A diradical based on odd-electron σ-bonds

Abstract

The concept of odd-electron σ–bond was first proposed by Linus Pauling. Species containing such a bond have been recognized as important intermediates encountered in many fields. A number of radicals with a one-electron or three-electron σ-bond have been isolated, however, no example of a diradical based odd-electron σ-bonds has been reported. So far all stable diradicals are based on two s/p-localized or π-delocalized unpaired electrons (radicals). Here, we report a dication diradical that is based on two Se∴Se three-electron σ–bonds. In contrast, the dication of sulfur analogue does not display diradical character but exhibits a closed-shell singlet.

Stable diradicals are generally based on two s/p-localized or π-delocalized unpaired electrons (radicals). Here, the authors report a dication diradical that is based on two Se∴Se three-electron σ-bonds.

Introduction

Radicals are species that possess an unpaired electron^1–7. In general, there are two classes of stable radicals: s/p-localized and π-delocalized. In the former, the unpaired electron resides on an s/p-orbital of one atom, while in the latter, the unpaired electron is π-delocalized over two or more atoms. Apart from these two classes, there is the third class of radicals that have an unpaired electron delocalized in an σ orbital or antibonding σ* orbital between two atoms, leading to a one-electron σ-bond and a three-electron σ-bond (Fig. 1), respectively. The concept of the odd-electron σ-bond was first proposed by Pauling⁸, and species with these intriguing bonds have been recognized as important intermediates in chemistry and biochemistry^9–21. A number of radicals with a one-electron^22–25 or three-electron σ-bond^12,26–32 have been isolated and structurally studied (Fig. 1).

Fig. 1. Schematic representation of odd-electron σ-bonds and selected examples.

a The B·B one-electron σ–bond proved by EPR. b The B·B one-electron σ–bond proved by X-ray diffraction. c The P·P one-electron σ–bond. d The Cu·B heteronuclear one-electron σ–bond. e The Xe·Xe one-electron σ–bond. f The N∴N three-electron σ–bond. g The S∴S and Se∴Se three-electron σ–bonds. h The Pd∴Pd and Ni∴Ni three-electron σ–bonds. i The Rh∴Si and Ir∴Si heteronuclear three-electron σ–bonds.

Diradicals are species with two unpaired electrons (radicals), which are of importance both in understanding of bonding nature and application as functional materials^33–37. So far all stable diradicals are based on two s/p-localized or π-delocalized unpaired electrons (radicals); however, no example of a diradical based odd-electron σ-bonds has been reported. In 2014, we isolated selenium and sulfur radical cations (NapSe₂Ph₂)⁺ and (NapS₂Ph₂)⁺ (highlighted in Fig. 1)^29,30 that feature a Se∴Se and S∴S three-electron σ-bond, respectively.

We now report a diradical (2²⁺, Fig. 2) that is based on two Se∴Se three-electron σ-bonds. In contrast, the dication of sulfur analog (1²⁺) does not display diradical character but exists as a closed-shell singlet instead.

Fig. 2. Preparation, cyclic voltammograms, and two-electron oxidation of tetrachalcogenides 1 and 2.

a Preperation of compounds 1 and 2. b The cyclic voltammetry of 1. c Two-electron oxidation of 1. d The cyclic voltammetry of 2. e Two-electron oxidation of 2.

Results

Syntheses of dications

Tetrachalcogenides 1 and 2 were synthesized in two steps from 1,4,5,8-tetrabromo naphthalene³⁸ and ⁿBuLi with corresponding diphenyl dichalcogenide at −78 °C, respectively (Fig. 2). Their cyclic voltammetry (CV) in CH₂Cl₂ at room temperature with supporting electrolyte ⁿBu₄NPF₆ displays two reversible oxidation peaks at oxidation potentials of +0.84, 1.07 V (1) and +0.74, 1.04 V (2) (Fig. 2). Prompted by CV data, 1 and 2 were treated with two equivalents of Li[Al(OR_F)₄] (OR_F = OC(CF₃)₃)³⁹ and NOSbF₆ in CH₂Cl₂ to afford dications 1²⁺ and 2²⁺ in modest yields, respectively (Fig. 2). These dications are air sensitive but thermally stable under nitrogen or argon atmosphere. They were characterized by chemical analysis, UV absorption spectroscopy, EPR spectroscopy, single-crystal X-ray diffraction, and superconducting quantum interference device (SQUID) measurements.

