Variation from closed-shell to open shell electronic structures in oligothiophene bis(dioxolene) complexes

Abstract

A series of oligothiophene bis(dioxolene) complexes, SQ–Th_n–SQ (SQ = S = ½Tp^Cum,MeZn^II(3-tert-butyl-orthosemiquinonate); Tp^Cum,Me = tris(5-cumenyl-3-methylpyrazolyl)borate anion) have been synthesized, structurally characterized, and studied as a function of the number of thiophene bridging units, n (n = 0–3) using a combination of variable–temperature (VT) electronic absorption and EPR spectroscopies, and VT magnetic susceptibility measurements. The thiophene bridge bond lengths determined by X-ray crystallography display dramatic differences across the SQ–Th_n–SQ series. Bridge bond deviation values (Σ|Δ_i|) display a progressive change in the nature of the bridge fragment bonding as the number of thiophene groups increases, with quinoidal bridge character for n = 1 (SQ–Th–SQ) and biradical character with “aromatic” bridge bond lengths for n = 3 (SQ–Th₃–SQ). Remarkably, for n = 2 (SQ–Th₂–SQ) the nature of the bridge fragment is intermediate between quinoid and biradical aromatic, which we describe as having open-shell character as opposed to biradicaloid since the open-shell biradical configuration does not have the correct symmetry to mix with the quinoidal ground-state configuration. This bridge bonding character is reflected in the energies of the lowest lying open-shell states for these three molecules. The SQ–Th–SQ molecule is diamagnetic at all temperatures studied, and we provide evidence for SQ–SQ antiferromagnetic exchange coupling and population of triplet states in SQ–Th₂–SQ and SQ–Th₃–SQ, with J_SQ–SQ(ave) = −279 cm⁻¹ (VT EPR/electronic absorption/magnetic susceptibility) and J_SQ–SQ = −117 cm⁻¹ (VT EPR/electronic absorption/magnetic susceptibility), respectively. The results have been interpreted in the context of state configurational mixing within a simplified 4-electron, 3-orbital model that explicitly contains contributions of a bridge fragment. Variable–temperature spectroscopic- and magnetic susceptibility data are consistent with two low-lying open-shell states for SQ–Th₃–SQ, but three low-lying states (one closed-shell and two open-shell) for SQ–Th₂–SQ. This model provides a simple symmetry-based framework to understand the continuum of electronic and geometric structures of this class of molecules as a function of the number of thiophene units in the bridge.

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Introduction

Conjugated π-systems that possess biradical character^1–6 hold tremendous promise as novel architectures for molecular and molecule-based materials due to their remarkable magnetic, optical, and electronic properties. As a result, these π-conjugated biradical systems are expected to contribute to the organic semiconductor,^7–9 singlet fission,¹ break junction,¹⁰ spintronics,^11,12 non-linear optical, and exchange-coupled electron spin qubit^13–17 knowledge base and function as models for understanding the effects of dipolar coupling and molecular vibrations on spin relaxation.¹⁸ It has recently been shown that the introduction of biradicaloid character into the bridge fragment in break-junction molecular conductance studies dramatically modifies the distance dependence of the conductance,^10,19,20 leading to reversed conductance decay behavior where an increase in conductance with increasing molecular wire length is observed.^10,20 One-dimensional molecular wires typically display an exponential distance dependence on conductance in the coherent tunneling regime.^21–24 This biradicaloid conductance study²⁰ is important since, in the context of the Su, Schrieffer and Heeger model,^25,26 biradical species have 1-D topological insulator properties. Namely, they possess occupied and unoccupied delocalized states and localized topologically protected conducting edge states in the bandgap region.

Along with Chichibabin's hydrocarbon derivatives and analogs,^1,27–30 phenoxy radicals are the most common organic radical employed in the construction of conjugated π-systems with biradicaloid character, and their magnetic, optical, and vibrational properties have been extensively studied (Fig. 1A).^{1,3,4,31–36} These compounds display small HOMO–LUMO gaps, and the large spin density on the para-carbon of 3,6-di-tert-butylphenoxy³⁷ when bonded to thiophene bridge units results in strong through-bond coupled, closed-shell ground states that are NMR-active for bridges comprised of 0–4 thiophene units,^38–40 although characteristics of open-shell configurations have been reported for Phen–Th₂–Phen.^32,34 In contrast to oligothiophene-bridged structures, a single para-phenyl bridge unit results in a closed-shell quinoidal electronic structure,³⁶ but two-^41,42 or more para-phenylene bridge units result in thermally-accessible open-shell character. Understanding biradical electronic structure has been complicated due to various experimental issues and the challenging nature of the open-shell computational problem. Here, we present the results of a detailed structural, magnetic, and spectroscopic study on a series of SQ–Th_n–SQ (n = 0–3) molecules in order to gain greater insight into the electronic structure of these biradical systems, and discuss the results of these studies in terms of the quinoid, biradical, and biradicaloid character in the electronic ground and excited states of these molecules.

Fig. 1 (A) Kekulé π-systems comprised of phenoxy radical-terminated oligothiophenes. (B) Chichibabin's hydrocarbon, CH. (C) Bis(semiquinone) complexes presented in this study.

