Probing the Fluxional Bonding Nature of Rapid Cope rearrangements in Bullvalene C10H10 and Its Analogs C8H8, C9H10, and C8BH9

Bullvalene C10H10 and its analogs semibullvalene C8H8, barbaralane C9H10, and 9-Borabarbaralane C8BH9 are prototypical fluxional molecules with rapid Cope rearrangements at finite temperatures. Detailed bonding analyses performed in this work reveal the existence of two fluxional π-bonds (2 2c-2e π → 2 3c-2e π → 2 2c-2e π) and one fluxional σ-bond (1 2c-2e σ → 1 4c-2e σ → 1 2c-2e σ) in their ground states and transition states, unveiling the universal π + σ double fluxional bonding nature of these fluctuating cage-like species. The highest occupied natural bond orbitals (HONBOs) turn out to be typical fluxional bonds dominating the dynamics of the systems. The 13C-NMR and 1H-NMR shielding tensors and chemical shifts of the model compound C8BH9 are computationally predicted to facilitate future experiments.

Chemical bond is the most fundamental and important concept in chemistry. Classical bonds include localized two-center-two-electron (2c-2e) bonds and delocalized multi-center-two-electron (mc-2e, m ≥ 3) bonds. Our group predicted the existence of fluxional σand π-bonds (FBs) in planar B 18 2− and B 19 − , half-sandwich KB 18 − , tubular Ta@B 20 − , Ta@B 21 , and Ta@B 22 + , and cage-like B 39 − in four recent papers [1][2][3][4] . Multicenter FBs in these fluctuating boron nanoclusters form and break constantly in concerted mechanisms at room temperatures. It is these FBs that facilitate the fluxional behaviors of these electron-deficient boron-based nanoclusters which possess energy barriers lower than the differences of the corresponding zero-point energy corrections. However, boron nanoclusters are known to be unstable in air and moisture and have hitherto been observed and characterized in gas phase only. Fluxional bonds in stable systems beyond boron which fluctuate rapidly and reversibly at finite temperatures remain to be explored in chemistry.
Prototypical fluxional molecules in organic chemistry include the norcaradiene-cycloheptatriene system, various annulenes, and homotropilidenes. Bridged homotropilidenes with degenerate valence-bond tautomerisms, such as the cage-like bullvalene C 10 H 10 , semibullvalene C 8 H 8 , barbaralane C 9 H 10 , and 9-borabarbaralane C 8 BH 9 , are of particular interest which exhibit reversible fluxionalities in rapid Cope rearrangements through a transition state with a bis-homoaromatic array of orbitals [5][6][7][8][9][10][11][12][13][14][15][16][17] . A topological analysis of experimental electron densities of the ground-state C 3v bullvalene was reported in 1996 18 . C 10 H 10 , C 8 H 8 , and C 9 H 10 have the experimental free energy barriers of ΔG ≠ = 12.8 kcal/mol at 100 °C, 5.5 kcal/mol at −143 °C, and 7.8 kcal/mol at −77 °C in NMR measurements, respectively 11 , while the model compound C 8 BH 9 has the calculated ΔG ≠ = 10.36 kcal/mol at 27 °C 17 . Semibullvalene C 8 H 8 has proven to have the lowest fluxional energy barrier, fastest rearrangement rate, and lowest fluctuating temperature in the series 11 . Despite their differences in compositions and ground state structures, cage-like C 10 H 10 , C 8 H 8 , C 9 H 10 , and C 8 BH 9 have similar transition state structures in rapid Cope rearrangements which have obvious multicenter bonding characteristics. However, the specific bonding patterns and fluxional bonding nature which facilitate the fluctuating behaviors of these intriguing molecules still remain unknown to date in both theory and experiments.
We aim to tackle the problem at first-principles theory level in this work. Detailed bonding analyses reveal a universal bonding pattern with two fluxional π-bonds and one fluxional σ-bond in the ground states and transition states of the C 10 H 10 , C 8 H 8 , C 9 H 10 , and C 8 BH 9 series, unveiling the σ + π double fluxional bonding nature of Institute of Molecular Science, Shanxi University, Taiyuan, 030006, China. *email: lisidian@sxu.edu.cn open these rapidly and reversibly fluctuating species. Their highest occupied natural bond orbitals appear to be typical fluxional bonds which dominate the fluxional behaviors of the systems in Cope rearrangements. We have also calculated the 13 C-NMR and 1 H-NMR shielding tensors and chemical shifts of the model compound C 8 BH 9 to facilitate future NMR measurements.
Theoretical Procedure. The ground-state (GS) and transition-state (TS) structures of the concerned species were fully optimized at density functional theory (DFT) level of PBE0 19 with the basis sets of 6-311 + G(d) 20 . Frequency checks were performed to make sure all the optimized structures are true GMs or TSs. All the PBE0 structural optimizations and coupled cluster CCSD(T) [21][22][23] single-point calculations in this work were performed using the Gaussian 09 package 24 . Detailed bonding analyses were performed on the concerned species using the adaptive natural density partitioning (AdNDP) [25][26][27] method. The AdNDP approach recovers both the localized and delocalized bonding elements of the concerned systems and has been successfully applied to a wide range of nanoclusters and molecules 1-4,28-38 . Natural bonding orbital (NBO) analyses were performed utilizing the NBO 6.0 program 39 . The nuclear magnetic resonance (NMR) shielding tensors are calculated using the Continuous Set of Gauge Transformations (CSGT) method [40][41][42] implemented in Gaussian09 program.