Crystal structures

Crystals suitable for X-ray crystallographic studies were obtained by cooling solutions of neutral tetrachalcogenides and their oxidized species. Their crystal structures are shown in Fig. 3. Some structural parameters are listed in Table 1. In the molecular geometries of 1 and 2, one Ch–C_Ph (Ch = S, Se) bond is nearly perpendicular to the other at both sides of the naphthalene skeleton. Upon oxidation, in 1²⁺ the two S–C_Ph bonds at the same side of the naphthalene skeleton are nearly linear (torsion angle ∠C_PhSSC_Ph = 6°) and all four S–C_Ph bonds are coplanar to the naphthalene skeleton, while in 2²⁺ two Se–C_Ph bonds at the same side are parallel and all Se–C_Ph bonds are nearly perpendicular to the naphthyl plane (∠CSeC = 100°). The average Se–C bond (Se–C_Ph and Se–C_Nap) lengths in 2²⁺ are slightly shorter while ∠C–Se–C angles are slightly larger than those in neutral 2. The Se•••Se separation (2.905(1) Å) is shorter than that (3.054(2) Å) in 2, but longer than the Se–Se single bond length (ca. 2.34 Å)⁴⁰. The Se–C_Ph bond alignment and structural parameters of 2²⁺ are similar to those of (NapSe₂Ph₂)⁺³⁰, indicating there is a three-electron σ-bond between two Se atoms, and the whole dication possesses two three-electron σ-bonds. In contrast, though the S•••S separation (2.774(2) Å) is also shorter than that (2.937(2) Å) in 1, it is much longer than a regular S–S single bond (ca. 2.05 Å) and comparable to those of molecules with weak intramolecular S•••S interactions⁴¹. The S–C_nap bond length (1.727(4) Å) of 1²⁺ is also notably shorter than those of 1 (1.792(2) Å) and (NapS₂Ph₂)⁺ (1.768(3) Å)³⁰. Moreover, the naphthalene skeleton of 1²⁺ becomes quinoidal (C8–C9 1.351(6) Å).

Fig. 3. 50% ellipsoid drawings of 1, 1²⁺, 2, and 2²⁺.

Yellow, carbon; red, selenium; blue, sulfur. Hydrogen atoms are not shown. Selected bond length (Å) and angle (deg): 1 S1^…S2′ 2.937(2), S1–C1 1.788(3), S1–C7 1.797(2), C7–C8 1.375(3), C8–C9 1.404(3), C9–C10 1.365(4), C10–C11 1.438(3), C11–C11′ 1.473(4), S2–C10 1.787(2), S2–C12 1.787(3), C1–S1–C7 102.3(1), C1–S1–S2′ 163.3(7), C10–S2–C12 102.4(1), C12–S2–S1′ 83.2(7); 1²⁺ S1–S2′ 2.774(2), S1–C1 1.769(4), S1–C7 1.735(4), C7–C8 1.412(6), C8–C9 1.351(6), C9–C10 1.418(6), C10–C11 1.426(6), C11–C11′ 1.467(7), S2–C10 1.720(4), S2–C12 1.763(5), C1–S1–C7 105.0(2), C1–S1–S2′ 164.5(2), C10–S2–C12 105.3(2), C12–S2–S1′ 161.8(2); 2 Se1^…Se4 3.061(5), Se2^…Se3 3.048(5), Se1–C1 1.917(10), Se1–C7 1.931(9), C7–C8 1.349(13), C8–C9 1.388(13), C9–C10 1.338(12), C10–C11 1.439(12), C11–C28 1.460(10), C7–C28 1.436(12), Se2–C10 1.959(8), Se2–C12 1.934(9), C1–Se1–C7 99.4(4), C1–Se1–Se4 124.4(6), C10–Se2–C12 98.2(4), C12–Se2–Se3 175.9(2); 2²⁺ Se1–Se2′ 2.905(1), Se1–C1 1.901(5), Se1–C7 1.920(5), C7–C8 1.362(7), C8–C9 1.397(7), C9–C10 1.359(7), C10–C11 1.421(6), C11–C11′ 1.457(8), Se2–C10 1.924(5), Se2–C12 1.908(5), C1–Se1–C7 101.2(2), C1–Se1–Se2′ 102.0(1), C10–Se2–C12 99.2(2), C10–Se2–Se1′ 95.7(1).