Biradicaloid systems have consistently been described in terms of two Lewis structures that are in resonance (Fig. 1). These resonance structures are the closed-shell quinoid form and open-shell biradical from, the latter of which derives from a HOMO → LUMO one-electron promotion. This idea leads to the possibility of a continuum of biradicaloid descriptions, with the biradical and quinoid forms at the extrema and “biradicaloid” describing a quantum mechanical admixture (i.e., resonance) of open-shell biradical and quinoid. Additional complexity exists in such systems where the open-shell biradical Lewis structure can distort (e.g., along a torsional coordinate), which leads to non-planar structures. Here, the electronic structures of the low-lying biradical and quinoid states have been described as being in thermal equilibrium with one another, although experimental evidence for this equilibrium has been limited.²⁹

The first biradicaloid was synthesized in 1907 (Chichibabin's hydrocarbon; CH, Fig. 1B)⁴³ and inspired decades of controversy that was described as the “Biradical Paradox”.^44,45 The paradox being: solution EPR of CH indicated |J| ≪ |a| (a = isotropic proton hyperfine coupling constant), despite clear evidence that |J| was in fact much larger than |a| due to the diamagnetic character displayed by the compound. Many studies were conducted to explain this phenomenon,^44–49 however it wasn't until 1987 that Montgomery, et al.⁵⁰ conclusively showed through X-ray diffraction that CH contained a quinoidal bond length pattern. Upon obtaining a pure sample of CH, it was actually found to be EPR silent due to the magnitude of |J|, and paramagnetic impurities (dimers,⁵¹ or radical quenching through proton abstraction⁵²) were responsible for the conflicting results. However, it is important to note that there are still non-covalent interactions between radicals that can complicate the analysis, and obfuscate the electronic structure description of biradicaloids.⁴⁵

Metal complexes of S = ½ orthosemiquinone (SQ) are powerful alternatives to phenoxy radical-based molecules since they allow for the inclusion of both diamagnetic and paramagnetic transition metal ions into the molecular scaffold. In addition, the spin density distribution of SQ vs. phenoxy places ∼65% less spin density for SQ at the point of attachment³⁷ to a bridging organic π-system (positions marked with “●” in Fig. 1A and C). Thus, the incorporation of SQ allows for thermal population of the triplet state at lower temperatures compared to phenoxy biradicals. Herein, we present dinuclear metal complexes comprised of two bridge terminal SQ groups, where both SQs are complexed to a diamagnetic (Tp^Cum,MeZn^II)⁺ complex ion (Tp^Cum,Me = tris(5-cumenyl-3-methylpyrazolyl)borate^53–55 bridged by 0–3 thiophene groups; Fig. 1C). The Tp^Cum,Me anionic ligand was first used for steric protection of SQ groups by Pierpont,⁵⁵ and subsequently by us.^21,56–61 Our crystallographic results clearly show a decrease in “quinoidal” bond lengths as the number of thiophene bridge fragments increases. This observation is consistent with both variable–temperature magnetic susceptibility results as well as variable–temperature electronic absorption spectroscopic studies, which illustrate thermal population of the exchange coupled triplet state with increasing temperature. In addition, we present molecular orbital (MO) and state models that provide a fundamental symmetry-based framework to understand the continuum of electronic structures in this class of molecules as a function of the number of thiophene units in the bridge.

Results and analysis

Here, we present synthetic results, X-ray crystallographic results, and associated analyses for the SQ–SQ, SQ–Th–SQ, SQ–Th₂–SQ, and SQ–Th₃–SQ series of compounds. Since their ground state electronic structures span a continuum from closed-shell singlet quinoidal to open-shell singlet biradical, we will present analyses of the magnetic and spectroscopic results together for each compound at the end of this section. Detailed computations and electronic absorption band assignments for SQ–Th–SQ and SQ–Th₂–SQ and SQ–Th₃–SQ are beyond the scope of this manuscript and will be presented elsewhere.

Synthesis and structural data

Synthetic details and structural data are presented in the ESI† and below for all complexes in this study.

Synthesis of SQ–Th_n–SQ molecules. A series of oligothiophene bis(semiquinone) complexes (SQ–SQ, SQ–Th–SQ, SQ–Th₂–SQ, and SQ–Th₃–SQ) were synthesized as illustrated in Scheme S1 (see ESI†). Suzuki coupling of the oligothiophene (n = 1–3) dibromide with MOM₂CatBpin yielded the respective (MOM₂Cat)₂Th_n (n = 1–3). Methoxymethyl (MOM) deprotections are performed by subjecting (MOM₂Cat)₂Th_n (n = 1–3) to concentrated HCl in CH₂Cl₂/MeOH and stirring overnight. Scheme S2† illustrates the differing synthetic pathway toward SQ–SQ. Suzuki coupling of MOM₂CatBpin to MOM₂CatBr yields (MOM₂Cat)₂, which is then subjected to the same sequence of reactions as the SQ–Th_n–SQ series. Complexing Cat₂Th_n (n = 0–3) with Tp^Cum,MeZn(OH) in the presence of K₂CO₃ in CH₂Cl₂/MeOH was then performed under an inert atmosphere. Subsequently, the reactions were then opened to air and stirred overnight to allow for CAT oxidation to SQ to yield the final complexes.

