Inorganic benzenes with inverted singlet-triplet gaps

Inorganic benzenes with inverted singlet-triplet gaps | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Inorganic benzenes with inverted singlet-triplet gaps Hironori Kaji, Katsuyuki Shizu, Kuraudo Ishihara, Hiroki Uratani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8056562/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Inorganic-type benzenes have attracted significant attention due to their unique physical and chemical properties that are different from organic benzene. In this study, we theoretically investigate the possibility of inorganic benzenes as wide-gap materials with inverted singlet and triplet (iST) excited states. Since iST materials allow efficient triplet to singlet conversion without thermal activation, they are promising as fluorescent and assist dopant materials for light-emitting diodes. From theoretical calculations, borazine (B 3 N 3 H 6 ), one of the most well-known inorganic benzenes, and its derivatives are expected not only to show iST but also to exhibit fast radiative decays surpassing those of typical iST materials: azaphenalene derivatives. Borthiin (B 3 S 3 H 3 ), boroselenol (B 3 Se 3 H 3 ), and the gallium-nitride analogue of benzene (Ga 3 N 3 H 6 ) are also expected to show iST with wide optical gaps. Physical sciences/Materials science/Materials for devices Physical sciences/Chemistry/Materials chemistry Figures Figure 1 Figure 2 Figure 3 Introduction Inorganic-type benzenes are six-membered six-π-electron systems having electronic structures analogous to organic benzene (hereafter referred to simply as benzene as usual). 1 Borazine (B 3 N 3 H 6 ) is one of the most representative inorganic benzenes consisting of alternating boron (B) and nitrogen (N) atoms arranged in a hexagonal ring (Fig. 1 a). 2 While numerous materials exhibiting visible to near-infrared emission have been widely explored for organic light-emitting diodes (OLEDs), those with ultraviolet (UV) to deep-UV (DUV) emission for OLEDs remain underdeveloped, despite their broad potential across wide variety of applications. 3 Hexagonal boron nitride (hBN), a structural analogue of graphene, has known to be a semiconductor that shows a wide optical band gap and is promising as an UV to DUV emitter in optoelectronic applications. 4 , 5 Boron nitride nanotubes (BNNTs), 6 structural analogues of carbon nanotubes, also show wide band gaps suitable for such applications. 7 Recent advances in the synthesis makes it possible to develop diverse inorganic benzenes including boron-nitride-based compounds consisting of four-B and two-N atoms 8 (B 4 N 2 R 2 R’ 2 R” 2 ), boroxine 9 (B 3 O 3 H 3 ), borthiin 10 (B 3 S 3 R 3 ), boroselenol 11 (B 3 Se 3 R 3 ), phosphaborazine 12 (B 3 P 3 R 3 R’ 3 ), phosphazene 13 (N 3 P 3 R 6 ) and its gallium analogue 14 (Ga 3 P 3 R 3 R’ 3 ), aluminum analogue (alumazene 15 ; Al 3 N 3 R 3 R’ 3 ) and its phosphor and arsenic analogues 16 (Al 3 P 3 R 3 R’ 3 and Al 3 As 3 R 3 R’ 3 , respectively), as well as triphospha- and triarsa-trisilabenzenes 17 (Si 3 P 3 R 3 and Si 3 As 3 R 3 , respectively), and germanium analogue (germanazene 18 ; Ge 3 N 3 R 3 ), where R, R’, and R’’ denote substituents. The structural diversity of these inorganic benzenes allows us to develop novel materials with unique photophysical properties that are unattainable in conventional carbon-based aromatic systems. The doubly degenerate highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of borazine are predominantly localized on the N and B atoms, respectively (Fig. 1 b). Thus, the HOMO→LUMO excitation of borazine can be viewed as the short-range charge-transfer 19 (SRCT) electronic excitation between the N and B atoms. For the inorganic-type benzenes listed above, S 1 can be energetically lower than T 1 as confirmed below, leading to a unique electronic property called the inverted singlet-triplet (iST or INVEST): the S 1 -T 1 energy difference Δ E ST is negative. Here, Δ E ST = E (S 1 ) − E (T 1 ); E (S 1 ) and E (T 1 ) are the S 1 and T 1 energies, respectively. The presence of iST was originally suggested theoretically by Borden 20 , Kollmar and Staemmler 21 for cyclobutadiene in the 1970s. Experimental iST study was performed by Leupin and Wirz for cycl[3.3.3]azine 22 in 1980. After a long silence, interest in iST was reignited by a pivotal theoretical study by de Silva in 2019, which clearly demonstrated the possibility of negative singlet-triplet gap by considering double excitations. 23 Experimental observations have also emerged for azaphenalene derivatives, following the work by Domcke’s group in 2019, 24–28 Because iST allows T 1 →S 1 transition without thermal activation, iST materials can show efficient reverse intersystem crossing (RISC) from T 1 to S 1 and are promising as fluorescent materials for organic light-emitting diodes (OLEDs). However, to date, the rate constants for S 1 →S 0 fluorescence ( k F ) are not large enough, on the order of 10 6 s - 1 . In this study, we theoretically investigate the potential iST character of inorganic benzenes. Our quantum chemical calculations indicate that borazine derivatives are promising candidates for electroluminescent UV emitters exhibiting both negative Δ E ST and k F of 10 7 -10 8 s - 1 (see Table 1 below). These k F values, one to two orders of magnitude higher than those of previously reported iST molecules, represent a significant advancement in emitter performance. Borthiins and boroselenol are also found to show negative Δ E ST and are candidates for core units to develop wide gap iST materials for OLEDs. The gallium-nitride (GaN) analogue of benzene (Ga 3 N 3 H 6 ) is also predicted to show iST character with a wide optical gap. Results Inorganic benzenes Figures 1 and 2 shows the structures and abbreviated names of the borazine family investigated in this study: borazine ( 1: ben-BN ) and one- and two-dimensional (1D and 2D) fused borazines ( 2a: naph-BN − 2 k: bis-BN ). In Fig. 2 , the H atoms are omitted for clarity; the optimized structures with H atoms are shown in Supplementary Information (Supplementary Fig. 1). 2k: bis-BN can be viewed as a model of hBN. Δ E ST , E (S 1 ), E (T 1 ), the S 0 -S 1 transition dipole moment ( µ ), S 0 -S 1 oscillator strength ( f ), and k F of 1 : ben-BN − 2 k: bis-BN calculated with the spin-component scaling second-order approximate coupled-cluster (SCS-CC2) are listed in Table 1 . Those calculated with the second-order algebraic diagrammatic construction (ADC(2)) are also listed in Supplementary Table 1, see Methods section for the calculation detail. Importantly, all of 1 : ben-BN − 2 k: bis-BN show negative Δ E ST ( 6.53 eV), suggesting that these compounds are promising as wide-gap core materials with iST character. It would be possible to develop materials with preferred emission wavelengths through appropriate structural modifications. To confirm SRCT character of 1 : ben-BN , we calculated electron-density difference (Δ ρ ) maps arising from the S 0 →S 1 and S 0 →T 1 excitations (Fig. 1 c). The Δ ρ maps were calculated by subtracting the total electron density of S 0 from that of S 1 or T 1 , using the S 0 structure. Figure 1 c shows the Δ ρ maps for the S 0 →S 1 (B 1 ), S 0 →T 1 (A 1 ), and S 0 →T 1 (B 1 ) excitations of 1: ben-BN , where T 1 (A 1 ) and T 1 (B 1 ) represent doubly degenerate T 1 of different symmetries, A 1 and B 1 , respectively. Blue regions show negative Δ ρ where the electron density decreases and yellow regions show positive Δ ρ where the electron density increases. The negative Δ ρ is strongly localized on the N atoms, whereas the positive Δ ρ is strongly localized on the B atoms, suggesting that a short-range electron transfer from the N to B atoms occurs upon the excitations. In addition, Δ ρ shows spatially alternating negative and positive regions, which are characteristic for B and N containing molecules with small positive Δ E ST 29 – 31 and heptazine derivatives with negative Δ E ST . 32 Fig. 2 shows calculated Δ ρ maps for the S 0 →S 1 (B 1 ) and S 0 →T 1 (A 1 ) excitations of 2k: bis-BN . Like 1 : ben-BN , 2k: bis-BN has spatially alternating negative and positive regions, indicating SRCT character. Under the Franck-Condon approximation, the k F of a molecule is proportional to f : $$\:{k}_{\text{F}}=\frac{{e}^{2}}{2\pi\:{m}_{e}{\epsilon\:}_{0}{c}^{3}}{\omega\:}^{2}f$$ 1 where f is $$\:f=\frac{2{m}_{\text{e}}\omega\:{\mu\:}^{2}}{3{e}^{2}\hslash\:}$$ 2 Here, e is the elementary charge, m e is the mass of an electron, ε 0 is the vacuum permittivity, c is the speed of light, ω is the angular frequency of light ( ω = E (S 1 )/ℏ, where ℏ is the Dirac constant). From Eqs. ( 1 ) and ( 2 ), a large µ is desirable to increase f and k F , which enhance luminescence efficiency. From Table 1 , it is found that f is large for 1D structures, especially when the fused ring becomes longer ( 1: ben-BN → 2a: naph-BN → 2b: anth-BN → 2d: tetra-BN ), whereas it vanishes when the molecular structure is 3-fold triangular symmetric ( 1 : ben-BN , 2g : phenal-NB , and 2h : phenal-BN ). 