Table 1.

Comparison of structural parameters (average) of neutral and dications.

	1 (X-ray)	1 (DFT)	12+ (X-ray)	12+-cs (DFT)	32+-cs (DFT)
S…S, Å	2.937(2)	3.025	2.774(2)	2.859	2.868
S–CPh, Å	1.787(3)	1.799	1.766(4)	1.787	1.796
S–CNap, Å	1.792(2)	1.801	1.727(4)	1.750	1.754
∠C–S–C, deg	102.3(1)	103.1	105.2(2)	105.8	105.9
∠S–S–CPh, deg	163.3(1) 83.2(1)	173.7 94.0	163.1(2)	149.6	169.2
	2 (X-ray)	2 (DFT)	22+ (X-ray)	22+-os (DFT)
Se…Se, Å	3.054(5)	3.103	2.905(1)	2.971	2.928
Se–CPh, Å	1.935(8)	1.946	1.910(7)	1.914	1.916
Se–CNap, Å	1.945(9)	1.94	1.917(6)	1.936	1.890
∠C–Se–C, deg	98.6(3)	97.8	100.2(1)	101.9	101.8
∠Se–Se–CPh, deg	118.1(3)	113.2	98.8(1)	105.9	138.2
	176.9(3)	168.6

Spectroscopic characterization and SQUID measurements

These dications were further characterized by UV absorption spectroscopy, EPR spectroscopy, and SQUID measurements. The UV–Vis absorption spectra of 1²⁺•2[Al(OR_F)₄]⁻ and 2²⁺•2[Al(OR_F)₄]⁻ solutions show characteristic absorptions at 710 and 610 nm, respectively, (Supplementary Figs. 2 and 4).

The EPR spectrum (Fig. 4a) of the frozen solution of 2²⁺•2[Al(OR_F)₄]⁻ appears typical of a triplet state with the zero-field parameters D (136.0 G), E (53.0 G) and an anisotropic g factor (g_x = 2.0190, g_y = 2.0250, and g_z = 2.0020) determined by spectral simulation. The g_iso value (2.0153) is slightly smaller than that of (NapSe₂Ph₂)^•+ (2.0236)²⁹. The average spin–spin distance was estimated to be 5.9 Å from the D parameter, which is comparable to the distance (6.6 Å) between the middle points of Se^…Se bonds in the X-ray structure. The forbidden Δm_s = ±2 transition was not observed from the frozen solution due to the low spin concentration, but observed at the half region of the EPR spectrum on the powder sample of 2²⁺•2[Al(OR_F)₄]⁻ (Fig. 4b), indicating that 2²⁺ is a diradical dication. An increasing susceptibility with temperature was observed for the powder sample of 2²⁺ (Fig. 4c). Careful fitting with Bleaney–Bowers equation⁴² gave a singlet–triplet energy gap (ΔE_S–T = −0.29 kcal mol⁻¹), confirming that 2²⁺ has an open-shell singlet (OS) ground state. To exclude the intermolecular electronic interaction, frozen solution variable-temperature EPR spectroscopy was performed (Supplementary Fig. 5). AT is the product of the intensity for the Δm_s = 2 resonance and the temperature (T)⁴³.

