A diradical based on odd-electron σ-bonds

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.

We now report a diradical (2 2+ , Fig. 2) that is based on two Se∴Se three-electron σ-bonds. In contrast, the dication of sulfur analog (1 2+ ) does not display diradical character but exists as a closed-shell singlet instead.
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 1 2+ the two S-C Ph bonds at the same side of the naphthalene skeleton are nearly linear (torsion angle ∠C Ph SSC Ph = 6°) and all four S-C Ph bonds are coplanar to the naphthalene skeleton, while in 2 2+ 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 2 2+ 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 2 2+ are similar to those of (NapSe 2 Ph 2 ) +30 , indicating there is a three-electron σbond 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 interactions 41 . The S-C nap bond length (1.727(4) Å) of 1 2+ is also notably shorter than those of 1 (1.792(2) Å) and (NapS 2 Ph 2 ) + (1.768(3) Å) 30 . Moreover, the naphthalene skeleton of 1 2+ becomes quinoidal (C8-C9 1.351(6) Å).

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 1 2+ The EPR spectrum (Fig. 4a) of the frozen solution of 2 2+ •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 (NapSe 2 Ph 2 ) •+ (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 2 2+ •2[Al(OR F ) 4 ] − (Fig. 4b), indicating that 2 2+ is a diradical dication. An increasing susceptibility with temperature was observed for the powder sample of 2 2+ (Fig. 4c). Careful fitting with Bleaney-Bowers equation 42 gave a singlet-triplet energy gap (ΔE S-T = −0.29 kcal mol −1 ), confirming that 2 2+ 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 .
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 1 2+ are EPR silent, which together with the diamagnetism observed by SQUID measurement (Fig. 4d) indicates 1 2+ 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 2 2+ and 1 2+ 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. 2 2+ has an OS ground state (2 2+ -os) while 1 2+ has a closed-shell singlet ground state (1 2+ -cs) (Supplementary Table 2). The closed-shell state of 2 2+ (2 2+ -cs) has a similar geometry to that of 1 2+ -cs. However, a geometry optimization starting with 2 2+ -cs does not reach 2 2+ -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 3 2+ 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 1 2+ . However, the energy difference between the closed-shell singlet and the triplet is lower than that of 1 2+ but higher than that of 2 2+ , showing the atom dependence (Supplementary Table 2).
Consistent with the experimental data, all four S-C ph bonds in 1 2+ -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 1 2+ indicates considerable intramolecular S•••S interaction 40 , which is supported by Wiberg bond order of S-S bond (0.19). In 2 2+ -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 ∇ 2 ρ(r), the bond paths and critical points of 1 2+ and 2 2+ 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 timedependent DFT (TD-DFT) calculations (Supplementary Figs. 2 and 4), the UV absorptions are mainly assigned to HOMO→-LUMO (for 1 2+ ) and HOMO-1 (α/β)→LUMO (α/β) (for 2 2+ ), respectively, (Fig. 5). Since it is a complicated system to perform complete-activespace 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 2 2+ 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.

Methods
General. All manipulations were carried out under an N 2 atmosphere by using standard Schlenk or glove box techniques. Solvents were dried prior to use. Preparation of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane): A solution of n BuLi (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 Et 2 O (150 ml) at −78°C and stirring was maintained for 2 h. Then a solution of PhSSPh (2.40 g, 11.00 mmol) in Et 2 O (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 Et 2 O. The combined organic phase was dried over Na 2 SO 4 and concentrated under vacuum. The crude product was purified by chromatography using petroleum ether: CH 2 Cl 2 (10: 1) as the eluent to give 1.00 g of (4,8-dibromonaphthalene-1,5-diyl)bis(phenylsulfane) (40%) as light yellow solid. 1 H NMR(400 MHz, CD 2 Cl 2 ) δ 7.14 (d, 3   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 (CH 2 Cl 2 ) 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 Bader 44 . The multiconfigurational CASSCF 45,46 calculations were performed on the (U)B3LYP/6-31+G(d, p) optimized geometry of 2 2+ -os with the def2-SVP basis set using ORCA 4.2.0 program 47 .

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.