2d : tetra-BN shows the largest k F of 1.5×10 8 s − 1 among molecules in Fig. 2 . These results suggest that breaking the C 3 symmetry and extending the molecular framework in one direction are key factors for increasing µ , f and the resulting k F . Table 1 Point groups and Δ E ST , E (S 1 ), E (T 1 ), µ , f , and k F of inorganic benzenes calculated with the SCS-CC2/cc-pVTZ//PBE0/6-31G(d) method. Molecular formula Point group Δ E ST (meV) E (S 1 ) (eV) E (T 1 ) (eV) µ (au) f k F (s − 1 ) 1 : ben-BN B 3 N 3 H 6 D 3h −295 6.83 7.13 0.0000 0.0 0.0 2a : naph-BN B 5 N 5 H 8 C 2v −95 6.64 6.73 0.1502 3.7×10 − 3 7.0×10 6 2b : anth-BN B 7 N 7 H 10 C 2v −21 6.63 6.65 0.4159 2.8×10 − 2 5.4×10 7 2c : phenan-BN B 7 N 7 H 10 C s −127 6.57 6.70 0.2990 1.4×10 − 2 2.7×10 7 2d : tetra-BN B 9 N 9 H 12 C 2v −51 6.62 6.67 0.7023 8.0×10 − 2 1.5×10 8 2e : cryc-BN B 9 N 9 H 12 C s −59 6.56 6.62 0.1300 2.7×10 − 3 5.1×10 6 2f : pyr-BN B 8 N 8 H 10 C 2v −221 6.54 6.76 0.0562 5.1×10 − 4 9.4×10 5 2g : phenal-NB B 7 N 6 H 9 D 3h −260 6.59 6.85 0.0000 0.0 0.0 2h : phenal-BN B 6 N 7 H 9 D 3h −128 6.54 6.67 0.0000 0.0 0.0 2i : olymp-NB B 10 N 9 H 11 C 2v −243 6.54 6.78 0.0284 1.3×10 − 4 2.4×10 5 2j : olymp-BN B 9 N 10 H 11 C 2v −97 6.53 6.63 0.2545 1.0×10 − 2 1.9×10 7 2k : bis-BN B 14 N 14 H 14 C 2v −57 6.54 6.59 0.2110 7.1×10 − 3 1.3×10 7 3 : (6, 6)NB-BN B 24 N 24 H 24 S 6 −141 6.26 6.40 0.0000 0.0 0.0 4e : [6]CPP-BN B 18 N 18 H 24 S 6 −145 6.26 6.40 0.0000 0.0 0.0 5 : [6]CMP-BN B 18 N 18 H 24 C 3v −186 6.45 6.64 0.0000 0.0 0.0 6e : [6]PP-BN B 18 N 18 H 26 C 2 −77 6.58 6.66 0.0458 3.4×10 − 4 6.4×10 5 7f : [6]MP-BN B 18 N 18 H 26 C 1 −214 6.49 6.70 0.0556 4.9×10 − 4 9.0×10 5 8a : B 12 N 12 -fullerene B 12 N 12 T h −134 6.47 6.60 0.0000 0.0 0.0 9 : ben-BS B 3 S 3 H 3 D 3h −109 5.02 5.13 0.0000 0.0 0.0 10 : ben-BSe B 3 Se 3 H 3 D 3h −160 4.42 4.58 0.0000 0.0 0.0 11 : ben-BO B 3 O 3 H 3 D 3h 326 8.11 7.79 0.0000 0.0 0.0 12 : ben-GaN Ga 3 N 3 H 6 D 3h −230 5.52 5.75 0.0000 0.0 0.0 13 : prism-GaN Ga 3 N 3 H 6 C s 507 4.11 3.61 0.7097 5.1×10 − 2 3.7×10 7 Ring- and fullerene-type borazines Figure 3 shows cyclic borazines, which are parts of BNNTs. The Δ E ST , E (S 1 ), µ , f , and k F values are also shown in Table 1 . 3: (6, 6)NB-BN is a subunit of a BNNT, consisting of 12 fused borazine rings. The structure of 3: (6, 6)NB-BN was designed with reference to a carbon nanobelt structure in ref. 33 (a subunit of a (6, 6)-carbon nanotube) and then, optimized at the PBE0/6-31G(d) level of theory. 3: (6, 6)NB-BN shows a negative Δ E ST of − 141 meV and a large E (S 1 ) of 6.26 eV (Table 1 ). Figure 3 also shows the calculated Δ ρ maps for the S 0 →S 1 (A g ) and S 0 →T 1 (A g ) excitations of 3: (6, 6)NB-BN . Similarly to the above cases, the negative Δ ρ (blue regions) is strongly localized on the N atoms, whereas the positive Δ ρ (yellow regions) is strongly localized on the B atoms, suggesting that S 1 and T 1 of 3: (6, 6)NB-BN also have pure SRCT character. The f value of 3: (6, 6)NB-BN vanishes because of the symmetric ring structure, which would make 3: (6, 6)NB-BN non-emissive. 4e: [6]CPP-BN is another subunit of the BNNT; the diameter of 4e: [6]CPP-BN (8.36 Å) is slightly larger than that of 3: (6, 6)NB-BN (8.32 Å). 4e: [6]CPP-BN consists of six borazine rings and is the borazine analogue of [6]cycloparaphenylene ([6]CPP) 34 , a subunit of a (6,6)-carbon nanotube. The Δ E ST , E (S 1 ), µ , f , and k F of 4e: [6]CPP-BN are similar to those of 3: (6, 6)NB-BN , despite the difference in conjugated state. 5 : [6]CMP-BN also consists of six borazine rings but forms a different ring configuration; the borazine analogue of [6]cyclometaphenylene. 35 The Δ E ST of 5: [6]CMP-BN (− 186 meV) is smaller than those of 3: (6, 6)NB-BN and 4e: [6]CPP-BN . Similarly to 3: (6, 6)NB-BN and 4e: [6]CPP-BN , the symmetric ring structure results in f = 0. To understand the influence of the ring structures on the f values, we compared the f values of 4e: [6]CPP-BN and 5: [6]CMP-BN with those of their 1D counterparts, 6e: [6]PP-BN and 7f: [6]MP-BN . Unlike 4e: [6]CPP-BN and 5: [6]CMP-BN , 6e: [6]PP-BN and 7f: [6]MP-BN have non-zero f values, leading to k F of the order of 10 5 –10 6 s − 1 , suggesting that the symmetric ring formation largely decreases f value. The calculated Δ E ST , E (S 1 ), µ , f , and k F values for five to twelve membered borazine rings and their 1D counterparts are summarized in Supplementary Information (molecules 4d: [5]CPP-BN − 4 k : [12]CPP-BN in Supplementary Fig. 2, molecules 6a: [2]PP-BN − 6 k: [12]PP-BN in Supplementary Fig. 3, and Supplementary Table 2). The ring molecules ( 4d: [5]CPP-BN − 4 k : [12]CPP-BN ) has zero or nearly zero f values, whereas the 1D counterparts ( 6d: [5]PP-BN − 6 h: [9]PP-BN ) have non-zero f values with k F of 10 4 –10 6 s − 1 . Linear metaphenylene-type molecules ( 7a: [3]MP-BN − 7 f: [6]MP-BN ) also have non-zero f values with k F of 10 5 –10 7 s − 1 (Supplementary Fig. 4 and Supplementary Table 2). Borazine analogues of fullerenes have been experimentally observed. 36 – 38 B 12 N 12 -fullerene is a borazine analogue of C 24 fullerene and consists of the four- and six-membered rings (note that 8a: B 12 N 12 -fullerene and all fullerene-type compounds have no H atoms). 8a: B 12 N 12 -fullerene shows a negative Δ E ST of − 134 meV, which is comparable to those of 3: (6, 6)NB-BN and 4e: [6]CPP-BN (− 141 and − 145 meV, respectively). S 1 and T 1 of 8a: B 12 N 12 -fullerene are triply degenerate (denoted as A 2 , B 1 , and B 2 ) owing to its highly symmetric structure. Figure 3 shows Δ ρ maps for the S 0 →S 1 and S 0 →T 1 excitations of 8a: B 12 N 12 -fullerene . The negative and positive Δ ρ distributions suggest that S 1 and T 1 of 8a: B 12 N 12 -fullerene shows pure SRCT character. Like the ring borazines of 3: (6, 6)NB-BN , 4e: [6]CPP-BN , and 5: [6]CMP-BN , 8a: B 12 N 12 -fullerene has zero f value and is expected to be non-emissive. The calculated results for borazine analogues of C 48 and C 72 fullerenes are shown in Supplementary Information (molecules 8b: B 24 N 24 -fullerene and 8c: B 36 N 36 -fullerene in Supplementary Fig. 5 and Supplementary Table 2). Although 8b: B 24 N 24 -fullerene and 8c: B 36 N 36 -fullerene show positive Δ E ST , the Δ E ST values (~ k B T at room temperature) are sufficiently small to induce rapid T 1 →S 1 transition. Inorganic-type benzenes other than borazine Finally, we investigate the potential of inorganic-type benzenes other than borazine-based compounds as wide-gap iST materials ( 9: ben-BS − 1 3: prism-GaN in Figs. 4 and 14: ben-B 4 N 2 − 2 3: ring-Ge 3 N 3 in Supplementary Fig. 6). Derivatives of 9: ben-BS − 1 1: ben-BO and 14: ben-B 4 N 2 − 2 3: ring-Ge 3 N 3 have been experimentally synthesized, 8–18 whereas 12 : ben-GaN and 13: prism-GaN have been only theoretically predicted. 39 , 40 Substituents required for organic synthesis are replaced with H atoms. Borthiin ( 9: ben-BS ) and boroselenol ( 10: ben-BSe ) show negative Δ E ST ( < − 100 meV), whereas the oxygen (O) analog (boroxine, 11: ben-BO ) shows a large positive Δ E ST of 326 meV (Table 1 ). To understand the difference in the Δ E ST values of 9: ben-BS − 1 1: ben-BO , we compared the Δ ρ maps for the S 0 →S 1 and S 0 →T 1 excitations of 9: ben-BS − 1 1: ben-BO (Fig. 4 ). For 9: ben-BS and 10: ben-BSe , the negative Δ ρ is strongly localized on the S and Se atoms, whereas the positive Δ ρ is strongly localized on the B atoms. The Δ ρ patterns are similar to those observed for borazine ( 1: ben-BN , Fig. 1 ). Meanwhile, for 11: ben-BO , the negative Δ ρ is largely distributed on the B-O and B-H bonds whereas the positive Δ ρ is strongly localized on B atoms, which breaks down SRCT character. This pattern of Δ ρ suggests the significant overlap of the MOs, which may yield large exchange interaction that dominates over the spin polarization (double excitation) effect, leading to the large positive Δ E ST of 326 meV. GaN is a wide-bandgap semiconductor and widely used for blue and white light-emitting diodes. 41 – 44 Hence, although the GaN analogue of benzene (Ga 3 N 3 H 6 ) has not been synthesized yet, it is worth investigating its potential iST property. Two structures have been theoretically proposed for Ga 3 N 3 H 6 : a planar benzene-type structure 39 ( 12: ben-GaN ) where Ga and N atoms are arranged alternatively and a prismane-type structure 40 ( 13: prism-GaN ) where two Ga and N atoms are adjacent to each other. Calculated Δ ρ maps for the S 0 →S 1 and S 0 →T 1 excitations of 12: ben-GaN show SRCT with spatially alternating negative and positive regions, whereas those of 13: prism-GaN has large distributions on the Ga-Ga bonds. Consequently, 12: ben-GaN shows negative Δ E ST of − 230 meV, whereas 13: prism-GaN shows a large positive Δ E ST of 507 meV (Table 1 ). Thus, like borazine, the GaN analogue of benzene ( 12: ben-GaN ) is predicted to show iST owing to its SRCT character in the S 0 →T 1 and S 0 →S 1 excitations. For other inorganic-type molecules, 14: ben-B 4 N 2 , 15: ben-BP , 16: ben-NP , 17: ring-Ga 3 P 3 , 18: ben-AlN , 19: ring-Al 3 P 3 , 20: ring-Al 3 As 3 , 21: ring-(Si(N 2 CH 3 )) 3 P 3 , 22: ring-(Si(N 2 CH 3 )) 3 As 3 , and 23: ring-Ge 3 N 3 (Supplementary Fig. 6), Δ E ST were calculated to be positive (> 100 meV, Supplementary Table 3). Among the fifteen inorganic benzenes ( 9: ben-BS – 23: ring-Ge 3 N 3 ) examined in Fig. 4 and Supplementary Fig. 6, only 9: ben-BS , 10: ben-BSe , and 12: ben-GaN were expected to show iST. Discussion We theoretically investigated the potential iST character of inorganic-type benzenes mainly focusing on borazines. 2D-sheet, ring, and fullerene type borazines showed the SRCT from N to B atoms in S 0 →S 1 and S 0 →T 1 excitations, which leads to the large inverted S 1 and T 1 energies. Other than borazines, ben-BS (B 3 S 3 H 3 , borthiin), ben-BSe (B 3 Se 3 H 3 , boroselenol), and the ben-GaN (Ga 3 N 3 H 6 ) were found to show iST. These molecules have large S 1 energies, leading to the development of promising electroluminescent UV emitters and wide-gap hosts with iST properties. Totally, we found 43 compounds with negativeΔ E ST s. Among them, several compounds exhibit k F of 10 7 -10 8 s - 1 , which will be expected as efficient emitters. In addition, by introducing various functional groups to these compounds, it is expected that excellent iST emitting materials with tunable emission wavelengths can be developed. Methods Geometry optimization The ground-state (S 0 ) geometries of inorganic-type benzene materials were optimized at the PBE0/6-31G(d) level of theory and their singlet and triplet excited states were calculated using the SCS-CC2 method with the cc-pVTZ basis for the S 0 geometries (Supplementary Tables 4–60 show the optimized geometries). The method is denoted as SCS-CC2/cc-pVTZ//PBE0/6-31G(d). The SCS-CC2 method considers double-electron excitation and has been shown to accurately predict Δ E ST of molecules consisting of B and N backbones. 