X-ray crystallographic structure determination and analysis. X-ray quality crystals were grown for SQ–SQ and SQ–(Th)_n–SQ (n = 1–3) and their structures were obtained via X-ray diffraction (Fig. 2, 3 and Table S4†). The average ring torsion angles for the dioxolene groups relative to each other (SQ–SQ) or relative to the bridge (SQ–Th_n–SQ) are 0.64° (SQ–SQ), 3.93° (SQ–Th–SQ), 10.16° (SQ–Th₂–SQ), and 14.76° (SQ–Th₃–SQ). We also calculate bond deviation parameters, Σ|Δ_i|, from the absolute value of the difference between the bond lengths of the dioxolene moieties for each compound and those of 3,5-di-tert-butyl-1,2-semiquinonate (Table S4†), which can be considered a “non-delocalized into a bridge fragment” semiquinone radical.⁶² Bond deviation parameters highlight bond length changes that signify delocalization of the SQ π-system into the bridge, and the values of Σ|Δ_i| for SQ–Th–SQ, SQ–Th₂–SQ, and SQ–Th₃–SQ are 0.150 ± 0.019 Å, 0.119 ± 0.014 Å, and 0.080 ± 0.017 Å, respectively. Bond length deviation parameters were also determined for thiophene bridges by comparing the bridges of SQ₂Th, SQ₂Th₂, and SQ₂Th₃ to their respective diamagnetic, fully aromatic analogs 2,5-diphenyl-thiophene,⁶³ 5,5′-diphenyl-2,2′-bithiophene,⁶⁴ and 3′,4′-dibutyl-5,5′′-diphenyl-2,2′:5′,2′′-terthiophene, respectively.⁶⁵ Only bonds between atoms within the oligothiophene π-system, excluding substituents, were included in the calculation of Σ|Δ_i|. The bridge Σ|Δ_i| values were 0.110 ± 0.024 Å (SQ–Th–SQ), 0.081 ± 0.017 Å (SQ–Th₂–SQ), and 0.026 ± 0.028 Å (SQ–Th₃–SQ), which suggests a trend toward a more aromatic bridge unit in going from SQ–Th₂–SQ to SQ–Th₃–SQ.

Fig. 2 Thermal ellipsoid (50% probability) plots from 100 K crystal structures of SQ₂Th, SQ₂Th₂, and SQ₂Th₃. Hydrogens and cumenyl groups are omitted for clarity.

Fig. 3 (A) Relevant bridge bond lengths (in Å) from X-ray crystal structures (data collected at 100 K). Arrows denote increase in SQ-bridge bond lengths with increasing number of Th units (blue), increase in Th ring bond lengths with decreasing number of Th units (green), and increase in Th bond lengths with increasing number of Th units (red). (B) Bridge bond line drawings that correspond to the bond lengths shown in (A).

Spectroscopic and magnetic data for SQ–SQ and SQ–Th–SQ

Magnetic resonance spectroscopy. Frozen glass EPR spectra were not observed for SQ–SQ and SQ–Th–SQ at 95 K in 2-MTHF. This observation is consistent with diamagnetic S = 0 quinoidal closed shell ground states for these complexes and no thermal population of an S = 1 triplet state. We also attempted to collect EPR spectra at elevated temperatures for SQ–Th–SQ in a poly(vinylchloride) solid solution film matrix but we observed no signal associated with an excited triplet at temperatures as high as 360 K. Additionally, the SQ–Th–SQ¹H-NMR spectra display no paramagnetic broadening of the aromatic proton signals (Fig. S5†), in marked contrast to SQ–Th₂–SQ, and this provides additional support that SQ–Th–SQ possesses a closed-shell singlet ground state with no thermally accessible triplet state(s).

Variable–temperature magnetic susceptibility measurements. Crystals grown for X-ray diffraction were used for variable–temperature (VT) magnetic susceptibility measurements. Consistent with the EPR and NMR data, the magnetic susceptibility data for SQ–Th–SQ also show that the ground state is diamagnetic (see ESI†) with no evidence of a paramagnetic state being thermally populated in the 5–300 K temperature range.

Electronic absorption spectroscopy. Fig. 4 displays the room temperature solution electronic absorption spectra for SQ–SQ and SQ–Th–SQ in cyclohexane. Both complexes exhibit effectively panchromatic absorption throughout the UV-visible range that, for SQ–Th–SQ, extends into the NIR region of the spectrum.

Fig. 4 Overlay of electronic absorption spectra of SQ–SQ, and SQ–Th–SQ. Spectra were recorded at room temperature as solutions in cyclohexane.

Electronic structure of the SQ–SQ and SQ–Th–SQ complexes. In the active electron approximation,^58,66,67 the simplest orbital basis for describing the ground state of bis-semiquinones is constructed from the two SQ singly occupied molecular orbitals (SOMOs), labeled a and b in Fig. 5A. Thus, the orbital and state diagram in Fig. 5A details how the electronic structure of SQ–Th_n–SQ can be described in terms of an Anderson-type two orbital,⁶⁸ two electron model. This model yields 4-states,⁶⁹ and has been used for understanding biradicaloid character in similar systems.^1,6,69,70 The two-orbital model was originally developed using hydrogenic orbitals that allow for the configurational mixing of open- and closed-shell singlet configurations, since there is only one triplet configuration. Fig. 5A also shows the generalized symmetry labels for the two open-shell (a¹b¹ → ¹B^OS and ³B^OS) and two closed-shell configurations (a²b⁰ and a⁰b² → 2 × ¹A^CS) that derive from this model in the strong coupling (non-asymptotic) limit. Importantly, when rigorous or local effective symmetry is present in these molecules, symmetry dictates that only totally symmetric S = 0 open-shell singlet configurations will mix with the totally symmetric S = 0 quinoidal configuration to generate biradicaloid character. However, within the context of this simple two-orbital model there are no open-shell singlet excited states that can mix with the quinoidal ¹A^CS ground state since the two SQ SOMOs possess different symmetries.

Fig. 5 Symmetrized models for understanding biradicaloid electronic structure. (A) Anderson-type 2-orbital, 4-state model. Symmetry labels A and B are generic and refer to the symmetries of molecular orbitals that are symmetric (A) and antisymmetric (B) with respect to a symmetry element that relates the two halves of the molecule. Clearly, for C_2h and C_2v structures these symmetry elements will be different, but the A and B labels remain valid. (B) 3-Orbital, 4-electron MO model ( = spin on left ZnSQ fragment, = Th_n bridge fragment, = spin on right ZnSQ fragment) used to explain the electronic structure of the SQ–Th_n–SQ (ZnSQ_a-bridge-ZnSQ_b) complexes studied in this manuscript. Note that the superexchange interaction in this model, which leads to the open shell singlet–triplet splitting, derives from mixing with the excited configuration of the same symmetry. Six representative configurations and states are shown: CS = closed-shell, OS = open shell, DE1CS = lowest doubly-excited closed-shell, and DE2CS = highest doubly-excited closed-shell. The state representations are derived from the 1a, b, and 2a MO occupancies.

