Aromaticity is a fundamental chemical concept of ever-increasing diversity. According to Hückel’s and Baird’s rules, cyclic conjugated species with 4n+2 π-electrons are aromatic in the singlet electronic ground state (S0) and antiaromatic in the lowest triplet state (T1), and vice-versa. Thus, species with aromaticity in both states have not yet been reported. Here we carry out density functional theory calculations on recently synthesized organometallics, namely osmapentalyne and osmapentalenes, and demonstrate the first example (16-electron osmapentalene) of aromaticity in both S0 and T1 states, which we term adaptive aromaticity. Further electronic structure analysis reveals that the excitation pattern for the formation of the T1 state plays a crucial role in the achievement of adaptive aromaticity. Our findings highlight the role of a transition metal in unorthodox excitation behavior, and may aid the design of adaptive aromatics for photochemical and molecular magnetism applications.
Aromaticity has been one of the most important concepts in chemistry since the discovery of benzene in 1825. The classical [4n+2] rule to rationalize aromaticity was first proposed by Erich Hückel in 1931 and was later developed by Doering1,2. In 1960s, Dewar gave the first explanation on Hückel’s rule, which was later extended to Möbius topology by Heilbronner and Zimmerman but inverted3,4,5,6. The concept of ground-state aromaticity has been well developed and serves as a robust tool for rationalizing chemical reactions and properties7,8.
Excited-state aromaticity9,10,11,12 can be traced back to 1972, when Baird proposed that the aromaticity of planar annulenes in the S0 state should be reversed in the T1 state13, which was later applied to both Hückel and Möbius topologies by Aihara14. Experimentally, Wan and co-workers reported the formation of a 4π aromatic intermediate (or transition state) in a photosolvolysis reaction15. Schleyer and co-workers supported Baird’s rule by theoretical investigation of aromaticity in 4nπ annulenes in their singlet and triplet states16. Recently, Kim and Osuka characterized the excited-state (anti)aromaticity in expanded porphyrins17,18,19,20,21,22. Ottosson and co-workers reported a series of “aromatic chameleons” that are prone to be aromatic in both the T1 and S1 states23,24,25,26,27. Note that Baird’s rule can also be applied to the S1 state28,29,30. Recently, Xia and co-workers synthesized several novel aromatic osmapentalynes and osmapentalenes31,32. Through density functional theory (DFT) calculations, we revealed that these organometallics exhibit Craig-type Möbius aromaticity resulting from eight-center eight-electron (8c–8e) d π -p π conjugation. Note that such Craig-type Möbius aromaticity was computationally demonstrated in 4nπ planar metallacycles early in 2010 by Mauksch and Tsogoeva33 and in osmasilapentalyne34 and dimetalla10 annulenes by us35. However, the aromaticity of these novel organometallics in the excited-state has not been reported so far. Despite these extensive studies on aromaticity, to date no example has been reported to be aromatic in both the S0 and T1 (or S1) states. Here we demonstrate the first example, to the best of our knowledge, of a complex with aromaticity in both the S0 and T1 states, termed as adaptive aromaticity. This is supported by DFT calculations on simplified model complexes (verified in our previous studies) to examine aromaticity in their T1 states.
The geometries of model complexes 1–3
We first examined the geometries of model complexes 1–3 (Fig. 1a) in both the S0 and the T1 states. As shown in Fig. 1b, the C–C bond lengths of these complexes in the S0 state are in the range of 1.371–1.414 Å, which are much longer than a double bond (1.329 Å in CH2=CH2) and significantly shorter than a single bond (1.531 Å in CH3–CH3) calculated at the same level of theory, revealing highly delocalized C–C bonds and thus suggesting their aromaticity. In sharp contrast, the bond length alternations (BLAs) in their T1 states are 0.071, 0.016, and 0.066 Å, suggesting a distinctive difference of complex 2 among these three complexes. In line with the BLAs, the harmonic oscillator model of aromaticity (HOMA) value of complex 2 in the T1 state (0.950) is quite larger than those of the other two complexes (0.721 for 1 and 0.801 for 3). The particularly small difference of HOMA values (ΔΗΟΜΑ, 0.006, Supplementary Table 1) between the S0 and T1 states in complex 2 suggests its triplet-state aromaticity.
