally anticipated; these transition states are 50.00 kcal mol⁻¹ above the corresponding D₂-symmetric global minima (MMMM)- and (PPPP)-2-H₈. Then, the geometry optimization (to a minimum) of the C_2h-symmetric structure, in which two adjacent center di-thiophene moieties are approximately flattened, produces the second transition state, (PM)-TS2, as indicated by the presence of one imaginary frequency. This achiral transition state is 53.10 kcal mol⁻¹ above the global minima, and thus it determines the barrier for racemization. Optimization to a minimum of one of the extreme structures derived from IRC computations on (MM)-TS1 and (PM)-TS2 produces intermediate C₂-symmetric minima (MMP)-2-H₈ and (PPM)-2-H₈, respectively. These enantiomeric minima are 39.31 kcal mol⁻¹ above the corresponding D₂-symmetric global minima (Table 4 and Fig. 7). These results should be compared to previously studied racemization of 3-H₆ at the same level of theory, for which the stationary points along the racemization pathway are as follows: C₂-symmetric TS (M)-TS1 at 42.75 kcal mol⁻¹, local C₂-symmetric minimum (MP)-3-H₆ at 39.52 kcal mol⁻¹, and C₁-symmetric TS (P)-TS2 at 51.03 kcal mol⁻¹.(28) In summary, racemization of 2-H₈ is considerably more complex and the overall barrier is higher by about 2 kcal mol⁻¹, compared to that of 3-H₆.(28)

Table 4.

Barriers for ring inversion (racemization) in double helices 2-H₈ and 2-TMS₈ at the B3LYP/6-31G(d,p)+ZPVE and B3LYP/6-31G(d)+ZPVE levels of theory. (M)/(P) labels indicate configuration (helicity) of chiral axes associated with 3,3′-bithienylene moieties.

Stationary points	Point group	Critical point	Imaginary frequencies (cm−1)	E° + ZPVE	RMSF	Rel. energy (kcal mol−1)a
(PPPP)-2-H8	D 2	minimum	none	−4411.779383	1.34	0.00
(MM)-TS1	C 1	TS	i58.3	−4411.699706	3.07	50.00
(PP)-TS1	C 1	TS	i58.3	−4411.699706	3.07	50.00
(PPM)-2-H8	C 2	minimum	none IRC#1	−4411.716731	2.39	39.31
(MMP)-2-H8	C 2	minimum	none IRC#10	−4411.716731	2.56	39.31
(PM)-TS2	C 2h	TS	i38.8 (Au)	−4411.694759	1.14	53.10
(PPPP)-2-TMS8	D 2	minimum	none	−7680.357925	0.16	0.00
(PPM)-2-TMS8	C 2	minimum	none	−7680.301032	0.24	35.70
(MMP)-2-TMS8	C 2	minimum	none	−7680.301032	0.24	35.70
(PM)-TS2	C i	TS	i18.2 (Au)	−7680.288072	2.92	43.83
(MP)-2-TMS8	C2h	4 imaginary frequencies	i33.8 (Au), i33.5 (Bg), i19.5 (Au), i6.9 (Bg)	−7680.286728	0.22	44.68

^a1 Hartree = 627.51 kcal mol⁻¹.

Figure 7.

Potential energy surface for racemization of 2-H₈ at the B3LYP/6-31G(d,p)+ZPVE level of theory. (M)/(P) labels indicate configuration (helicity) of chiral axes associated with 3,3′-bithienylene moieties. For (PP)-TS1, (MPP)-2-H₈, and (PM)-TS2, the structures are oriented to show near-planar 3,3’-bithienylene moieties perpendicular to the plane of the paper (screen).