To account for any admixture of open-shell singlet character into the quinoidal ¹A^CS ground state the model needs to be expanded, and a minimally expanded 3-orbital, 4-electron model, with select configurations, is shown in Fig. 5B. This model includes an effective bridge orbital that provides a mechanism for excited open shell configurations to mix into the quinoidal ¹A^CS ground state. A partial state energy diagram is given in Fig. 6, which displays many features in common with Tanabe–Sugano diagrams^71,72 used to understand the nature of ligand field excitations in transition metal complexes. As one moves from SQ–Th–SQ to SQ–Th₃–SQ, the SQ–SQ interaction decreases and closed-shell configurations increase in energy, which drives the system from closed-shell quinoidal to open-shell biradical.

Fig. 6 State energy diagrams that derive from a 4-orbital, 3-electron model. (A) Closed-shell SQ–Th–SQ, (B) mixed-configuration (¹A^CS and ¹A^OS) SQ–Th₂–SQ. (C) Open-shell SQ–Th₃–SQ. Gray box in (B) highlights thermally-populated states used to fit both susceptibility and spectroscopic data for SQ–Th₂–SQ. See text for details.

Crystallographically-determined bond deviation parameters and the diamagnetic nature of the complexes for SQ–SQ and SQ–Th–SQ clearly indicate that these molecules possess dominant quinoidal closed-shell S = 0 electronic ground states. As a result, the admixture of open shell configurations (e.g., the ¹A^OS in Fig. 5) must be quite small.

Spectroscopic and magnetic data for SQ–Th₃–SQ

Variable–temperature magnetic susceptibility measurements. The structural data for SQ–Th₃–SQ shows a bond length pattern characteristic of aromatic Th rings (Fig. 3), and this is consistent with an open-shell ground-state electronic structure for this complex. To correlate the observed SQ–Th₃–SQ structural parameters with the ground state electronic structure, we performed variable–temperature magnetic susceptibility measurements. These data are presented as the χ_paraT product vs. T in Fig. 7 and show that a paramagnetic state is populated at temperatures above ∼50 K. Since the SQ moieties are more weakly coupled than those in SQ–SQ and SQ–Th–SQ, we use an antiferromagnetically exchange coupled S₁ = S₂ = ½ dimer model that employs the H = −2J(S₁·S₂) Heisenberg exchange Hamiltonian to generate the magnetic susceptibility expression in eqn (1), where J is the pairwise magnetic exchange coupling constant between the two SQ radical spins, k_B is the Boltzmann constant, g is the electronic g-value, and T is the temperature.

Fig. 7 Paramagnetic susceptibility-temperature product (χ_paraT) vs. temperature for a crystalline sample of SQ–Th₃–SQ, measured by variable–temperature magnetic susceptibility experiments at a magnetic field strength of 0.1 Tesla (data: ; fit: —).

We fit eqn (1) to the data to yield J = −121 cm⁻¹, with a corresponding singlet–triplet energy gap of 2J = ΔE(S − T) = 242 cm⁻¹. The susceptibility data indicate an electronic structure that correlates with the state diagram shown in Fig. 6C, with a ground state and an exchange coupled triplet state at higher energy (2J).

Electron paramagnetic resonance (EPR) spectroscopy. Low temperature glass and VT polymer film EPR data were collected for SQ–Th₃–SQ and are shown in Fig. 8A and B, respectively. The glass matrix data were collected at 120 K in 2-MTHF, and the spectrum in Fig. 8A is characteristic of a randomly-oriented, S = 1 triplet with a rhombic g-tensor.⁷³ Zero-field splitting (zfs) parameters, determined by simulations of the experimental spectrum, were determined to be |D/hc| = 0.00342 cm⁻¹ and |E/hc| = 0.00062 cm⁻¹. The exchange coupling between the two SQ radicals was determined from the temperature dependence of the EPR spectra for SQ–Th₃–SQ. In the VT experiments, SQ–Th₃–SQ was dissolved in a poly(vinyl chloride) polymer matrix and the integrated signal intensity of the Δm_s = 2 resonance at g ∼ 4 was measured as a function of temperature. The doubly-integrated Δm_s = 2 signal is shown plotted as a function of T⁻¹ in Fig. 8B. The same exchange Hamiltonian was used to generate eqn (2).

Fig. 8 (A) Powder EPR spectrum of SQ-Th₃-SQ (—) and simulation parameters. (Inset) Δm_s = 2 transition. Fit () includes 32% S = ½ impurities. For simulation details, see text and ESI.† (B) Doubly-integrated Δm_s = 2 EPR transition intensities () vs. inverse temperature and fit () for SQ-Th₃-SQ. See text for fit details. Samples were ∼1 mM dissolved in an evaporated film of poly(vinyl chloride).

We fit eqn (2) to the VT EPR data to yield J = −119 cm⁻¹, which is in excellent agreement with the exchange parameter determined from our analysis of the VT magnetic susceptibility data (J = −121 cm⁻¹). Thus, the VT EPR data support the solid-state magnetic susceptibility data, with both data sets being consistent with an aromatic ring-bridged biradical (i.e., open-shell singlet) ground state. This electronic structure determination is also fully consistent with the bond length patterns (Σ|Δ_i| values for both SQ and Th rings, vide supra) obtained from the X-ray structure of SQ–Th₃–SQ.