Aromaticity analyses based on magnetic properties
To further evaluate the (anti)aromaticity of these osmacycles, we performed the nucleus-independent chemical shift (NICS) calculations in both their S0 and the T1 states36,37, two-dimensional NICS grids are capable to display the magnetic shielding in aromatic rings and de-shielding in antiaromatic rings38,39. Compared with other NICS indices, the NICS(1)zz is chosen here as it can be easily computed and also highly effective in evaluating π aromaticity in both the S0 and the T1 states40,41. All these complexes in the S0 state (1-S 0 , 2-S 0 , and 3-S 0 ) and complex 2 in the T1 state (2-T 1 ) are aromatic, according to the significantly negative (shielded) NICS(1)zz values in these osmacycles (Fig. 2a–c, e). On the contrary, complex 1 in the T1 state (1-T 1 ) shows antiaromaticity indicated by the highly positive NICS(1)zz values inside the rings (Fig. 2d). Complex 3 in the T1 state (3-T 1 ), however, does not show either shielding or de-shielding effects at the ring centers, thus suggesting its nonaromaticity (Fig. 2f). In comparison, the NICS grids of benzene and pentalene in the T1 state (Supplementary Fig. 2) reveal their antiaromaticity and aromaticity, respectively. Note that NICS scans for complexes 1–3 in the S0 and T1 states in Supplementary Fig. 3 further support the reliability of choosing NICS(1)zz.
To further verify the (anti)aromaticity of these complexes, we computed the anisotropy of the induced current density (ACID) for these complexes (Fig. 3), which can provide intuitive pictures showing the induced currents caused by an external magnetic field42,43. Clockwise currents along the perimeter of the fused rings in 1-S 0 , 2-S 0 , 3-S 0 , and 2-T 1 indicate aromaticity, in line with the NICS grids. In sharp contrast, the ring current in 1-T 1 is anti-clockwise, characteristic of antiaromaticity. The current density vectors in 3-T 1 are tiny and in disorder, supporting its nonaromaticity (Fig. 3).
Aromaticity analyses based on electron localization function
In general, it is much safer to draw a conclusion on aromaticity based on different physicochemical properties. Topological analyses of the electron localization function (ELF)44, and in particular the π-contribution, ELF π , is an excellent tool to directly link molecular electronic structure properties with (anti)aromaticity45,46 . Thus, we carried out ELF π analysis to examine the delocalization of π electrons along the perimeter of osmacycles. The π orbitals were taken from our previous calculations, which are responsible for Möbius aromaticity resulting from 8c–8e d π -p π conjugation (Supplementary Fig. 4). According to the previous study on a series of polybenzenoid hydrocarbons, the ELF π bifurcation values (BV(ELF π )s) in the range of 0.65–0.96 indicate C–C delocalized π bonds47. The BV(ELF π )s for carbon–carbon bonds in 1-S 0 , 2-S 0 , 3-S 0 , and 2-T 1 are in the range of 0.742–0.955 (Fig. 1b). A small span of BV(ELF π ) (ΔBV(ELF π )) for C–C bonds is also an indicator of aromaticity47. As shown in Fig. 1b, the ΔBV(ELF π )s in 2-S 0 and 2-T 1 are close to each other, indicating the adaptive aromaticity. In contrast, the ΔBV(ELF π )s in 1-T 1 is more than six times of that in 1-S 0 , close to that (0.764 in Supplementary Fig. 5) of benzene in the T1 state, suggesting the antiaromaticity. The intermediate ΔBV(ELF π ) (0.474) of 3-T 1 indicates its nonaromaticity in the T1 state. The ELF π domains at the isovalue of 0.70 (Supplementary Fig. 6) reveal an electron delocalization on the carbon chains among 1-S 0 , 2-S 0 , 3-S 0 , and 2-T 1 . All these results are in line with those from NICS and ACID analyses.
Aromaticity analyses based on frontier molecular orbitals
To probe the origin of adaptive aromaticity in complex 2, we analyzed its frontier molecular orbitals and compared them with the other two complexes (Fig. 4, Supplementary Figs. 7–9). As shown in Fig. 4, the highest occupied molecular orbital (HOMO) of complex 2 in the S0 state is particularly similar to that of complex 1. However, its lowest unoccupied molecular orbital (LUMO) is significantly different from that of complex 1. For instance, the LUMO of complex 2 is mainly in-plane antibonding interaction between the metal d orbital and the p orbital (lone pair) of the chloride ligand, whereas the LUMO of complex 1 is mainly out-of-plane π-antibonding interaction between the metal center and carbon chain. For complex 3, its HOMO is similar to the LUMO of complex 2, whereas the LUMO is similar to that of complex 1. In comparison with conventional organic aromatics, the excitation pattern of metallaaromatics in the T1 state is more complicated and thus becomes less predictable because the formation of the T1 state is not always out-of-plane ππ* excitation. Specifically, the HOMO and LUMO of complex 1 are both out-of-plane π MOs, leading to a formation of the T1 state by out-of-plane ππ* excitation. Thus, its T1 state follows Baird’s rule and is antiaromatic. In sharp contrast, the T1 state of complex 2 is formed by the electronic excitation from the out-of-plane HOMO to the in-plane LUMO of the ground state. As the highest singly occupied molecular orbital (HSOMO) is in-plane, its contribution to the out-of-plane π aromaticity is expected to be minor. Thus, it is understandable that complex 2 does not follow Baird’s rule in terms of triplet-state aromaticity. Similarly, for complex 3, the HOMO in the S0 state is an in-plane π orbital. Its T1 state is, therefore, not formed by out-of-plane ππ* excitation. So complex 3 is not expected to follow Baird’s rule in the T1 state, too. All these qualitative analyses are also supported by ACID calculations on these key frontier molecular orbitals (Fig. 4).