Results and Discussions
Structures and stabilities. We start from the optimized structures of the GSs and TSs of concerned species first. As shown in Fig. 1, C 3v C 10 H 10 (1), C s C 8 H 8 (4), C s C 9 H 10 (7), and C s C 8 BH 9 (10) as true minima of the systems possess cage-like structures with the lowest vibrational frequencies of 227, 303, 285, and 194 cm −1 at PBE0 level ( Fig. 1), respectively. They all contain three C-C σ single bonds in the C 3 triangle on the top and two C − ⃛ C σ + π double bonds (C3 ⃛ − C5 and C4 − ⃛ C6) on the two long edges of the C 7 heptagon in the front, with a mirror plane perpendicular to the paper surface. Their equivalent counterparts GSs′ C 10 H 10 (3), C s C 8 H 8 (6), C s C 9 H 10 (9), and C s C 8 BH 9 (12) with a C 3 triangle at the bottom are degenerate in energy with the GSs discussed above. Obviously, there exists no delocalized bonding interaction in the true minima GSs and GSs′ in which each carbon atom follows the octet rule. In contrast, the more open high-symmetry transition states C 2v C 10 H 10 (2), C 2v C 8 H 8 (5), C 2v C 9 H 10 (8), and C 2v C 8 BH 9 (11) with one imaginary frequency at −386i, −336i, −351i, and −456i cm −1 at PBE0, respectively, all feature two effective C − ⃛ C − ⃛ C multicenter π-bonding interactions over C1 ⃛ − C3 ⃛ − C5 and C2 − ⃛ C4 ⃛ − C6 units along the two long edges of the C 8 octohedron in the front (with r c1-c3 = r c2-c4 = r c3-c5 = r c4-c6 = 1.39 Å). They lie 12.9, 9.0, 10.2, and 14.0 kcal/mol higher in energy than their ground states at CCSD(T)//PBE0 level at 298 K, respectively. Such energy barriers appear to be much higher than that previously reported in boron nanoclusters [1][2][3][4] . This can be qualitatively understood based on the fact that, due to its prototypical electron-deficiency, boron has the strong propensity to form delocalized σ and π bonds in highly reactive boron nanoclusters with extremely small energy barriers [1][2][3][4] , while the fluxional processes in 1, 4, 7, and 10 possess much higher energy barriers because they involve the formations and breakages of C-C interactions in stable organic species. The C1-C2 single bond with r c1-c2 = 1.53~1.59 Å on the top in the C 3v or C s GSs has been elongated to r c1-c2 = r c5-c6 = 1.92~2.04 Å in the C 2v TSs. The calculated C1--C2 and C5--C6 distances in the C 2v TSs appear to be about 0.5 Å longer than the sum of the single-bond covalent radii of two carbon atoms (r c-c = 1.50 Å) 43 , indicating that the C1--C2 and C5--C6 interactions across the two long edges in C 2v TSs are much weaker than a usual C-C single bond. Such C--C distances also appear to be much longer than the C-C single bond (1.579 Å) observed between the two inverted carbon atoms in propellane 44,45 . The calculated distances of r c3-c4 = 2.9~3.2 Å in C 2v TSs (2, 5, 8, 11) clearly show that there exists no bonding interaction between C3-C4. These transition states with two weak C--C interactions (C1--C2 and C5--C6) on the top and at the bottom of the C 8 octahedron are at the critical points of Cope intramolecular rearrangements, where the original C1-C2 single σ-bond in the GS is to be broken while the C5-C6 σ-interaction in GS′ is to be formed simultaneously in the same process and vice versa. The six carbon atoms (1)(2)(3)(4)(5)(6) in the front of the C 2v TSs can be divided into two equivalent groups weakly bonded together, with two effective parallel C ) along the two long edges of the C 8 octagon and two weak C--C interactions (C1--C2 and C5-C6) on the top and at the bottom between them. C 10 H 10 , C 8 H 8 , C 9 H 10 , and C 8 BH 9 possess the calculated free energy barriers of ΔG ≠ = 13.32 kcal/mol at 100 °C, 5.94 kcal/mol at −143 °C, 7.86 kcal/mol at −77 °C, and 10.84 kcal/mol at 27 °C at PBE0 level, respectively, well in line with the corresponding values previously reported for these species at finite temperatures 11,17 . AdNDP bonding analyses. The calculated AdNDP natural bond orbital energy levels of the GSs/GSs′ and TSs of C 10 H 10 and C 8 BH 9 are comparatively shown in Fig. 2, with that of C 8 H 8 and C 9 H 10 depicted in Fig. S2. These natural bond orbital energy levels reveal the bonding patterns of the concerned molecules clearly, exhibit the symmetries of the concerned species perfectly, and