Electronic absorption spectroscopy. Complex temperature-dependent electronic absorption spectra are observed for SQ–Th₃–SQ (Fig. 9). As noted for SQ–SQ and SQ–Th–SQ, we also observe panchromatic absorption for SQ–Th₃–SQ that extends throughout the UV-visible and into the NIR region of the spectra. In marked contrast to room temperature SQ–Th–SQ electronic absorption data, the corresponding 296 K spectrum of SQ–Th₃–SQ exhibits structured, moderately intense bands across the entire spectral region. The VT electronic absorption spectra (Fig. 9A) were collected on a sample dissolved in a poly(styrene) thin film. Clear isosbestic points are observed at 15 540, 17 182, and 21 150 cm⁻¹, consistent with only two species contributing to the electronic absorption spectra across the 4–196 K temperature range. Since both the variable–temperature EPR and magnetic susceptibility data indicate J ≈ −120 cm⁻¹, this leads to an S = 0 ground state singlet and a negligible population of the exchange coupled S = 1 triplet state at 4 K (at 4 K; n_S=1/n_S=0 ∼ 3 exp(−242/2.78) ∼ 0). Thus, the 4 K spectrum of SQ–Th₃–SQ is that of the exchange coupled singlet ground state.

Fig. 9 (A) Variable–temperature (4–298 K) electronic absorption spectra of SQ–Th₃–SQ in a poly(styrene) film. (B) Normalized transition intensities ( and ) and state populations ( and ) at 18 215 cm⁻¹ (triplet) and 22 422 cm⁻¹ (singlet).

The intensities of the temperature dependent bands at 22 422 cm⁻¹ and 18 215 cm⁻¹, which we associate with the singlet ground- and thermally-populated triplet states, respectively, are plotted as a function of temperature in Fig. 9B. A simple 2-state (singlet and triplet) Boltzmann expression was fit to these data to yield a singlet–triplet splitting of 222 cm⁻¹ (J = −111 cm⁻¹). This value of J determined from VT electronic absorption data is in excellent agreement with the exchange coupling parameter for SQ–Th₃–SQ that was determined from both magnetic susceptibility (J = −121 cm⁻¹) and variable–temperature EPR spectroscopy (J = −119 cm⁻¹), vide supra. The temperature dependent and contributions to the VT electronic absorption spectra of SQ–Th₃–SQ have allowed us to extract the pure individual spectra that originate from the and states (Fig. 10), providing additional access to the nature of the excited state manifold.

Fig. 10 Singlet spectrum of SQ–Th₃–SQ () collected at 4 K. Triplet spectrum of SQ–Th₃–SQ () derived from subtracting the weighted 4 K spectrum from the 298 K spectrum.

Considering the state description in Fig. 6C, one can have spin-allowed excitations from the open shell aromatic ground state to configurationally mixed excited states (e.g., configurationally mixed ¹A^OS and¹A^CS in the 3-orbital model; Fig. 5B) that possess closed-shell quinoidal character. Therefore, the electronic absorption spectrum that originates from the aromatic-bridge biradical ground state contains transitions to biradicaloid/open-shell singlet excited states. In marked contrast, there are no triplet excited states that possess closed-shell quinoidal character. This is why the spectra that originate from the and states are very different in their appearance, and strongly suggests considerable mixing between open- and closed-shell excited singlet configuration states. Strong mixing between these singlet excited states can drive one or more of these states below the lowest energy excited triplet state, and this is the likely origin for the dramatic red shift of the singlet spectrum compared to the triplet spectrum (Fig. 10).

Spectroscopic and magnetic data for SQ–Th₂–SQ

Variable–temperature magnetic susceptibility measurements. Crystals grown for X-ray diffraction were used to perform VT magnetic susceptibility measurements on SQ–Th₂–SQ and the data are shown in Fig. 11. These data confirm that the sample is diamagnetic up to ∼120 K. At higher temperatures, a slight increase in χ_paraT is observed, and this is indicative of an S = 1 triplet state being thermally populated.

Fig. 11 Paramagnetic susceptibility-temperature product (χ_paraT) vs. temperature () for a crystalline sample of SQ–Th₂–SQ, measured by variable–temperature magnetic susceptibility experiments at a magnetic field strength of 0.1 Tesla. Data were fit () to the same model as the VT EPR and EAS data, see Fig. 6B and text. Regarding the magnitude of the χ_paraT product in this plot, note that χ_paraT is equal to 1.0 emu K mol⁻¹ for a pure S = 1 triplet state.

Electron paramagnetic resonance (EPR) spectroscopy. The EPR spectrum of SQ–Th₂–SQ in a solid solution polymer film matrix is provided in Fig. 12A. This spectrum exhibits a rhombic S = 1 triplet powder pattern at 295 K. The zfs parameters were determined by spectral simulations and yielded |D/hc| = 0.00578 cm⁻¹ and |E/hc| = 0.00086 cm⁻¹. VT EPR spectra for SQ–Th₂–SQ were also recorded and the doubly-integrated Δm_s = 2 signal at g ∼ 4 is shown plotted as a function of inverse temperature (T⁻¹) in Fig. 12B.

Fig. 12 (A) Powder EPR spectrum of SQ–Th₂–SQ (—, left). Fit () includes 34% S = ½ impurities. For simulation parameters, see text and ESI.† (B) Doubly-integrated Δm_s = 2 EPR transition intensities () vs. inverse temperature for SQ–Th₂–SQ. Samples were ∼1 mM dissolved in an evaporated film of poly(vinyl chloride). Data were fit () to a model that includes three lowest energy spin states, see text and Fig. 6B.