29 – 31 The S 0 -geometry optimization was performed using the Gaussian 16 program package. 45 Calculation of electronic properties Δ E ST , E (S 1 ), E (T 1 ), µ , and f were calculated using the Turbomole program package. 46 k F was calculated from Eqs. 1 and 2 . ADC(2) method also considers double-electron excitation and has been used to compute Δ E ST of iST molecules. 47 The results for ADC(2) calculations are reported in Supporting Information (Supplementary Tables 1–3). Declarations Competing interests The authors declare no competing interests. Author contributions Theoretical calculations were mainly performed by K.S. and partly by K.I. and H.U. H.K. supervised the project. All authors contributed to the writing of this paper and have approved the final version. Acknowledgment The quantum chemical calculations using the Gaussian 16 and Turbomole program packages were performed on the SuperComputer System, Institute for Chemical Research, Kyoto University. It was also supported by JSPS KAKENHI grant numbers: 19K05629 and JP20H05840 (Grant-in-Aid for Transformative Research Areas, “Dynamic Exciton”), JSPS Core-to-Core Program (JPJSCCA20220004), and JST CREST (JPMJCR2431). 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Sanz-Rodrigo, J., Ricci, G., Olivier, Y. & Sancho-García, J. C. Negative Singlet–Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting. J. Phys. Chem. A 125, 513–522 (2021). Povie, G., Segawa, Y., Nishihara, T., Miyauchi, Y. & Itami, K. Synthesis of a carbon nanobelt. Science 356, 172–175 (2017). Xia, J. & Jasti, R. Synthesis, Characterization, and Crystal Structure of [6]Cycloparaphenylene. Angew. Chem. Int. Ed. 51, 2474–2476 (2012). Xue, J. Y. et al. Cyclo- meta -phenylene Revisited: Nickel-Mediated Synthesis, Molecular Structures, and Device Applications. J. Org. Chem. 79, 9735–9739 (2014). Stéphan, O. et al. Formation of small single-layer and nested BN cages under electron irradiation of nanotubes and bulk material. Appl. Phys. A 67, 107–111 (1998). Golberg, D., Bando, Y., Stéphan, O. & Kurashima, K. Octahedral boron nitride fullerenes formed by electron beam irradiation. Appl. Phys. Lett. 73, 2441–2443 (1998). Oku, T., Nishiwaki, A., Narita, I. & Gonda, M. Formation and structure of B 24 N 24 clusters. Chem. Phys. Lett. 380, 620–623 (2003). Matsunaga, N., Cundari, T. R., Schmidt, M. W. & Gordon, M. S. A comparative study of the bonding in heteroatom analogues of benzene. Theor. Chim. Acta 83, 57–68 (1992). Matsunaga, N. & Gordon, M. S. Stabilities and Energetics of Inorganic Benzene Isomers: Prismanes. J. Am. Chem. Soc. 116, 11407–11419 (1994). Amano, H., Kito, M., Hiramatsu, K. & Akasaki, I. P-Type Conduction in Mg-Doped GaN Treated with Low-Energy Electron Beam Irradiation (LEEBI). Jpn. J. Appl. Phys. 28, L2112 (1989). Nakamura, S., Mukai, T. & Senoh, M. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl. Phys. Lett. 64, 1687–1689 (1994). Nakamura, S. & Krames, M. R. History of Gallium–Nitride-Based Light-Emitting Diodes for Illumination. Proceedings of the IEEE 101, 2211–2220 (2013). Akasaki, I. Nobel Lecture: Fascinated journeys into blue light. Rev. Mod. Phys. 87, 1119–1131 (2015). Frisch, M. J. et al. Gaussian 16 Rev. C.01 (Wallingford, CT, 2016). TURBOMOLE V7.4.1 2019, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com . Domcke, W., Sobolewski, A. L. & Schlenker, C. W. Photooxidation of water with heptazine-based molecular photocatalysts: Insights from spectroscopy and computational chemistry. J. Chem. Phys. 153, 100902 (2020). Additional Declarations There is NO Competing Interest. Supplementary Files InorganicBenzeneiSTNatPhotonSIsubmitted.docx Supplementary Information Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8056562","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":555929061,"identity":"396c833c-e265-474a-ad29-b7b6d4f198f1","order_by":0,"name":"Hironori Kaji","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIie3RsWoCMRzH8Z8Uzg5/yZpg6zNEhGKh+CyRAyc7udx407lYuvoa3RxzBDoF+goRwanDdXM4aHNiHVpMOwrmuyQEPvyTOyAWO8M4oHQF3IB+HAdJuYQHDdH/JLiiXySUmOu1eahHntj+psowztvG4X51mnRJKfNYpITOYiC19YQmEsKeJj00JNcERne8LD7HOaZ+eBEgzCkzrI/ET2HvYdLlfgoS3VzsQPgfU8TSqfLJvyWh15m0FoOCb6UOvYW/TdNqV496jNIXl2W4fWbpeiMCX8z/EbVfElzLwwYwIg+Rtv7euONZ6yNIYrFY7ML6AhKCTCxJA1KMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-5111-3852","institution":"Kyoto University","correspondingAuthor":true,"prefix":"","firstName":"Hironori","middleName":"","lastName":"Kaji","suffix":""},{"id":555929062,"identity":"d936d154-e21a-48a2-ac37-fe00a9b94427","order_by":1,"name":"Katsuyuki Shizu","email":"","orcid":"","institution":"Kyoto University","correspondingAuthor":false,"prefix":"","firstName":"Katsuyuki","middleName":"","lastName":"Shizu","suffix":""},{"id":555929063,"identity":"c560a8a3-da42-4eb4-91cc-f77654b86173","order_by":2,"name":"Kuraudo Ishihara","email":"","orcid":"","institution":"Kyoto University","correspondingAuthor":false,"prefix":"","firstName":"Kuraudo","middleName":"","lastName":"Ishihara","suffix":""},{"id":555929064,"identity":"806ea6e6-ba8b-4779-95c6-c48c65dcae52","order_by":3,"name":"Hiroki Uratani","email":"","orcid":"https://orcid.org/0000-0002-8411-3429","institution":"Kyoto University","correspondingAuthor":false,"prefix":"","firstName":"Hiroki","middleName":"","lastName":"Uratani","suffix":""}],"badges":[],"createdAt":"2025-11-07 11:26:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8056562/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8056562/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99312780,"identity":"d2f70dfa-13e0-445b-8610-91272ac26981","added_by":"auto","created_at":"2025-12-31 16:19:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":192051,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eShort-range charge-transfer\u003c/strong\u003e \u003cstrong\u003eelectronic excitations in borazine.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Chemical structure of borazine (\u003cstrong\u003e1:\u003c/strong\u003e benzene-type boron nitride, \u003cstrong\u003eben-BN\u003c/strong\u003e). \u003cstrong\u003eb\u003c/strong\u003e Frontier orbitals of \u003cstrong\u003e1:\u003c/strong\u003e \u003cstrong\u003eben-BN\u003c/strong\u003e calculated at the HF/cc-pVTZ//PBE0/6-31G(d) level of the theory. Two MOs are degenerate in both HOMO and LUMO. \u003cstrong\u003ec\u003c/strong\u003e Electron-density difference (Δ\u003cem\u003eρ\u003c/em\u003e) maps arising from the S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e), and S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) excitations in \u003cstrong\u003e1:\u003c/strong\u003e \u003cstrong\u003eben-BN\u003c/strong\u003e. Here, T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e) and T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) represent doubly degenerate T\u003csub\u003e1\u003c/sub\u003e of different symmetries, A\u003csub\u003e1\u003c/sub\u003e and B\u003csub\u003e1\u003c/sub\u003e, respectively. Blue regions show negative Δ\u003cem\u003eρ\u003c/em\u003e, where the electron density decreases. Yellow regions show positive Δ\u003cem\u003eρ\u003c/em\u003e, where the electron density increases.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8056562/v1/147ec9c744fe03ab33382f9b.png"},{"id":98994397,"identity":"738e63d4-c79b-45d6-8e72-2d3c3496eeda","added_by":"auto","created_at":"2025-12-25 11:43:45","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":223182,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic structures of borazine and one- and two-dimensional fused borazines.\u003c/strong\u003e Hydrogen atoms are omitted for clarity. \u003cstrong\u003e1:\u003c/strong\u003e borazine (\u003cstrong\u003eben-BN\u003c/strong\u003e), \u003cstrong\u003e2a: \u003c/strong\u003enaphthalene-type BN (\u003cstrong\u003enaph-BN\u003c/strong\u003e), \u003cstrong\u003e2b: \u003c/strong\u003eanthracene-type BN (\u003cstrong\u003eanth-BN\u003c/strong\u003e), \u003cstrong\u003e2c: \u003c/strong\u003ephenanthrene-type BN (\u003cstrong\u003ephenan-BN\u003c/strong\u003e), \u003cstrong\u003e2d: \u003c/strong\u003etetracene-type BN (\u003cstrong\u003etetra-BN\u003c/strong\u003e), \u003cstrong\u003e2e: \u003c/strong\u003ecrycene-type BN (\u003cstrong\u003ecryc-BN\u003c/strong\u003e), \u003cstrong\u003e2f: \u003c/strong\u003epyrene-type BN (\u003cstrong\u003epyr-BN\u003c/strong\u003e), \u003cstrong\u003e2g: \u003c/strong\u003ephenalene-type nitride boron (\u003cstrong\u003ephenal-NB\u003c/strong\u003e), \u003cstrong\u003e2h: \u003c/strong\u003ephenalene-type BN (\u003cstrong\u003ephenal-BN\u003c/strong\u003e), \u003cstrong\u003e2i: \u003c/strong\u003eolympicene-type NB (\u003cstrong\u003eolymp-NB\u003c/strong\u003e), \u003cstrong\u003e2j: \u003c/strong\u003eolympicene-type BN (\u003cstrong\u003eolymp-BN\u003c/strong\u003e), and \u003cstrong\u003e2k: \u003c/strong\u003ebisanthrene-type BN (\u003cstrong\u003ebis-BN\u003c/strong\u003e). Electron-density difference (Δ\u003cem\u003eρ\u003c/em\u003e) maps arising from the S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) and S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e) excitations of \u003cstrong\u003e2k: bis-BN\u003c/strong\u003e are also shown. Blue regions show negative Δ\u003cem\u003eρ\u003c/em\u003e (where the electron density decreases). Yellow regions show positive Δ\u003cem\u003eρ\u003c/em\u003e (where the electron density increases).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8056562/v1/d25787b45e247d720b333da3.png"},{"id":99311844,"identity":"09863a72-0017-4715-8dc9-961dcdfc4201","added_by":"auto","created_at":"2025-12-31 16:17:07","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":307863,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDFT-optimized structures of ring-type borazines (3, 4e, and 5), their one-dimensional counterparts (6e and 7f), and a fullerene-type BN compound (8a) at the PBE0/6-31G(d) level of theory.