Fig. 4. EPR spectra and temperature-dependent plots of χ_MT for the crystals of 2²⁺.

a The EPR spectrum of frozen solution of 2²⁺ (1 × 10⁻⁴ mol/l) at 183 K (in black) with simulation (in red). b The EPR spectrum of the powder sample of 2²⁺ at 183 K with the forbidden transition at the half magnetic field. c Temperature-dependent plots of χ_MT for the crystals of 2²⁺ from 2 to 320 K (in black) with the fitting plot via the Bleaney–Bowers equation (in red). d Temperature-dependent plots of χ_MT for the crystals of 1²⁺ from 2 to 320 K.

The plot of ln(AT) versus 1/T gives the singlet–triplet gap ΔE_S–T of −0.14 kcal mol⁻¹, which is close to that obtained from SQUID measurement, further confirming the intra-antiferromagnetic interaction. In contrast, both the frozen solution and powder samples of 1²⁺ are EPR silent, which together with the diamagnetism observed by SQUID measurement (Fig. 4d) indicates 1²⁺ has a closed-shell structure in the ground state.

Theoretical calculations

To explore their electronic structures, we performed density functional theory (DFT) calculations on neutral molecules and dications. We first used the crystal structure of 2²⁺ and 1²⁺ as the starting geometries for optimization of their close-shell singlets (CS), open-shell singlets (OS), and triplets at the (U)B3LYP/6-31+G(d,p) level. 2²⁺ has an OS ground state (2²⁺-os) while 1²⁺ has a closed-shell singlet ground state (1²⁺-cs) (Supplementary Table 2). The closed-shell state of 2²⁺ (2²⁺-cs) has a similar geometry to that of 1²⁺-cs. However, a geometry optimization starting with 2²⁺-cs does not reach 2²⁺-os, probably due to a high energy barrier. The optimized geometries of these dications with the lowest energy reasonably agree with the X-ray crystal structures (Table 1). A hypothetical mixed dication species 3²⁺ with two S atoms and two Se atoms at each side of the naphthalene skeleton was also computed (Table 1), which has a closed-shell singlet ground state with the geometry similar to that of 1²⁺. However, the energy difference between the closed-shell singlet and the triplet is lower than that of 1²⁺ but higher than that of 2²⁺, showing the atom dependence (Supplementary Table 2).

Consistent with the experimental data, all four S–C_ph bonds in 1²⁺-cs are nearly coplanar with the naphthalene skeleton, leading to a quinoidal geometry reflected by the HOMO (Fig. 5a). The decrease of the S•••S separation from 1 to 1²⁺ indicates considerable intramolecular S•••S interaction⁴⁰, which is supported by Wiberg bond order of S–S bond (0.19). In 2²⁺-os, the spin density is mainly on Se atoms with an additional extension to the four phenyl rings and naphthalene skeleton (Fig. 5b). The calculated Wiberg bond order for two Se–Se bonds (0.43, 0.43), together with calculated Se–Se antibonding and bonding orbitals (Fig. 5b), indicates the formation of a 2c–3e hemi bond between Se atoms at both sides of the naphthalene skeleton. The calculated miniscule singlet–triplet energy gap (−0.20 kcal mol⁻¹) is in agreement with the value determined from SQUID measurement. Figure 6 shows the Laplacian distribution ∇²ρ(r), the bond paths and critical points of 1²⁺ and 2²⁺ in a plane that contains Ch (Ch = S, Se) atoms and the naphthalene skeleton. It clearly shows the S–S and Se–Se bonding character, as indicted by the bond critical point between the Ch–Ch centers. Judging from the time-dependent DFT (TD-DFT) calculations (Supplementary Figs. 2 and 4), the UV absorptions are mainly assigned to HOMO→LUMO (for 1²⁺) and HOMO-1 (α/β)→LUMO (α/β) (for 2²⁺), respectively, (Fig. 5).

