Radicals are species that possess an unpaired electron1,2,3,4,5,6,7. 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 biochemistry9,10,11,12,13,14,15,16,17,18,19,20,21. A number of radicals with a one-electron22,23,24,25 or three-electron σ-bond12,26,27,28,29,30,31,32 have been isolated and structurally studied (Fig. 1).

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

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 NN three-electron σ–bond. g The SS and SeSe three-electron σ–bonds. h The PdPd and NiNi three-electron σ–bonds. i The RhSi and IrSi 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 materials33,34,35,36,37. 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 SeSe and SS three-electron σ-bond, respectively.

We now report a diradical (22+, Fig. 2) that is based on two SeSe 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.
figure 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.


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(ORF)4] (ORF = 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–CPh (Ch = S, Se) bond is nearly perpendicular to the other at both sides of the naphthalene skeleton. Upon oxidation, in 12+ the two S–CPh bonds at the same side of the naphthalene skeleton are nearly linear (torsion angle CPhSSCPh = 6°) and all four S–CPh bonds are coplanar to the naphthalene skeleton, while in 22+ two Se–CPh bonds at the same side are parallel and all Se–CPh bonds are nearly perpendicular to the naphthyl plane (CSeC = 100°). The average Se–C bond (Se–CPh and Se–CNap) 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–CPh 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–Cnap 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+.
figure 3

Yellow, carbon; red, selenium; blue, sulfur. Hydrogen atoms are not shown. Selected bond length (Å) and angle (deg): 1 S1S2′ 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 Se1Se4 3.061(5), Se2Se3 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.

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(ORF)4] and 22+•2[Al(ORF)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(ORF)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 (gx = 2.0190, gy = 2.0250, and gz = 2.0020) determined by spectral simulation. The giso 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 SeSe bonds in the X-ray structure. The forbidden Δms = ±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(ORF)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 (ΔES–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 Δms = 2 resonance and the temperature (T)43.

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

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 χMT 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 χMT for the crystals of 12+ from 2 to 320 K.

The plot of ln(AT) versus 1/T gives the singlet–triplet gap ΔES–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–Cph 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.
figure 5

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.
figure 6

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.


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 SeSe 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 pπ–pπ 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 pπ–pπ bonding between selenium and carbon atoms makes dication 22+ as a diradical containing two SeSe 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 pπ–pπ 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.



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(ORF)4] (ORF = 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(ORF)4] and 22+•2[Al(ORF)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(ORF)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(ORF)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(ORF)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(ORF)4]: By the procedure similar to the synthesis of 12+•2[Al(ORF)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 CASSCF45,46 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.