\u003c/strong\u003e \u003cstrong\u003e3:\u003c/strong\u003e (6, 6)carbon nanobelt-type BN (\u003cstrong\u003e(6, 6)NB-BN\u003c/strong\u003e), \u003cstrong\u003e4e:\u003c/strong\u003e [6]cycloparaphenylene-type BN (\u003cstrong\u003e[6]CPP-BN\u003c/strong\u003e), \u003cstrong\u003e6e: \u003c/strong\u003e[6]paraphenylene-type BN (\u003cstrong\u003e[6]PP-BN\u003c/strong\u003e), \u003cstrong\u003e5: \u003c/strong\u003e[6]cyclometaphenylene-type BN (\u003cstrong\u003e[6]CMP-BN\u003c/strong\u003e), \u003cstrong\u003e7f: \u003c/strong\u003e[6]metaphenylene-type BN (\u003cstrong\u003e[6]MP-BN\u003c/strong\u003e), \u003cstrong\u003e8a: \u003c/strong\u003eC\u003csub\u003e24\u003c/sub\u003e-fullerene-type BN (\u003cstrong\u003eB\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eN\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e-fullerene\u003c/strong\u003e). Hydrogen atoms are omitted for clarity except for \u003cstrong\u003e8a: B\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eN\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e-fullerene\u003c/strong\u003e. Electron-density difference (Δ\u003cem\u003eρ\u003c/em\u003e) maps arising from the S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003eg\u003c/sub\u003e) and S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003eg\u003c/sub\u003e) excitations of \u003cstrong\u003e3: (6, 6)NB-BN\u003c/strong\u003e and the S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e2\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e→S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e2\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e2\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e), and S\u003csub\u003e0\u003c/sub\u003e→T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e2\u003c/sub\u003e) excitations of \u003cstrong\u003e8a: B\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eN\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e-fullerene\u003c/strong\u003e are also shown. Blue regions show negative Δ\u003cem\u003eρ\u003c/em\u003e (where the electron density decreases). Yellow regions show positive Δ\u003cem\u003eρ\u003c/em\u003e (where the electron density increases). The twisted structure is most stable for \u003cstrong\u003e7f: [6]MP-BN\u003c/strong\u003e, due to the steric hindrance among H atoms.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8056562/v1/2216e191465c0c2edafa3eac.png"},{"id":99322914,"identity":"169e0298-850f-419e-9f62-7a15905a9899","added_by":"auto","created_at":"2025-12-31 16:44:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2523680,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8056562/v1/510d200d-b3ef-4859-981f-e7169e4b5d2d.pdf"},{"id":99312913,"identity":"42f41e22-9937-4c0e-be53-9145c873caf0","added_by":"auto","created_at":"2025-12-31 16:19:36","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1176875,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"InorganicBenzeneiSTNatPhotonSIsubmitted.docx","url":"https://assets-eu.researchsquare.com/files/rs-8056562/v1/526be62e7ea3d88dadf09310.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Inorganic benzenes with inverted singlet-triplet gaps","fulltext":[{"header":"Introduction","content":"\u003cp\u003eInorganic-type benzenes are six-membered six-π-electron systems having electronic structures analogous to organic benzene (hereafter referred to simply as benzene as usual).\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e Borazine (B\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e) is one of the most representative inorganic benzenes consisting of alternating boron (B) and nitrogen (N) atoms arranged in a hexagonal ring (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea).\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e While numerous materials exhibiting visible to near-infrared emission have been widely explored for organic light-emitting diodes (OLEDs), those with ultraviolet (UV) to deep-UV (DUV) emission for OLEDs remain underdeveloped, despite their broad potential across wide variety of applications.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e Hexagonal boron nitride (hBN), a structural analogue of graphene, has known to be a semiconductor that shows a wide optical band gap and is promising as an UV to DUV emitter in optoelectronic applications.\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e Boron nitride nanotubes (BNNTs),\u003csup\u003e6\u003c/sup\u003e structural analogues of carbon nanotubes, also show wide band gaps suitable for such applications.\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e Recent advances in the synthesis makes it possible to develop diverse inorganic benzenes including boron-nitride-based compounds consisting of four-B and two-N atoms\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e (B\u003csub\u003e4\u003c/sub\u003eN\u003csub\u003e2\u003c/sub\u003eR\u003csub\u003e2\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e2\u003c/sub\u003eR\u0026rdquo;\u003csub\u003e2\u003c/sub\u003e), boroxine\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e (B\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e), borthiin\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e (B\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003e), boroselenol\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e (B\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003e), phosphaborazine\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e (B\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e3\u003c/sub\u003e), phosphazene\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e (N\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e6\u003c/sub\u003e) and its gallium analogue\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e (Ga\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e3\u003c/sub\u003e), aluminum analogue (alumazene\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e; Al\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e3\u003c/sub\u003e) and its phosphor and arsenic analogues\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e (Al\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e3\u003c/sub\u003e and Al\u003csub\u003e3\u003c/sub\u003eAs\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003eR\u0026rsquo;\u003csub\u003e3\u003c/sub\u003e, respectively), as well as triphospha- and triarsa-trisilabenzenes\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e (Si\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003e and Si\u003csub\u003e3\u003c/sub\u003eAs\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003e, respectively), and germanium analogue (germanazene\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e; Ge\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eR\u003csub\u003e3\u003c/sub\u003e), where R, R\u0026rsquo;, and R\u0026rsquo;\u0026rsquo; denote substituents. The structural diversity of these inorganic benzenes allows us to develop novel materials with unique photophysical properties that are unattainable in conventional carbon-based aromatic systems.\u003c/p\u003e \u003cp\u003eThe doubly degenerate highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of borazine are predominantly localized on the N and B atoms, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). Thus, the HOMO\u0026rarr;LUMO excitation of borazine can be viewed as the short-range charge-transfer\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e (SRCT) electronic excitation between the N and B atoms. For the inorganic-type benzenes listed above, S\u003csub\u003e1\u003c/sub\u003e can be energetically lower than T\u003csub\u003e1\u003c/sub\u003e as confirmed below, leading to a unique electronic property called the inverted singlet-triplet (iST or INVEST): the S\u003csub\u003e1\u003c/sub\u003e-T\u003csub\u003e1\u003c/sub\u003e energy difference Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e is negative. Here, Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e = \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e)\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e); \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e) and \u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e) are the S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e energies, respectively.\u003c/p\u003e \u003cp\u003eThe presence of iST was originally suggested theoretically by Borden\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, Kollmar and Staemmler\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e for cyclobutadiene in the 1970s. Experimental iST study was performed by Leupin and Wirz for cycl[3.3.3]azine\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e in 1980. After a long silence, interest in iST was reignited by a pivotal theoretical study by de Silva in 2019, which clearly demonstrated the possibility of negative singlet-triplet gap by considering double excitations.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e Experimental observations have also emerged for azaphenalene derivatives, following the work by Domcke\u0026rsquo;s group in 2019,\u003csup\u003e24\u0026ndash;28\u003c/sup\u003e Because iST allows T\u003csub\u003e1\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e transition without thermal activation, iST materials can show efficient reverse intersystem crossing (RISC) from T\u003csub\u003e1\u003c/sub\u003e to S\u003csub\u003e1\u003c/sub\u003e and are promising as fluorescent materials for organic light-emitting diodes (OLEDs). However, to date, the rate constants for S\u003csub\u003e1\u003c/sub\u003e\u0026rarr;S\u003csub\u003e0\u003c/sub\u003e fluorescence (\u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e) are not large enough, on the order of 10\u003csup\u003e6\u003c/sup\u003e s\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. In this study, we theoretically investigate the potential iST character of inorganic benzenes. Our quantum chemical calculations indicate that borazine derivatives are promising candidates for electroluminescent UV emitters exhibiting both negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of 10\u003csup\u003e7\u003c/sup\u003e-10\u003csup\u003e8\u003c/sup\u003e s\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below). These \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e values, one to two orders of magnitude higher than those of previously reported iST molecules, represent a significant advancement in emitter performance. Borthiins and boroselenol are also found to show negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e and are candidates for core units to develop wide gap iST materials for OLEDs. The gallium-nitride (GaN) analogue of benzene (Ga\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e) is also predicted to show iST character with a wide optical gap.