When an occupied π bonding orbital in an aromatic species excites an electron to form the T1 state, its contribution to the diatropic ring currents will be reduced, such as the HSOMO-1 of complexes 1–2 and benzene, as indicated by the ACID plots (Fig. 4). Meanwhile, even a single electron in an antibonding π orbital might have significant contribution to the paratropic ring currents, which is demonstrated here by the HSOMOs in the T 1 state of 1, 3, and benzene (Fig. 4). The rest low-lying π orbitals are still doubly occupied and remain almost unchanged. Therefore, these orbitals are not discussed here. The aromaticity reversal in 1 could be ascribed to the reduced diatropic ring current of HSOMO-1 and newly generated significantly paratropic ring current of HSOMO, similar to those of benzene in the T1 state. The aromaticity of 2 is slightly reduced in the T1 state because its HSOMO is in-plane and the contribution to π aromaticity is negligible. The ignorable contribution by HSOMO of 2 was confirmed by further calculations on the radical formed by removing an electron from this orbital. As shown in Supplementary Fig. 10, the dicationic species 2′ is aromatic in the doublet state. As for 3, there is no loss of electrons in the out-of-plane π bonding orbitals in the T1 state, whereas the newly generated paratropic ring current of HSOMO neutralizes the diatropic ring current caused by almost unchanged π orbitals, leading to the nonaromaticity in the T1 state of complex 3. In a word, the in-plane LUMO of complex 2 plays a crucial role in the achievement of its aromaticity in the T1 state, resulting in the first example of adaptive aromaticity.
Aromaticity analyses based on the spin density
In Baird’s original paper, he pointed out that the π–π* excitation tends to be “localized” within a subunit of a molecule13. For instance, the lowest triplet state of acenaphthylene has a larger contribution from excitation localized at an ethylenic bond than rather that delocalized across the entire π network13. In a recent study, we found that the localization of the spin density is found for antiaromatic species in the T1 state, whereas triplet-state aromatic compounds have a tendency to delocalize their spin densities41. How about the population of the spin density in complexes 1-T 1 , 2-T 1 , 3-T 1 , and 2′? As shown in Fig. 5, different from our previous observation in main-group systems, the localization of the spin density is found for aromatic species 2-T 1 and 2′, whereas the delocalization of the spin density for 1-T 1 and 3-T 1 . Such a difference could be mainly attributed to the effect of transition metals and the character of their HSOMOs.
Adaptive aromaticity in 16e− osmapentalenes with bulky phosphines
To assure that the simplification of phosphorus ligands does not alter the nature of adaptive aromaticity in 2, we examined two bulky ligands—trimethyl phosphine (PMe3) and triphenyl phosphine (PPh3), which are commonly used in experiments. The NICS(1)zz grids computed for 16e− osmapentalenes with these two ligands are basically same as those for the simplified model 2 (Supplementary Fig. 2), validating adaptive aromaticity concept concluded in this study.
We have demonstrated that osmapentalene 2 is aromatic in both the S0 and T1 states, which is supported by various aromaticity indices including NICS(1)zz, ACID, HOMA, and ELF π analyses. In addition, osmapentalyne 1 follows Baird’s rule and exhibits aromaticity reversal from the S0 state to the T1 state, indicating a “Dr. Jekyll and Mr. Hyde” split personality feature48. On the other hand, osmapentalenes 2 and 3 do not possess the out-of-plane ππ* T1 state, and thus are out of the scope of Baird’s rule. Electronic structure analyses based on molecular orbital theory reveal a distinctive excitation pattern for the formation of the T1 state of complex 2, leading to the first example to achieve adaptive aromaticity, which has been rationalized by the ACID analyses. Thus, in-plane excitation rather than out-of-plane ππ* is essential to achieve the adaptive aromaticity. Our findings highlight the importance of a transition metal in a rare excitation fashion to feature double “Dr. Jekyll” personality in the S0 and T1 states, potentially opening an avenue to design adaptive aromatics for photochemistry and molecular magnets.