Fig. 5. Molecular orbitals and spin density distribution.

a Frontier molecular orbitals of 1²⁺. b The spin density distribution and some molecular orbitals of 2²⁺.

Fig. 6. Plots of the Laplacian ∇²ρ(r) and resonance structures.

Plots of the Laplacian ∇²ρ(r) for 1²⁺ (a) and 2²⁺ (b). Red dashed lines indicate areas of charge concentration (∇²ρ(r) < 0), while solid blue lines show areas of charge depletion (∇²ρ(r) > 0). The solid lines connecting the atomic nuclei are the bond paths. Green dots are bond critical points and red dots are ring critical points. c Resonance structures of 1²⁺.

Since it is a complicated system to perform complete-active-space SCF (CASSCF) calculation that will take a large active space, we performed a CAS(2,4) calculation with B3LYP optimized geometry to check whether we can call confidently that 2²⁺ possesses an OS state. The resulting Löwdin natural orbitals (NOs) derived from the CASSCF density matrix and their occupation is given in Supplementary Fig. 6. The corresponding occupation number and the shape of the NOs corroborate with the DFT finding.

Discussion

We, here, have shown that tetrachalcogenides 1 and 2 with a naphthalene bridge underwent two-electron oxidations, which afforded room temperature stable dications 1²⁺ and 2²⁺. 1²⁺ is shown to possess a closed-shell singlet ground state while 2²⁺ is a diradical containing two Se∴Se three-electron σ-bonds with the electronic coupling of −0.29 kcal mol⁻¹. The difference of electronic structures between two dications 1²⁺ and 2²⁺ is attributed to the easier p_π–p_π interaction between sulfur and carbon atoms than that between selenium and carbon atoms in terms of atomic size matching. The experimentally obtained geometry of 1²⁺ may be rationalized by that two sulfur atoms from each side of the molecule loses one electron and form a quinoidal structure (I and II, Fig. 6c) with a 14c–16e π-bond upon two-electron oxidation. Though the S•••S separation was observed from 1 to 1²⁺ decreases, the S–S bond length in 1²⁺ (2.77 Å) is much longer than a typical S–S single bond (2.05 Å)⁴¹. Thus the geometry of 1²⁺ is best described as the hybrid of resonance structures of I and II, which is supported by the calculated HOMO (Fig. 5a). In contrast, the difficult formation of p_π–p_π bonding between selenium and carbon atoms makes dication 2²⁺ as a diradical containing two Se∴Se three-electron σ-bonds. 2²⁺ represents the first example of a diradical based on odd-electron σ-bonds. The hypothetical mixed singlet species 3²⁺ has a similar quinoidal geometry as 1²⁺, which may also be induced by sulfur and carbon p_π–p_π interaction. The work sheds new light on the concepts of both diradicals and odd-electron bonds. Synthesis of more diradicals based on odd-electron bonds is under way in our laboratory.

Methods

General

All manipulations were carried out under an N₂ atmosphere by using standard Schlenk or glove box techniques. Solvents were dried prior to use. 1,4,5,8-tetrabromo naphthalene³⁸ and Li[Al(OR_F)₄] (OR_F = OC(CF₃)₃)³⁹ were synthesized according to the literature procedures. NOSbF₆, diphenyldisulfane (PhSSPh), diphenyldiselane (PhSeSePh), isochromeno[6,5,4-def]isochromene-1,3,6,8-tetraone, and ⁿBuLi (1.60 M, in hexane) were purchased from Energy Chemical. CV was performed on an IM6ex electrochemical workstation, with platinum as the working and counter electrodes, Ag/Ag⁺ as the reference electrode and 0.2 M ⁿBu₄NPF₆ as the supporting electrolyte. The NMR spectra were performed using a Bruker DRX-400 at room temperature in ppm downfield from internal Me₄Si. EPR spectra were obtained using Bruker EMX-10/12 X-band variable-temperature apparatus. UV–Vis spectra were recorded on the Lambda 750 spectrometer. Element analyses of 1²⁺•2[Al(OR_F)₄]⁻ and 2²⁺•2[Al(OR_F)₄]⁻ were performed at Shanghai Institute of Organic Chemistry, the Chinese Academy of Sciences. Magnetic measurements were performed using a Quantum Design SQUID VSM magnetometer with a field of 0.1 T. X-ray crystal structures were obtained by using Bruker D8 CMOS detector at 193 K. Crystal data and structure refinement are listed in Supplementary Table 1.