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eInorganic benzenes\u003c/h2\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the structures and abbreviated names of the borazine family investigated in this study: borazine (\u003cb\u003e1: ben-BN\u003c/b\u003e) and one- and two-dimensional (1D and 2D) fused borazines (\u003cb\u003e2a: naph-BN\u003c/b\u003e \u0026minus;\u0026thinsp;2\u003cb\u003ek: bis-BN\u003c/b\u003e). In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the H atoms are omitted for clarity; the optimized structures with H atoms are shown in Supplementary Information (Supplementary Fig.\u0026nbsp;1). \u003cb\u003e2k: bis-BN\u003c/b\u003e can be viewed as a model of hBN. Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e), the S\u003csub\u003e0\u003c/sub\u003e-S\u003csub\u003e1\u003c/sub\u003e transition dipole moment (\u003cem\u003e\u0026micro;\u003c/em\u003e), S\u003csub\u003e0\u003c/sub\u003e-S\u003csub\u003e1\u003c/sub\u003e oscillator strength (\u003cem\u003ef\u003c/em\u003e), and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of \u003cb\u003e1\u003c/b\u003e: \u003cb\u003eben-BN\u003c/b\u003e \u0026minus;\u0026thinsp;2\u003cb\u003ek: bis-BN\u003c/b\u003e calculated with the spin-component scaling second-order approximate coupled-cluster (SCS-CC2) are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Those calculated with the second-order algebraic diagrammatic construction (ADC(2)) are also listed in Supplementary Table\u0026nbsp;1, see Methods section for the calculation detail. Importantly, all of \u003cb\u003e1\u003c/b\u003e: \u003cb\u003eben-BN\u003c/b\u003e \u0026minus;\u0026thinsp;2\u003cb\u003ek: bis-BN\u003c/b\u003e show negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e (\u0026thinsp;\u0026lt;\u0026thinsp;\u0026minus;\u0026thinsp;21 meV) and large \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e) (\u0026gt;\u0026thinsp;6.53 eV), suggesting that these compounds are promising as wide-gap core materials with iST character. It would be possible to develop materials with preferred emission wavelengths through appropriate structural modifications. To confirm SRCT character of \u003cb\u003e1\u003c/b\u003e: \u003cb\u003eben-BN\u003c/b\u003e, we calculated electron-density difference (Δ\u003cem\u003eρ\u003c/em\u003e) maps arising from the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e excitations (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). The Δ\u003cem\u003eρ\u003c/em\u003e maps were calculated by subtracting the total electron density of S\u003csub\u003e0\u003c/sub\u003e from that of S\u003csub\u003e1\u003c/sub\u003e or T\u003csub\u003e1\u003c/sub\u003e, using the S\u003csub\u003e0\u003c/sub\u003e structure. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec shows the Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e), S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e), and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) excitations of \u003cb\u003e1: ben-BN\u003c/b\u003e, where T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e) and T\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) represent doubly degenerate T\u003csub\u003e1\u003c/sub\u003e of different symmetries, A\u003csub\u003e1\u003c/sub\u003e and B\u003csub\u003e1\u003c/sub\u003e, respectively. Blue regions show negative Δ\u003cem\u003eρ\u003c/em\u003e where the electron density decreases and yellow regions show positive Δ\u003cem\u003eρ\u003c/em\u003e where the electron density increases. The negative Δ\u003cem\u003eρ\u003c/em\u003e is strongly localized on the N atoms, whereas the positive Δ\u003cem\u003eρ\u003c/em\u003e is strongly localized on the B atoms, suggesting that a short-range electron transfer from the N to B atoms occurs upon the excitations. In addition, Δ\u003cem\u003eρ\u003c/em\u003e shows spatially alternating negative and positive regions, which are characteristic for B and N containing molecules with small positive Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e\u003csup\u003e\u003cspan additionalcitationids=\"CR30\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e and heptazine derivatives with negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e.\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows calculated Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e(B\u003csub\u003e1\u003c/sub\u003e) and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003e1\u003c/sub\u003e) excitations of \u003cb\u003e2k: bis-BN\u003c/b\u003e. Like \u003cb\u003e1\u003c/b\u003e: \u003cb\u003eben-BN\u003c/b\u003e, \u003cb\u003e2k: bis-BN\u003c/b\u003e has spatially alternating negative and positive regions, indicating SRCT character.\u003c/p\u003e \u003cp\u003eUnder the Franck-Condon approximation, the \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of a molecule is proportional to \u003cem\u003ef\u003c/em\u003e:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{k}_{\\text{F}}=\\frac{{e}^{2}}{2\\pi\\:{m}_{e}{\\epsilon\\:}_{0}{c}^{3}}{\\omega\\:}^{2}f$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ef\u003c/em\u003e is\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:f=\\frac{2{m}_{\\text{e}}\\omega\\:{\\mu\\:}^{2}}{3{e}^{2}\\hslash\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cem\u003ee\u003c/em\u003e is the elementary charge, \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e is the mass of an electron, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the vacuum permittivity, \u003cem\u003ec\u003c/em\u003e is the speed of light, \u003cem\u003eω\u003c/em\u003e is the angular frequency of light (\u003cem\u003eω\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e)/ℏ, where ℏ is the Dirac constant). From Eqs.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), a large \u003cem\u003e\u0026micro;\u003c/em\u003e is desirable to increase \u003cem\u003ef\u003c/em\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e, which enhance luminescence efficiency. From Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, it is found that \u003cem\u003ef\u003c/em\u003e is large for 1D structures, especially when the fused ring becomes longer (\u003cb\u003e1: ben-BN\u003c/b\u003e \u0026rarr; \u003cb\u003e2a: naph-BN\u003c/b\u003e \u0026rarr; \u003cb\u003e2b: anth-BN\u003c/b\u003e \u0026rarr; \u003cb\u003e2d: tetra-BN\u003c/b\u003e), whereas it vanishes when the molecular structure is 3-fold triangular symmetric (\u003cb\u003e1\u003c/b\u003e: \u003cb\u003eben-BN\u003c/b\u003e, \u003cb\u003e2g\u003c/b\u003e: \u003cb\u003ephenal-NB\u003c/b\u003e, and \u003cb\u003e2h\u003c/b\u003e: \u003cb\u003ephenal-BN\u003c/b\u003e). \u003cb\u003e2d\u003c/b\u003e: \u003cb\u003etetra-BN\u003c/b\u003e shows the largest \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of 1.5\u0026times;10\u003csup\u003e8\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e among molecules in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. These results suggest that breaking the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry and extending the molecular framework in one direction are key factors for increasing \u003cem\u003e\u0026micro;\u003c/em\u003e, \u003cem\u003ef\u003c/em\u003e and the resulting \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePoint groups and Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e, \u003cem\u003ef\u003c/em\u003e, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of inorganic benzenes calculated with the SCS-CC2/cc-pVTZ//PBE0/6-31G(d) method.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"19\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c17\" colnum=\"17\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c18\" colnum=\"18\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c19\" colnum=\"19\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eMolecular formula\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003ePoint \u003c/p\u003e \u003cp\u003egroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eΔ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(meV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003e(eV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003e(eV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(au)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e\u003cem\u003ef\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e: ben-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;295\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e7.