To estimate the barrier for racemization of 2-TMS₈, we start with the geometry optimization, using the C_2h symmetry constraint, to obtain (PM)-2-TMS₈, a structure analogous to the transition state, (PM)-TS2, for 2-H₈. However, frequency calculation reveals that the C_2h-symmetric (PM)-2-TMS₈ is not a transition state but a stationary point on the PES with 4 imaginary frequencies. Because three of these imaginary frequencies correspond to vibrational modes primarily twisting the TMS groups, the structure is distorted by twisting four interlocked TMS groups, and the subsequent re-optimization under the C_i symmetry constraint produces the desired transition state (PM)-TS2 for 2-TMS₈. Following IRC calculations on the C_i-symmetric (PM)-TS2, geometry optimizations with C₁-symmetry constraints, starting from the most extreme IRC structures, produce two C₂-symmetric enantiomeric minima (PPM)- and (MMP)-2-TMS₈ with the structures analogous to (PPM)- and (MMP)-2-H₈. Remarkably, both the intermediate minima and the central transition state, (PM)-TS2, are significantly lower in energy, compared to their 2-H₈ counterparts, presumably reflecting steric crowding of TMS groups in the D₂-symmetric minima of 2-TMS₈. Nevertheless, the predicted value of 43.8 kcal mol⁻¹ for the C_i-symmetric (PM)-TS2 suggests that racemization barrier of 2-TMS₈ is still significant and indicates robust configurational stability at room temperature and above. Unfortunately, we were not able to locate the transition state (MM)-TS1 and its racemic counterpart, in which TMS groups are very crowded.

Voltammetry studies of 1-TMS₁₂ and 2-TMS₈:

Both double helices, 1-TMS₁₂ and 2-TMS₈ have similar first oxidation potentials, E^+/0 ≈ +1.33 V, corresponding to reversible oxidation to their radical cations (Fig. 8). This finding is in agreement with DFT computations at the UωB97xD/6-31G(d,p) and UωB97xD/6-31G(d) levels in water PCM model, showing that in global minima of all double helical radical cations, the spin density is localized on a single ortho-tetrathienylene with two α,α-linked dithienyls, i.e., α,β-COTh moiety (Figs. 2 and 3). In contrast, the second oxidation potentials are considerably higher, E^2+/+ ≈ +1.65 and E^2+/+ ≈ +1.9 V, for 1-TMS₁₂ and 2-TMS₈, corresponding to only partially reversible oxidation to their diradical dications. These very high values of E^2+/+ make preparation of diradical dications challenging.

Figure 8.

Square wave voltammetry (SWV) of double helices 1-TMS₁₂ and 2-TMS₈ at room temperature in dichloromethane.

EPR spectroscopy of radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈:

Because voltammetry studies showed moderate values of the first oxidation potentials, E^+/0 ≈ +1.33 V, for 1-TMS₁₂ and 2-TMS₈, we focus our EPR spectroscopic studies on the corresponding radical cations. Treatment of 1-TMS₁₂ and 2-TMS₈ with WCl₆ in DCM at −78 °C produces EPR spectra exhibiting sharp singlet peaks at 195 K (Scheme 1, Fig. 9). At room temperature, the spectra are somewhat broadened (Fig. 10). However, for 1^•+-TMS₁₂, that was generated using AgBF₄ as an oxidant, the spectra at 295 K are remarkably sharp (Fig. 9C), presumably due to exchange narrowing occurring via fast electron spin exchange with the excess of double helix 1-TMS₁₂.

Scheme 1.

Generation of radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈ followed by reductive quenching according to the Procedure A.

Figure 9.

EPR spectra of radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈ in DCM. The radical cations are generated by treatment of 1-TMS₁₂ and 2-TMS₈ with WCl₆ (~1 equiv), except for 1^•+-TMS₁₂ at 295 K (C), which is generated using an excess of AgBF₄ (10 equiv). Simulation parameters are summarized in Table 5. A and B: spectra at 195 K. C and D: spectra at room temperature.

Figure 10.

Main plots: overlay EPR spectra (spectral width of 3 mT is shown) illustrating persistence of radical cations 1^•+-TMS₁₂ and 2^•+-TMS₈ in DCM at 195 K (A and B) and room temperature (C and D). The radical cations are generated by treatment of 1-TMS₁₂ and 2-TMS₈ with WCl₆ (~1 equiv), using Procedure A. Inset plots: linear regressions for −ln(DI) vs time, where DI is double integrated EPR intensity; for 1^•+-TMS₁₂ at 293 K, decay according to the first order rate equation with τ_1/2 = 5 min is found; slope = 0.1264 ± 0.0517 (95% CI), i.e., the slope or the first order rate constant is statistically well-determined (p = 0.0044 < 0.05). For insets A, B, and D, slope = 0.000428 ± 0.000878 (95% CI), slope = 0.000276 ± 0.000422 (95% CI), and slope = 0.000952 ± 0.00135 (95% CI); that is, the CI > slope, thus there are no statistically valid slopes (p > 0.05), and therefore, values of τ_1/2 are most likely very large.