Preparation of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane): A solution of ⁿBuLi (6.90 ml, 1.60 M, 11.04 mmol) in hexane was added dropwise to a solution of 1,4,5,8-tetrabromo naphthalene (2.24 g, 5.05 mmol) in Et₂O (150 ml) at −78 °C and stirring was maintained for 2 h. Then a solution of PhSSPh (2.40 g, 11.00 mmol) in Et₂O (20 ml) was added dropwise to the mixture. Then the resulting mixture was allowed to reach to room temperature and stirring was continued for 12 h. The crude product was treated with 0.10 M solution of sodium hydroxide (3 × 30 ml) and extracted with Et₂O. The combined organic phase was dried over Na₂SO₄ and concentrated under vacuum. The crude product was purified by chromatography using petroleum ether: CH₂Cl₂ (10: 1) as the eluent to give 1.00 g of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane) (40%) as light yellow solid. ¹H NMR(400 MHz, CD₂Cl₂) δ 7.14 (d, ³J(H, H) = 8.1 Hz, 2H, Ar-H), 7.26–7.32 (m, 10 H, Ar-H) 7.60 (d, ³J(H, H) = 8.1 Hz, 2H, Ar-H); ¹³C NMR(125 MHz, CD₂Cl₂) δ 118.21, 128.24, 129.96, 132.89, 134.32, 134.35, 134.62, 137.09, and 137.36.

Preparation of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylselane): By the procedure similar to the synthesis of the (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane), a yellow solid is given. Yield: 1.01 g, 34.5%; ¹H NMR (400 MHz, CD₂Cl₂) δ 7.10 (d, ³J(H, H) = 8.16 Hz, 2H, Ar-H), 7.35–7.41 (m, 6H, Ar-H) 7.48 (d, ³J(H, H) = 8.15 Hz, 2H, Ar-H), 7.56–7.58 (m, 4H, Ar-H); ¹³C NMR(125 MHz, CD₂Cl₂) δ 118.75, 129.32, 130.27, 132.34, 133.30, 133.52, 135.13, 135.72, and 136.59.

Preparation of 1: A solution of ⁿBuLi (2.60 ml, 1.60 M, 4.16 mmol) in hexane was added dropwise to a solution of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane) (1.00 g, 1.99 mmol) in Et₂O (120 ml) at −78 °C and maintained stirring for 2 h. Then a solution of PhSSPh (0.92 g, 4.21 mmol) in Et₂O (20 ml) was added dropwise to the mixture. Then the resulting mixture was raised to room temperature and kept stirring for 12 h. The crude product was treated with 0.10 M solution of sodium hydroxide (3 × 30 ml) and extracted with Et₂O. The combined organic phase was dried over Na₂SO₄ and concentrated under vacuum. The crude product was purified by chromatography using petroleum ether: CH₂Cl₂ (5: 1) as the eluent to give 0.45 g (0.80 mmol) of 1 (40%) as a dark yellow solid. ¹H NMR (400 MHz, CD₂Cl₂) δ 7.17–7.18 (m, 2H, Ar-H), 7.20 (d, ³J(H, H) = 1.7 Hz, 4H, Ar-H), 7.21–7.23 (m, 2H, Ar-H), 7.24–7.25 (m, 2H, Ar-H), 7.26–7.28 (m, 8H, Ar-H), 7.29–7.30 (m, 6H, Ar-H); ¹³C NMR (125 MHz, CD₂Cl₂) δ 127.49, 129.65, 131.31, 133.68, 135.07, 136.37, and 138.57.