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2a\u003c/b\u003e: naph-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e5\u003c/sub\u003eN\u003csub\u003e5\u003c/sub\u003eH\u003csub\u003e8\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;95\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.1502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e3.7\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e7.0\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2b\u003c/b\u003e: anth-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e7\u003c/sub\u003eN\u003csub\u003e7\u003c/sub\u003eH\u003csub\u003e10\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.4159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e2.8\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e5.4\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2c\u003c/b\u003e: phenan-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e7\u003c/sub\u003eN \u003csub\u003e7\u003c/sub\u003eH\u003csub\u003e10\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;127\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.2990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e1.4\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e2.7\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2d\u003c/b\u003e: tetra-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e9\u003c/sub\u003eN\u003csub\u003e9\u003c/sub\u003eH\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;51\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.7023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e8.0\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e1.5\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e8\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2e\u003c/b\u003e: cryc-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e9\u003c/sub\u003eN\u003csub\u003e9\u003c/sub\u003eH\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;59\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.1300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e2.7\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e5.1\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2f\u003c/b\u003e: pyr-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e8\u003c/sub\u003eN\u003csub\u003e8\u003c/sub\u003eH\u003csub\u003e10\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;221\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e5.1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e9.4\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2g\u003c/b\u003e: phenal-NB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e7\u003c/sub\u003eN\u003csub\u003e6\u003c/sub\u003eH\u003csub\u003e9\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;260\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2h\u003c/b\u003e: phenal-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e6\u003c/sub\u003eN\u003csub\u003e7\u003c/sub\u003eH\u003csub\u003e9\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;128\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2i\u003c/b\u003e: olymp-NB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e10\u003c/sub\u003eN\u003csub\u003e9\u003c/sub\u003eH\u003csub\u003e11\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;243\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e1.3\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e2.4\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2j\u003c/b\u003e: olymp-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e9\u003c/sub\u003eN\u003csub\u003e10\u003c/sub\u003eH\u003csub\u003e11\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;97\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.2545\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e1.0\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e1.9\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e2k\u003c/b\u003e: bis-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e14\u003c/sub\u003eN\u003csub\u003e14\u003c/sub\u003eH\u003csub\u003e14\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;57\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.2110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e7.1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e1.3\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e3\u003c/b\u003e: (6, 6)NB-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e24\u003c/sub\u003eN\u003csub\u003e24\u003c/sub\u003eH\u003csub\u003e24\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e6\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;141\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e4e\u003c/b\u003e: [6]CPP-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e18\u003c/sub\u003eN\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e24\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e6\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;145\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e5\u003c/b\u003e: [6]CMP-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e18\u003c/sub\u003eN\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e24\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e3v\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;186\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e6e\u003c/b\u003e: [6]PP-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e18\u003c/sub\u003eN\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e26\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;77\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e3.4\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e6.4\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e7f\u003c/b\u003e: [6]MP-BN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e18\u003c/sub\u003eN\u003csub\u003e18\u003c/sub\u003eH\u003csub\u003e26\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;214\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e4.9\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e9.0\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e8a\u003c/b\u003e: B\u003csub\u003e12\u003c/sub\u003eN\u003csub\u003e12\u003c/sub\u003e-fullerene\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e12\u003c/sub\u003eN\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;134\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e6.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e6.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e9\u003c/b\u003e: ben-BS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;109\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e5.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e5.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e10\u003c/b\u003e: ben-BSe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;160\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e4.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e4.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e11\u003c/b\u003e: ben-BO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e326\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e8.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e7.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e12\u003c/b\u003e: ben-GaN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eGa\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e3h\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003e\u0026minus;230\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e5.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e5.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003e13\u003c/b\u003e: prism-GaN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eGa\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e507\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e4.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e3.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.7097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e5.1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c18\" namest=\"c17\"\u003e \u003cp\u003e\u003cb\u003e3.7\u0026times;10\u003c/b\u003e\u003csup\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c19\" namest=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eRing- and fullerene-type borazines\u003c/h3\u003e\n\u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows cyclic borazines, which are parts of BNNTs. The Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e, \u003cem\u003ef\u003c/em\u003e, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e values are also shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e is a subunit of a BNNT, consisting of 12 fused borazine rings. The structure of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e was designed with reference to a carbon nanobelt structure in ref. \u003csup\u003e33\u003c/sup\u003e (a subunit of a (6, 6)-carbon nanotube) and then, optimized at the PBE0/6-31G(d) level of theory. \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e shows a negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of \u0026minus;\u0026thinsp;141 meV and a large \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e) of 6.26 eV (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e also shows the calculated Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003eg\u003c/sub\u003e) and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e(A\u003csub\u003eg\u003c/sub\u003e) excitations of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e. Similarly to the above cases, the negative Δ\u003cem\u003eρ\u003c/em\u003e (blue regions) is strongly localized on the N atoms, whereas the positive Δ\u003cem\u003eρ\u003c/em\u003e (yellow regions) is strongly localized on the B atoms, suggesting that S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e also have pure SRCT character. The \u003cem\u003ef\u003c/em\u003e value of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e vanishes because of the symmetric ring structure, which would make \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e non-emissive. \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e is another subunit of the BNNT; the diameter of \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e (8.36 \u0026Aring;) is slightly larger than that of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e (8.32 \u0026Aring;). \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e consists of six borazine rings and is the borazine analogue of [6]cycloparaphenylene ([6]CPP)\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, a subunit of a (6,6)-carbon nanotube. The Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e, \u003cem\u003ef\u003c/em\u003e, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e are similar to those of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e, despite the difference in conjugated state. \u003cb\u003e5\u003c/b\u003e: \u003cb\u003e[6]CMP-BN\u003c/b\u003e also consists of six borazine rings but forms a different ring configuration; the borazine analogue of [6]cyclometaphenylene.