Measurements of spin concentrations reveal approximate 40 – 100% concentrations of radical cations, based on concentrations of neutral precursors. Most surprisingly, g-values for these radical cations are very small, with g = 2.0017 and 2.0012 for 1^•+-TMS₁₂ and 2^•+-TMS₈, respectively (Table 5). This suggest that spin density in the radical cations does not significantly delocalize onto the heavier atoms, such as sulfur and silicon, but it is strictly confined to carbon (and hydrogen) atoms. This finding is in agreement with the DFT computed spin densities (Fig. 3). Also, ORCA computations of g-tensors for 1^•+-TMS₁₂ and 2^•+-TMS₈ provide isotropic g-values (g_iso) that are in excellent agreement with the experiment (Table 5). These g-values of 2.001 – 2.002 should be compared to the much larger values of g = 2.006 and 2.005 for radical cations of thia[7]helicene and azathia[7]helicene, for which there is a significant fraction (0.3 – 0.4 electrons) of spin density on sulfur atoms.(21,24)

Table 5.

Summary of EPR spectroscopic parameters for radical cations and diradical dications.

	Experiment		ORCA	Experiment		ORCA
	g iso		g iso	Linewidth (mT)a		D (MHz)	E (MHz)
	rt	195 K		rt	195 K
1•+-TMS12	2.0016b	2.0017c	2.0015	0.0375	0.0681	-	-
				0.0159b	0.0669c
2•+-TMS8	2.0012	2.0012	2.0013	0.0022	0.0034	-	-
				0.249	0.0821
12•2+-TMS12	-	-	2.0018d	-	-	37.08	0.66
22•2+-TMS8	-	-	2.0034d	-	-	344.46	44.12

^aPeak-to-peak linewidth with Gaussian and Lorentzian components in mT.

^b1-TMS₁₂ was oxidized with 10 equiv of AgBF₄.

^c1-TMS₁₂ was oxidized with 1.1 equiv of WCl₆; spin concentration ~100%, using Procedure B.

^dFor triplet states of diradical dications, components of g-tensor, g_XX, g_YY and g_ZZ, are: 2.0001, 2.0021, 2.0032 (1^2•2+-TMS₁₂) and 1.9996, 2.0022, 2.0084 (2^2•2+-TMS₈).

Both 1^•+-TMS₁₂ and 2^•+-TMS₈ are persistent at 195 K, with long half-lives (τ_1/2) on the order of hours (Fig. 10AB). We are surprised to find that 1^•+-TMS₁₂ undergoes a relatively fast decomposition at room temperature, with τ_1/2 ≈ 5 min (Fig. 10C). In contrast, 2^•+-TMS₈ is persistent at room temperature, with a long τ_1/2 on the order of hours (Fig. 10D). This finding is contrary to the common assumption that the SOMO-HOMO energy inversion, which is found in 1^•+-TMS₁₂ but not in 2^•+-TMS₈, contributes to a greater stability of radical or radical ion. We note that spin density in 1^•+-TMS₁₂ is confined to the terminal α,β-COTh moiety (Fig. 3) and the two carbon atoms with significant spin densities (–0.05 electron each, based on Mulliken population analysis) at the β-positions in thiophenes are substituted with hydrogen atoms. In 2^•+-TMS₈, spin density is confined to the centrally located α,β-COTh moiety (Fig. 3), in which all carbons bearing significant spin density are sterically shielded by the two adjacent β,β-COTh moieties and TMS groups. This would suggest that the steric shielding trumps the SOMO-HOMO energy inversion, thus leading to a greater persistence of 2^•+-TMS₈.

Supplementary Material

supinfo

Data S1. Additional computational details (Figures S1 and S2)

Data S2. Additional voltammetry data for 1-TMS12 and 2-TMS8 (Figures S3 – S5)

Data S3. Preparation of radical cations 1•+-TMS12 and 2•+-TMS8 in DBP, using NOSbF6 as an oxidant, and their reductive quenching products (Figures S5 – S11)

Data S4. Preparation of radical cations 1•+-TMS12 and 2•+-TMS8 in DCM, using WCl6 as an oxidant, and their reductive quenching products (Figures S12 – S26)

Data S5. Cartesian coordinates for optimized geometries of closed-shell neutral double helices, radical cations, and diradical dications