Electronic absorption spectroscopy. The VT electronic absorption spectra for SQ–Th₂–SQ are shown in Fig. 13A and displays panchromatic absorption from the NIR to UV, similar to that of the other complexes in this series. An intense temperature-dependent band is observed at ∼12 300 cm⁻¹ that, when compared to the VT behavior of SQ–Th₃–SQ, displays a markedly weaker temperature dependence.

Fig. 13 (A) Variable–temperature (4–298 K) electronic absorption spectra of SQ–Th₂–SQ in a poly(styrene) film. (B) Normalized transition intensity of 13 000 cm⁻¹ band. Data fit using 3 lowest thermally-populated spin states. See Fig. 6B and text.

Analysis of the variable–temperature data. The bond deviation parameters for SQ–Th₂–SQ indicate a ground state electronic structure description that is between closed-shell quinoidal and open-shell biradical in nature (i.e., a biradicaloid, Fig. 3 and 6B). Here, we analyze the VT magnetic and spectroscopic data to develop insight into the proposed biradicaloid nature of the ground state, and the unusual temperature-dependent behavior of the data. Since the magnetic susceptibility, EPR, and electronic absorption data for SQ–Th₂–SQ are all temperature dependent, we initially considered the S = ½ dimer model we employed for understanding the temperature dependent data for SQ–Th₃–SQ. This model incorporates an S = 0 singlet ground state and a thermally accessible S = 1 triplet state. However, we were unable to obtain a singlet–triplet energy gap (2J) that was consistent with the VT magnetic susceptibility, EPR, and electronic absorption data sets. Therefore, we employed an expanded model (Fig. 6B, gray box) to describe the thermally accessible states in SQ–Th₂–SQ. This three-state model is comprised of a closed shell ground state (¹A^CS), with thermally populated open-shell singlet and triplet exchange-coupled states that are found at energies ΔE₁ and ΔE₂, respectively, above the closed-shell ground state. In this model, the energy difference ΔE₁ − ΔE₂ corresponds to the singlet–triplet splitting (2J) of the open shell biradical states using the exchange Hamiltonian, Note that these open-shell singlet and triplet exchange-coupled states were the lowest-lying states in SQ–Th₃–SQ, and the closed-shell quinoidal state for SQ–Th₂–SQ represents an electronic excited state in SQ–Th₃–SQ. We attribute the existence of biradicaloid and aromatic ring-bridged biradical populations to result from a temperature-dependent structural change (increased ring torsion amplitudes, Fig. 14) that leads to greater SQ–Th and Th–Th bond torsions in SQ–Th₂–SQ as the temperature is increased. Thus, the potential energy surfaces for the open-shell singlet and triplet are described as being distorted along this torsional coordinate, Q_torsion, relative to the closed shell singlet ground state. Thus, eqn (3) and (4) (C = Nβ²/3k_B and D represents monoradical impurity), and 5 (C is a proportionality constant) derived from the 3-state model in Fig. 6B were fit to the VT magnetic susceptibility, EPR, and electronic absorption data, respectively.

Fig. 14 Equilibrating biradicaloid and aromatic ring-bridged biradical forms that result from a temperature-dependent structural change (e.g., increased ring torsion amplitudes), which leads to greater SQ–Th and Th–Th bond torsions in SQ–Th₂–SQ as the temperature is increased. Thus, the potential energy surfaces for the open-shell singlet and triplet are described as being more distorted along this torsional coordinate, Q_torsion, relative to the closed shell ground state.

Best fits of eqn (3) to the VT magnetic susceptibility data yield ΔE₁ = 317 cm⁻¹ and ΔE₂ = 959 cm⁻¹. This results in the open-shell biradical singlet residing only 317 cm⁻¹ above the S = 0 quinoidal ground state, with a biradical singlet–triplet splitting of ΔE₁ − ΔE₂ = 2J = 642 cm⁻¹ (J = 321 cm⁻¹). In contrast to the VT magnetic susceptibility data, the VT EPR data directly probes the thermally populated open-shell triplet state as a spectroscopic observable. The best fit of eqn (4) to the VT EPR data gives ΔE₁ = 306 cm⁻¹ and ΔE₂ = 822 cm⁻¹. The ΔE₁ = 306 cm⁻¹ quinoid – biradical singlet–singlet gap is in remarkable agreement with that determined from the VT magnetic susceptibility experiments (ΔE₁ = 317 cm⁻¹). However, the ΔE₁ − ΔE₂ = 2J = 516 cm⁻¹ (J = 258 cm⁻¹) determined for the biradical singlet–triplet gap in the solid solution (polymer) phase is reduced by ∼20% compared to that determined by magnetic susceptibility experiments on samples in the polycrystalline state.

Eqn (5) was fit to the VT electronic absorption data, which directly probes the reduction in closed-shell biradicaloid singlet state population with increasing temperature by monitoring the temperature dependence of the ∼12 300 cm⁻¹ absorption band. The VT absorption data were collected in the solid solution (polymer matrix) phase and the temperature dependence is described with the same ΔE₁ and ΔE₂ parameters that were determined from the temperature dependence of the Δm_s = 2 EPR resonance. Thus, VT magnetic susceptibility, EPR, and electronic absorption spectroscopy all yield the same energy gap for populating the biradical singlet state (ΔE_{1 ave} = 310 cm⁻¹). The experimentally determined Boltzmann populations of the three thermally-accessible states for SQ–Th₂–SQ are presented graphically in Fig. 14. The biradical character present in the ¹A^CS ground state must therefore derive from strong configurational mixing with open shell singlet biradical excited state(s), and this is described in the state energy diagram depicted in Fig. 6B (e.g., ¹A^CS mixing with ¹A^OS).