Preparation of 2: By the procedure similar to the synthesis of 1, a yellow solid is given. Yield: 0.46 g, 30%; ¹H NMR (400 MHz, CD₂Cl₂) δ 7.24–7.25 (m, 2H, Ar-H), 7.26–7.27 (m, 4H, Ar-H), 7.28–7.30 (m, 6H, Ar-H), 7.35–7.36 (m, 4H, Ar-H), 7.37–7.38 (m, 4H, Ar-H), 7.48 (d, ³J(H, H) = 1.05 Hz, 4H, Ar-H); ¹³C NMR (125 MHz, CD₂Cl₂) δ 127.96, 129.77, 132.73, 133.31, 135.69, 135.95, and 138.64.

Preparation of 1²⁺•2[Al(OR_F)₄]⁻: Under anaerobic and anhydrous conditions, CH₂Cl₂ (35 ml) was added dropwise to the mixture of 1 (0.11 g, 0.20 mmol), NOSbF₆ (0.11 g, 0.42 mmol) and Li[Al(OR_F)₄] (0.41 g, 0.42 mmol) while stirring at room temperature. The resultant dark blue solution was stirred at room temperature for 12 h, and then filtered to remove the precipitate (LiSbF₆). The filtrate was concentrated and stored at −40 °C for 24 h to afford yellow X-ray-quality crystals of 1²⁺•2[Al(OR_F)₄]⁻. Isolated yield: 0.12 g, 24%; elemental analysis (calcd. found for C₆₆H₂₄Al₂F₇₂O₈S₄): C (31.77, 31.48) H (0.97, H 1.14).

Preparation of 2²⁺•2[Al(OR_F)₄]⁻: By the procedure similar to the synthesis of 1²⁺•2[Al(OR_F)₄]⁻, black crystals are given. Isolated yield: 0.10 g, 19%; elemental analysis (calcd found for C₆₆H₂₄Al₂F₇₂O₈Se₄): C (29.55, 29.16) H (0.90, H 1.13)

Quantum chemical calculations

Geometry optimization without symmetry constraint were performed using DFT at the (U)B3LYP/6-31+G(d, p) level. Frequency results were examined to confirm stationary points as minima (no imaginary frequencies). The UV–Vis absorption spectrum was calculated on the optimized geometry using TD-DFT method at the (U)B3LYP/6-31+G(d,p) level. To consider solvent (CH₂Cl₂) effects, polarized continuum model was adopted in the calculation of the single point energies involved in the disproportionation and dimerization, and UV–Vis absorption spectrum. Wiberg bond order was calculated at the (U)B3LYP/6-31+G(d,p) level with the Multiwfn program. These calculations were performed using Gaussian 16 A03 software. The electron density distribution was analyzed with Quantum Theory of Atom in Molecules method that was developed by Bader⁴⁴. The multiconfigurational CASSCF^45,46 calculations were performed on the (U)B3LYP/6-31+G(d, p) optimized geometry of 2²⁺-os with the def2-SVP basis set using ORCA 4.2.0 program⁴⁷.

Author contributions

X.W. conceived the project. W.Y. performed the chemical experiments and recorded all spectroscopic data. R.F. and Y.Z. performed the X-ray diffraction studies. L.Z., D.X., and S.P. carried out the calculations. G.F. and Lil.Z. analyzed the computational data and wrote the theoretical part. X.W. wrote the paper. W.W. helped with writing of the experimental section. All authors discussed the results and manuscript.

Data availability

The authors declare that all relevant data supporting the findings of this work are available from the corresponding authors on request. The X-ray crystallographic coordinates for structures reported in this study have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers 1959358-1959361. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary information is available for this paper at 10.1038/s41467-020-17303-4.