\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e The Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of \u003cb\u003e5: [6]CMP-BN\u003c/b\u003e (\u0026minus;\u0026thinsp;186 meV) is smaller than those of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e and \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e. Similarly to \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e and \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e, the symmetric ring structure results in \u003cem\u003ef\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0. To understand the influence of the ring structures on the \u003cem\u003ef\u003c/em\u003e values, we compared the \u003cem\u003ef\u003c/em\u003e values of \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e and \u003cb\u003e5: [6]CMP-BN\u003c/b\u003e with those of their 1D counterparts, \u003cb\u003e6e: [6]PP-BN\u003c/b\u003e and \u003cb\u003e7f: [6]MP-BN\u003c/b\u003e. Unlike \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e and \u003cb\u003e5: [6]CMP-BN\u003c/b\u003e, \u003cb\u003e6e: [6]PP-BN\u003c/b\u003e and \u003cb\u003e7f: [6]MP-BN\u003c/b\u003e have non-zero \u003cem\u003ef\u003c/em\u003e values, leading to \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of the order of 10\u003csup\u003e5\u003c/sup\u003e\u0026ndash;10\u003csup\u003e6\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, suggesting that the symmetric ring formation largely decreases \u003cem\u003ef\u003c/em\u003e value. The calculated Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e, \u003cem\u003ef\u003c/em\u003e, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e values for five to twelve membered borazine rings and their 1D counterparts are summarized in Supplementary Information (molecules \u003cb\u003e4d: [5]CPP-BN\u003c/b\u003e \u0026minus;\u0026thinsp;4\u003cb\u003ek\u003c/b\u003e: \u003cb\u003e[12]CPP-BN\u003c/b\u003e in Supplementary Fig.\u0026nbsp;2, molecules \u003cb\u003e6a: [2]PP-BN\u003c/b\u003e \u0026minus;\u0026thinsp;6\u003cb\u003ek: [12]PP-BN\u003c/b\u003e in Supplementary Fig.\u0026nbsp;3, and Supplementary Table\u0026nbsp;2). The ring molecules (\u003cb\u003e4d: [5]CPP-BN\u003c/b\u003e \u0026minus;\u0026thinsp;4\u003cb\u003ek\u003c/b\u003e: \u003cb\u003e[12]CPP-BN\u003c/b\u003e) has zero or nearly zero \u003cem\u003ef\u003c/em\u003e values, whereas the 1D counterparts (\u003cb\u003e6d: [5]PP-BN\u003c/b\u003e \u0026minus;\u0026thinsp;6\u003cb\u003eh: [9]PP-BN\u003c/b\u003e) have non-zero \u003cem\u003ef\u003c/em\u003e values with \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of 10\u003csup\u003e4\u003c/sup\u003e\u0026ndash;10\u003csup\u003e6\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Linear metaphenylene-type molecules (\u003cb\u003e7a: [3]MP-BN\u003c/b\u003e \u0026minus;\u0026thinsp;7\u003cb\u003ef: [6]MP-BN\u003c/b\u003e) also have non-zero \u003cem\u003ef\u003c/em\u003e values with \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of 10\u003csup\u003e5\u003c/sup\u003e\u0026ndash;10\u003csup\u003e7\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;4 and Supplementary Table\u0026nbsp;2).\u003c/p\u003e \u003cp\u003eBorazine analogues of fullerenes have been experimentally observed.\u003csup\u003e\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e B\u003csub\u003e12\u003c/sub\u003eN\u003csub\u003e12\u003c/sub\u003e-fullerene is a borazine analogue of C\u003csub\u003e24\u003c/sub\u003e fullerene and consists of the four- and six-membered rings (note that \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e and all fullerene-type compounds have no H atoms). \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e shows a negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of \u0026minus;\u0026thinsp;134 meV, which is comparable to those of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e and \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e (\u0026minus;\u0026thinsp;141 and \u0026minus;\u0026thinsp;145 meV, respectively). S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e of \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e are triply degenerate (denoted as A\u003csub\u003e2\u003c/sub\u003e, B\u003csub\u003e1\u003c/sub\u003e, and B\u003csub\u003e2\u003c/sub\u003e) owing to its highly symmetric structure. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e excitations of \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e. The negative and positive Δ\u003cem\u003eρ\u003c/em\u003e distributions suggest that S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e of \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e shows pure SRCT character. Like the ring borazines of \u003cb\u003e3: (6, 6)NB-BN\u003c/b\u003e, \u003cb\u003e4e: [6]CPP-BN\u003c/b\u003e, and \u003cb\u003e5: [6]CMP-BN\u003c/b\u003e, \u003cb\u003e8a: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e12\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e has zero \u003cem\u003ef\u003c/em\u003e value and is expected to be non-emissive. The calculated results for borazine analogues of C\u003csub\u003e48\u003c/sub\u003e and C\u003csub\u003e72\u003c/sub\u003e fullerenes are shown in Supplementary Information (molecules \u003cb\u003e8b: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e24\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e24\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e and \u003cb\u003e8c: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e36\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e36\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e in Supplementary Fig.\u0026nbsp;5 and Supplementary Table\u0026nbsp;2). Although \u003cb\u003e8b: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e24\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e24\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e and \u003cb\u003e8c: B\u003c/b\u003e\u003csub\u003e\u003cb\u003e36\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e36\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e-fullerene\u003c/b\u003e show positive Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, the Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e values (~\u0026thinsp;\u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e at room temperature) are sufficiently small to induce rapid T\u003csub\u003e1\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e transition.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eInorganic-type benzenes other than borazine\u003c/h3\u003e\n\u003cp\u003eFinally, we investigate the potential of inorganic-type benzenes other than borazine-based compounds as wide-gap iST materials (\u003cb\u003e9: ben-BS\u003c/b\u003e \u0026minus;\u0026thinsp;1\u003cb\u003e3: prism-GaN\u003c/b\u003e in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and 14: \u003cb\u003eben-B\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e \u0026minus;\u0026thinsp;2\u003cb\u003e3: ring-Ge\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e in Supplementary Fig.\u0026nbsp;6). Derivatives of \u003cb\u003e9: ben-BS\u003c/b\u003e \u0026minus;\u0026thinsp;1\u003cb\u003e1: ben-BO\u003c/b\u003e and \u003cb\u003e14: ben-B\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e \u0026minus;\u0026thinsp;2\u003cb\u003e3: ring-Ge\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e have been experimentally synthesized,\u003csup\u003e8\u0026ndash;18\u003c/sup\u003e whereas \u003cb\u003e12\u003c/b\u003e: \u003cb\u003eben-GaN\u003c/b\u003e and \u003cb\u003e13: prism-GaN\u003c/b\u003e have been only theoretically predicted.\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e Substituents required for organic synthesis are replaced with H atoms. Borthiin (\u003cb\u003e9: ben-BS\u003c/b\u003e) and boroselenol (\u003cb\u003e10: ben-BSe\u003c/b\u003e) show negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e (\u0026thinsp;\u0026lt;\u0026thinsp;\u0026minus;\u0026thinsp;100 meV), whereas the oxygen (O) analog (boroxine, \u003cb\u003e11: ben-BO\u003c/b\u003e) shows a large positive Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of 326 meV (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). To understand the difference in the Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e values of \u003cb\u003e9: ben-BS\u003c/b\u003e \u0026minus;\u0026thinsp;1\u003cb\u003e1: ben-BO\u003c/b\u003e, we compared the Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e excitations of \u003cb\u003e9: ben-BS\u003c/b\u003e \u0026minus;\u0026thinsp;1\u003cb\u003e1: ben-BO\u003c/b\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). For \u003cb\u003e9: ben-BS\u003c/b\u003e and \u003cb\u003e10: ben-BSe\u003c/b\u003e, the negative Δ\u003cem\u003eρ\u003c/em\u003e is strongly localized on the S and Se atoms, whereas the positive Δ\u003cem\u003eρ\u003c/em\u003e is strongly localized on the B atoms. The Δ\u003cem\u003eρ\u003c/em\u003e patterns are similar to those observed for borazine (\u003cb\u003e1: ben-BN\u003c/b\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Meanwhile, for \u003cb\u003e11: ben-BO\u003c/b\u003e, the negative Δ\u003cem\u003eρ\u003c/em\u003e is largely distributed on the B-O and B-H bonds whereas the positive Δ\u003cem\u003eρ\u003c/em\u003e is strongly localized on B atoms, which breaks down SRCT character. This pattern of Δ\u003cem\u003eρ\u003c/em\u003e suggests the significant overlap of the MOs, which may yield large exchange interaction that dominates over the spin polarization (double excitation) effect, leading to the large positive Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of 326 meV. GaN is a wide-bandgap semiconductor and widely used for blue and white light-emitting diodes.