In order to address whether the thermally-excited state of SQ–Th₂–SQ possesses any appreciable closed-shell singlet character, or whether this state is analogous to the aromatic biradical singlet ground state of SQ–Th₃–SQ, we analyzed the distance dependence of the singlet–triplet splitting in SQ–Th₂–SQ and SQ–Th₃–SQ. We have previously determined the distance decay constant (β = 0.22) for magnetic exchange mediated by aromatic thiophene bridges.²¹ Since β should be a transferrable property^74,75 for evaluating magnetic exchange mediated by these thiophene units, we have used this β value and the J_SQ–SQ(ave) = −279 cm⁻¹ for SQ–Th₂–SQ, which was the average derived from magnetic susceptibility, VT EPR, and VT electronic absorption spectroscopy, to derive the expected J value for SQ–Th₃–SQ. This analysis predicts J ≈ −119 cm⁻¹ for SQ–Th₃–SQ, which is in excellent agreement with the experimental J_ave = −117 cm⁻¹ that we determined for SQ–Th₃–SQ. This analysis provides strong support for the ΔE₁ − ΔE₂ gap representing the J_SQ-SQHeisenberg exchange interaction in both SQ–Th₂–SQ and SQ–Th₃–SQ, with an openshell biradical ground state configuration for SQ–Th₃–SQ, and thermally accessible open-shell triplet biradical states for both SQ–Th₂–SQ and SQ–Th₃–SQ.

Discussion

Biradicals are distinguished by the presence of singlet and triplet configurations that derive from a HOMO → LUMO one-electron promotion relative to the closed-shell quinoidal ground state. These configurations are described by the quinoid and biradical Lewis structures presented in Fig. 1. For biradicaloids, the ground state open-shell biradical character has been described in terms of a biradical index (y_i), which may be computed from natural orbital occupancies that derive from the results of spin unrestricted Hartree–Fock or DFT computations.¹ Here, y₀ derives from the occupancy of the lowest unoccupied natural orbital, and is often used to describe the degree of biradical character in the electronic ground state.¹ Additionally, a valence configuration interaction model, effectively related to the 4-state Anderson model⁶⁸ that has had a tremendous influence on our understanding of antiferromagnetic exchange in dimeric systems, has been employed to evaluate the degree of biradical character.^1,69 This model derives from the asymptotic limit of the H₂ molecule (very weak radical–radical coupling with no bridge orbitals) involving two effectively degenerate orbitals and the incorporation of closed-shell ionic configurations. This 2-electron, 2-orbital (4-state) model allows for configurational mixing between closed and open shell singlet configurations with ionic and covalent character. If coupling between the SQ SOMO orbitals (also a 2-electron, 2-orbital model) in actual or effective symmetry is assumed a priori, configurational mixing between closed- and open-shell singlets is symmetry forbidden. Since there are notable examples where an expanded model is required to explain the electronic structure and the nature of the radical–radical exchange interaction in biradical systems,^{21,57–61,76–80} we have minimally expanded the 2-electron, 2-orbital model to include a doubly-occupied bridge orbital that provides a mechanism for understanding the nature of open-shell singlet states that configurationally mix with quinoidal states.^{21,57–61,67,77,78}

With respect to the role of the thiophene bridge units in defining the ground state electronic and geometric structure of the SQ–Th_n–SQ series, the explicit consideration and addition of a single bridge-orbital reveals how open-shell and low-energy closed-shell singlet configurations (e.g., ¹A^OS and ¹A^CS, respectively; Fig. 5B and 6) can mix to yield “biradicaloid” electronic structures in both ground- (Fig. 6B) and excited (Fig. 6C) states. We note that the nature of these open-shell singlet states generally need not be formal biradical states (analogous to in the 3-orbital model) but could be any open-shell configuration of the proper symmetry to allow for configurational mixing with closed shell-singlet configurations (see Fig. 5 and 6 – e.g.¹A^OSFig. 5b). As a consequence, the cases presented here show how open-shell/closed-shell ¹A^OS–¹A^CS mixing contributes to modifying the degree of quinoidal-aromatic bond patterns in the thiophene bridge fragments. Although this configurational mixing leads to complex ground- and excited state electronic structures in these systems, a key experimental descriptor of the degree of biradical character in the electronic ground states is given by the experimentally derived bond deviation parameters Σ|Δ_i|,⁶² which can then be correlated with experimental magnetic and spectroscopic observables. This allows results of electronic structure computations to be evaluated in the context of the experimental data.

Regarding the concepts of quinoidal, biradical, and biradicaloid electronic structure descriptions, one needs to consider how these are defined. For example, the quinoidal closed-shell singlet configuration can mix with other closed- or open-shell singlet configurations of the same symmetry. One of these open-shell configurations is associated with what is described as possessing “biradical” character, where the unpaired electrons are primarily localized on the “radical” moieties of the molecule. Thus, from a Lewis structure approach, we define a true biradicaloid as representing a resonance hybrid comprised of the quinoidal and biradical Lewis structures depicted in Fig. 1. Typically, non-contributing or marginally contributing resonance structures describing the ground state (i.e., the biradical forms of SQ–SQ and SQ–Th–SQ) are thought of as representing high energy configurations. However, this is not necessarily correct. The dioxolene-bridge-dioxolene fragments of SQ–SQ and SQ–Th₂–SQ possess C_2h symmetry, and the closed-shell quinoid configuration and open-shell biradical configuration are forbidden to mix by symmetry even though they may be very close in energy. This is clearly highlighted for SQ–Th₂–SQ, where the quinoid and biradical singlet configurations are within k_BT of one another but possess different symmetries and do not mix. For these molecules, the biradicaloid character admixed into the ground-state configuration is best described as open-shell singlet character, since there is no resonance between the two Lewis structures drawn in Fig. 1. We therefore describe a ground-state electronic structure description of SQ–Th₂–SQ as being quinoidal, with open-shell singlet character.