show the relative energies of the symmetrically distributed chemical bonds of the systems directly. The localized AdNDP natural bond orbitals have the advantage over the delocalized canonical molecular orbitals (CMOs) in providing a pictorial representation of the relative energies of the concerned chemical bonds and their electron density distributions in space, well in line with chemical intuitions. As anticipated, C 3v GM C 10 H 10 (1) possesses 3 equivalent 2c-2e C-C π bonds with the occupation numbers of ON = 1.94 along the three long edges as its highest occupied natural bond orbitals (HONBOs) and 3 equivalent 2c-2e C-C σ bonds with ON = 1.93 on the top C 3 triangle as the second highest occupied natural bond orbitals (HONBO-1), together with the remaining 9 2c-2e C-C σ bonds and 10 2c-2e C-H σ bonds to form the GS in an overall bonding symmetry of C 3v (Fig. 3a). From C 3v GS to C 2v TS, two π-HONBOs of the GS in the front (2 2c-2e π bonds over C3-C5 and C4-C6) are converted into 2 3c-2e π bonds as HONBO-2 of the C 2v TS over C1 ⃛ − C3 − ⃛ C5 and C2 ⃛ − C4 ⃛ − C6 with ON = 1.96 on the two long edges, one σ-HONBO-1 of the GS in the front (1 2c-2e σ bond on C1-C2 on the top C 3 triangle) is transferred into 1 4c-2e σ-bond with ON = 1.95, the HONBO of the TS, which is evenly distributed on C1-C4 and C5-C6 with obvious bonding/antibonding characteristics, while the remaining 1 2c-2e π bond, 11 2c-2e C-C σ bonds, and 10 C-H σ bonds remain basically unchanged. The www.nature.com/scientificreports www.nature.com/scientificreports/ delocalized 4c-2e σ-bond is a σ + π mixture between two sets of titled p z -p z pair interactions, with the major contribution from a head-to-head σ-overlap and minor contribution from a shoulder-by-shoulder π-overlap. An opposite process occurs from C 2v TS to the second minimum C 3v GS′. Thus, as clearly shown in Fig. 3a, in a full fluxional process C 3v GS → C 2v TS → C 3v GS′ → C 2v TS′ → C 3v GS, C 10 H 10 undergoes a π-fluctuation of 2 2c-2e π (HONBOs) → 2 3c-2e π (HONBO-2) → 2 2c-2e π′ (HONBOs) → 2 3c-2e π′(HONBO-2) → 2 2c-2e π (HONBOs) and a σ-fluctuation of 1 2c-2e σ (HONBO-1) → 1 4c-2e σ (HONBO) → 1 2c-2e σ′ (HONBO-1) → 1 4c-2e σ′ (HONBO) → 1 2c-2e σ (HONBO-1) simultaneously in a concerted mechanism. Such a bonding fluctuation www.nature.com/scientificreports www.nature.com/scientificreports/ process occurs randomly in three equivalent directions perpendicular to the three equivalent C 7 heptagons around the C 3 molecular axis in both C 3v GS and GS′, generating 10!/3 equivalent isomers (~1.2 million) in total for C 10 H 10 , making all the ten H atoms magnetically equivalent with one signal observed in NMR measurements above 100 °C 15 .
The calculated NBO bond orders of the C 2v transition states of these molecules in Fig. S4 also well support the bonding patterns presented above, with C1--C2, C1 − ⃛ C3, C3 − ⃛ C5, and C5--C6 interactions possessing the bond orders of 0.35, 1.46, 1.46, and 0.35 in C 2v C 10 H 10 and 0.43, 1.43, 1.43, and 0.43 in C 2v C 8 BH 9 , respectively. The simultaneous formation of both the 2 3c-2e fluxional π-bonds and 1 4c-2e fluxional σ-bond in C 2v TS is a natural NMR shielding constants. NMR has proved to be a powerful tool for the determination of the energy barriers and rate constants of molecules with fluxional bonds in rapid Cope rearrangements 11 . The calculated absolute 13 C-and 1 H-NMR shielding tensors δ and chemical shifts ∆δ relative to tetramethylsilane (TMS) are tabulated for C 3v C 10 H 10 (1) and C s C 8 BH 9 (10) in Table 2 in ppm. Our calculated 13 C and 1 H chemical shifts (∆δ) of bullvalene C 10 H 10 agree well with that measured in NMR experiments at −59.9 °C and −59.2 °C, respectively 15 . (Table 2). The predicted 13 C-NMR spectrum of the GM C s C 8 BH 9 at 298 K exhibits five kinds of C atoms with the absolute magnetic shielding tensors of δ = 55.23, 60.28, 144.00, 144.77, and 160.20 ppm in the intensity ratios of 2:2:2:1:1, respectively, while the corresponding 1 H-NMR shielding tensors are calculated to be at δ = 23.04, 25.49, 25.75, 27.85, 28.41, and 29.19 ppm in the ratios of 1:2:2:1:2:1 (with 1 H-B having the lowest 1 H-NMR shielding constant). The B atom in C s C 8 BH 9 has the calculated 11 B-NMR shielding tensor of δ = 24.41 ppm.