\u003csup\u003e\u003cspan additionalcitationids=\"CR42 CR43\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e Hence, although the GaN analogue of benzene (Ga\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e) has not been synthesized yet, it is worth investigating its potential iST property. Two structures have been theoretically proposed for Ga\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e: a planar benzene-type structure\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e (\u003cb\u003e12: ben-GaN\u003c/b\u003e) where Ga and N atoms are arranged alternatively and a prismane-type structure\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e (\u003cb\u003e13: prism-GaN\u003c/b\u003e) where two Ga and N atoms are adjacent to each other. Calculated Δ\u003cem\u003eρ\u003c/em\u003e maps for the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e excitations of \u003cb\u003e12: ben-GaN\u003c/b\u003e show SRCT with spatially alternating negative and positive regions, whereas those of \u003cb\u003e13: prism-GaN\u003c/b\u003e has large distributions on the Ga-Ga bonds. Consequently, \u003cb\u003e12: ben-GaN\u003c/b\u003e shows negative Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of \u0026minus;\u0026thinsp;230 meV, whereas \u003cb\u003e13: prism-GaN\u003c/b\u003e shows a large positive Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of 507 meV (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Thus, like borazine, the GaN analogue of benzene (\u003cb\u003e12: ben-GaN\u003c/b\u003e) is predicted to show iST owing to its SRCT character in the S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e excitations. For other inorganic-type molecules, \u003cb\u003e14: ben-B\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e15: ben-BP\u003c/b\u003e, \u003cb\u003e16: ben-NP\u003c/b\u003e, \u003cb\u003e17: ring-Ga\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eP\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e18: ben-AlN\u003c/b\u003e, \u003cb\u003e19: ring-Al\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eP\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e20: ring-Al\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eAs\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e21: ring-(Si(N\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eCH\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e))\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eP\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, \u003cb\u003e22: ring-(Si(N\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eCH\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e))\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eAs\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e, and \u003cb\u003e23: ring-Ge\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e (Supplementary Fig.\u0026nbsp;6), Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e were calculated to be positive (\u0026gt;\u0026thinsp;100 meV, Supplementary Table\u0026nbsp;3). Among the fifteen inorganic benzenes (\u003cb\u003e9: ben-BS\u003c/b\u003e \u0026ndash; \u003cb\u003e23: ring-Ge\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003eN\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e) examined in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Supplementary Fig.\u0026nbsp;6, only \u003cb\u003e9: ben-BS\u003c/b\u003e, \u003cb\u003e10: ben-BSe\u003c/b\u003e, and \u003cb\u003e12: ben-GaN\u003c/b\u003e were expected to show iST.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eWe theoretically investigated the potential iST character of inorganic-type benzenes mainly focusing on borazines. 2D-sheet, ring, and fullerene type borazines showed the SRCT from N to B atoms in S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e0\u003c/sub\u003e\u0026rarr;T\u003csub\u003e1\u003c/sub\u003e excitations, which leads to the large inverted S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e energies. Other than borazines, ben-BS (B\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e, borthiin), ben-BSe (B\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e, boroselenol), and the ben-GaN (Ga\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e) were found to show iST. These molecules have large S\u003csub\u003e1\u003c/sub\u003e energies, leading to the development of promising electroluminescent UV emitters and wide-gap hosts with iST properties. Totally, we found 43 compounds with negativeΔ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003es. Among them, several compounds exhibit \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e of 10\u003csup\u003e7\u003c/sup\u003e-10\u003csup\u003e8\u003c/sup\u003e s\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, which will be expected as efficient emitters. In addition, by introducing various functional groups to these compounds, it is expected that excellent iST emitting materials with tunable emission wavelengths can be developed.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eGeometry optimization\u003c/h2\u003e \u003cp\u003eThe ground-state (S\u003csub\u003e0\u003c/sub\u003e) geometries of inorganic-type benzene materials were optimized at the PBE0/6-31G(d) level of theory and their singlet and triplet excited states were calculated using the SCS-CC2 method with the cc-pVTZ basis for the S\u003csub\u003e0\u003c/sub\u003e geometries (Supplementary Tables\u0026nbsp;4\u0026ndash;60 show the optimized geometries). The method is denoted as SCS-CC2/cc-pVTZ//PBE0/6-31G(d). The SCS-CC2 method considers double-electron excitation and has been shown to accurately predict Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of molecules consisting of B and N backbones.\u003csup\u003e\u003cspan additionalcitationids=\"CR30\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e The S\u003csub\u003e0\u003c/sub\u003e-geometry optimization was performed using the Gaussian 16 program package.\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eCalculation of electronic properties\u003c/h3\u003e\n\u003cp\u003eΔ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e, \u003cem\u003eE\u003c/em\u003e(S\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eE\u003c/em\u003e(T\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e, and \u003cem\u003ef\u003c/em\u003e were calculated using the Turbomole program package.\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e \u003cem\u003ek\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e was calculated from Eqs.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. ADC(2) method also considers double-electron excitation and has been used to compute Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003eST\u003c/sub\u003e of iST molecules.\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e The results for ADC(2) calculations are reported in Supporting Information (Supplementary Tables\u0026nbsp;1\u0026ndash;3).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e \u003cp\u003eTheoretical calculations were mainly performed by K.S. and partly by K.I. and H.U. H.K. supervised the project. All authors contributed to the writing of this paper and have approved the final version.\u003c/p\u003e\u003ch2\u003eAcknowledgment\u003c/h2\u003e \u003cp\u003eThe quantum chemical calculations using the Gaussian 16 and Turbomole program packages were performed on the SuperComputer System, Institute for Chemical Research, Kyoto University. It was also supported by JSPS KAKENHI grant numbers: 19K05629 and JP20H05840 (Grant-in-Aid for Transformative Research Areas, \u0026ldquo;Dynamic Exciton\u0026rdquo;), JSPS Core-to-Core Program (JPJSCCA20220004), and JST CREST (JPMJCR2431).\u003c/p\u003e\n\u003ch3\u003eData availability\u003c/h3\u003e\n\u003cp\u003eAll relevant data are available from the authors upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eOta, K. \u0026amp; Kinjo, R. 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Phys.\u003c/em\u003e 153, 100902 (2020).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8056562/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8056562/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInorganic-type benzenes have attracted significant attention due to their unique physical and chemical properties that are different from organic benzene. In this study, we theoretically investigate the possibility of inorganic benzenes as wide-gap materials with inverted singlet and triplet (iST) excited states. Since iST materials allow efficient triplet to singlet conversion without thermal activation, they are promising as fluorescent and assist dopant materials for light-emitting diodes. From theoretical calculations, borazine (B\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e), one of the most well-known inorganic benzenes, and its derivatives are expected not only to show iST but also to exhibit fast radiative decays surpassing those of typical iST materials: azaphenalene derivatives. Borthiin (B\u003csub\u003e3\u003c/sub\u003eS\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e), boroselenol (B\u003csub\u003e3\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e3\u003c/sub\u003e), and the gallium-nitride analogue of benzene (Ga\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e3\u003c/sub\u003eH\u003csub\u003e6\u003c/sub\u003e) are also expected to show iST with wide optical gaps.\u003c/p\u003e","manuscriptTitle":"Inorganic benzenes with inverted singlet-triplet gaps","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-25 11:43:40","doi":"10.21203/rs.3.rs-8056562/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-chemistry","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commschem","sideBox":"Learn more about [Communications Chemistry](http://www.nature.com/commschem/)","snPcode":"","submissionUrl":"","title":"Communications Chemistry","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c0ee889e-ab9d-4c57-af69-d299b71fc036","owner":[],"postedDate":"December 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":59171823,"name":"Physical sciences/Materials science/Materials for devices"},{"id":59171824,"name":"Physical sciences/Chemistry/Materials chemistry"}],"tags":[],"updatedAt":"2025-12-25T11:43:40+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-25 11:43:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8056562","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8056562","identity":"rs-8056562","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}