The low-energy thermally populated excited states are biradical in nature and possess SQ–SQ radical–radical Heisenberg exchange coupling interactions. The thermally accessible biradical states in SQ–Th₂–SQ and SQ–Th₃–SQ possess experimentally determined J values that are consistent with previously determined distance decay parameters (β values) for aromatic SQ bridge configurations.²¹ These low-energy open-shell states possess non-planar geometries. We suggest that this symmetry lowering derives from a two-stage pseudo Jahn–Teller effect,⁸¹ which involves vibronic coupling with specific excited states to electronically drive out-of-plane ring–ring distortions.

The SQ–Th_n–SQ (n = 0–3) molecules presented in this study provide clear examples of dominantly closed-shell quinoidal (SQ–Th_n–SQ; n = 0, 1) and open-shell biradical (SQ–Th₃–SQ) ground states. The SQ–Th₂–SQ complex is unique in this series, possessing some open-shell singlet character as evidenced by the experimentally-determined bridge bond deviation values (Σ|Δ_i|).⁶² Although the open shell biradical state of SQ–Th₂–SQ is a mere 310 cm⁻¹ above the quinoidal ground state, these states do not configurationally mix due to symmetry constraints. This thermally excited biradical state in SQ–Th₂–SQ becomes the ground state in SQ–Th₃–SQ (see Fig. 6). Additional evidence for admixed open- and closed-shell character in the ground state of SQ–Th₂–SQ is found in the excited states of SQ–Th₃–SQ, as revealed by the dramatic differences in spin-allowed ¹GS → ¹ES (ES = excited state configuration) and ³GS → ³ES transitions (e.g. the and transitions in Fig. 10). This mixing of open- and closed-shell excited states naturally derives from our 3-orbital, 4-electron model that indicates the importance of bridge states in the description of closed-shell quinoidal, open-shell biradical, and admixed singlet biradical character in the ground and excited states of these molecules. Our study reveals of the power of using a combined synthetic, spectroscopic, and magnetic approach to unravel the complex nature of these and related molecules.

Conclusions

In summary, the degree of closed shell quinoidal and open-shell aromatic character in the electronic ground state and thermally accessible excited states of SQ–Th–SQ, SQ–Th₂–SQ, and SQ–Th₃–SQ are markedly different. The expanded 3-orbital model discussed in this work has provided insight into the nature of the closed-shell ground state singlet in SQ–Th–SQ, an open-shell singlet for SQ–Th₃–SQ, and a configurationally mixed singlet ground state for SQ–Th₂–SQ, which possesses some open-shell character. The pattern of bridge bond lengths shown in Fig. 3 is consistent with the predictions enabled by this model, and reveals the alternation of short- and long C–C bonds characteristic of quinoidal resonance structures being most prominent for SQ–Th–SQ and least prominent for SQ–Th₃–SQ. In addition, the dioxolene bond deviation parameters⁶² (Σ|Δ_i|) clearly decrease from SQ–Th–SQ to SQ–Th₃–SQ, and this indicates maximal quinoidal character for SQ–Th–SQ. The results of our structural analyses are consistent with EPR, electronic absorption spectroscopy, and magnetic susceptibility studies for all of these complexes.

A primary strength of our approach to the biradicaloid problem lies in the simplicity of using symmetry/group theory to understand state mixing, and this is further exemplified by our use of a conceptually approachable, minimal basis 4-electron-, 3-orbital model that includes the bridge moiety. Thus, the degree of open-shell, closed-shell, and biradical character in the electronic ground state is determined by the molecular symmetry, and is modulated by the nature and of the bridge fragment (e.g., thiophene, phenylene, etc. and the number of bridge units). Doubly-excited states (e.g., ¹A^DECS; Fig. 5B) and open-shell singlet states with occupied π* and/or vacant π-bonding orbitals can attenuate the quinoidal bond length alternation pattern for closed-shell states if they have the same symmetry as the ground state. However, open-shell states have non-quinoidal, aromatic bridge units and do not mix with closed-shell singlet states. Importantly, the dioxolene moieties provide attenuated spin density in this series of compounds that allows for exemplars of quinoid, configurationally mixed quinoid/open-shell, and open-shell singlet biradical ground states in the complexes that we have detailed here. We are not aware of any other series of molecules that highlight the complex electronic structures associated with open-shell/closed-shell mixing as a function of the bridge repeat unit. Ongoing studies are focusing on spectral band assignments, correlating open-shell character with bond deviation parameters,⁶² and understanding how different bridges and metal ions can fine tune the nature of open- and closed-shell configurational mixing in analogs of the SQ–Th_n–SQ series.

Data availability

ESI† contains synthetic- and characterization details of all new molecules and metal complexes.

Author contributions

M. L. K. and D. A. S. conceptualized and supervised the project; P. D. M. synthesized and characterized all molecules and complexes; J. M. collected and analyzed variable temperature electronic absorption spectra; P. D. M., D. A. S., and M. L. K. wrote the original manuscript draft.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

D. A. Shultz thanks the National Science Foundation (CHE-1931291 and CHE-1764181) for financial support. M. L. Kirk acknowledges the National Science Foundation (NSF CHE-1900237) for financial support.

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Footnote

† Electronic supplementary information (ESI) available: Experimental details. Synthetic-, X-ray crystallographic-, and magnetic susceptibility details and data. CCDC 2260981–2260983. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3sc02341a

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