All the DFT calculations except fragment analyses were carried out with Gaussian 03 software package49. Geometric optimizations together with frequency calculations were performed at the (U)B3LYP level of theory. The 6-311++G(d,p) basis set was employed for C, H, and O atoms. For P, Cl, Os, and Ru atoms the pseudopotential basis set LANL2DZ was used, with polarization functions for P (ζ(d)=0.340), Cl (ζ(d)=0.514), and Os (ζ(f)=0.886)50,51, NICS calculations were carried out at (U)B3LYP-GIAO/6-311++G(d, p) level. The gauge invariant atomicorbitals (GIAO) and continuous set of gauge transformations (CSGT) methods were used to compute the NICS values and ACID plots, respectively. Fragment analyses (Supplementary Figs. 7–9) were performed using ADF (2017.104) program package at B3LYP/TZ2P level of theory52,53, Zero-order regular approximation (ZORA) was applied for consideration of scalar relativistic effects. An auxiliary set of diffuse functions was included in the calculations. ELF π analyses were conducted using Multiwfn with wavefunctions obtained from geometry optimizations54. The ELF π bifurcation points were accurately located with the help of topology analysis implemented in Multiwfn, by searching critical points within spheres and using each nucleus in the molecule as sphere center in turn. Cartesian coordinates (Supplementary Table 2) of structures and high-resolution ACID plots (Supplementary Figs. 11–29) are provided in the Supplementary Information.
All data generated or analyzed during this study are included in this published article (and its supplementary information files) and are available from the corresponding author upon reasonable request.
Hückel, E. Quantentheoretische beiträge zum benzolproblem. Z. Phys. 70, 204–286 (1931).
Doering, W. V. E. & Detert, F. L. Cycloheptatrienylium oxide. J. Am. Chem. Soc. 73, 876–877 (1951).
Dewar, M. J. S. A molecular orbital theory of organic chemistry—VIII. Tetrahedron 22, 75–92 (1966).
Zimmerman, H. E. On molecular orbital correlation diagrams, the occurrence of Möbius systems in cyclization reactions, and factors controlling ground- and excited-state reactions. I. J. Am. Chem. Soc. 88, 1564–1565 (1966).
Zimmerman, H. E. Möbius-Hückel concept in organic chemistry. Application of organic molecules and reactions. Acc. Chem. Res 4, 272–280 (1971).
Heilbronner, E. Hückel molecular orbitals of Möbius-type conformations of annulenes. Tetrahedron Lett. 5, 1923–1928 (1964).
Schleyer, P. v. R. Introduction: delocalization Pi and Sigma. Chem. Rev. 105, 3433–3435 (2005).
Gleiter, R. & Haberhauer, G. Aromaticity and Other Conjugation Effects. (Wiley‐VCH, Weinheim, 2012).
Ueda, M. et al. Energetics of Baird aromaticity supported by inversion of photoexcited chiral [4n]annulene derivatives. Nat. Commun. 8, 346 (2017).
Papadakis, R. et al. Metal-free photochemical silylations and transfer hydrogenations of benzenoid hydrocarbons and graphene. Nat. Commun. 7, 12962 (2016).
Ottosson, H. Organic photochemistry: Exciting excited-state aromaticity. Nat. Chem. 4, 969–971 (2012).
Rosenberg, M., Dahlstrand, C., Kilså, K. & Ottosson, H. Excited state aromaticity and antiaromaticity: Opportunities for photophysical and photochemical rationalizations. Chem. Rev. 114, 5379–5425 (2014).
Baird, N. C. Quantum organic photochemistry. II. Resonance and aromaticity in the lowest 3ππ* state of cyclic hydrocarbons. J. Am. Chem. Soc. 94, 4941–4948 (1972).
Aihara, J.-i. Aromaticity-based theory of pericyclic reactions. B. Chem. Soc. Jpn. 51, 1788–1792 (1978).
Wan, P. & Krogh, E. Evidence for the generation of aromatic cationic systems in the excited state. Photochemical solvolysis of fluoren-9-ol. J. Chem. Soc. Chem. Commun. 4, 1207–1208 (1985).
Gogonea, V., Schleyer, P.v. R. & Schreiner, P. R. Consequences of triplet aromaticity in 4nπ-electron annulenes: Calculation of magnetic shieldings for open-shell species. Angew. Chem. Int. Ed. 37, 1945–1948 (1998).
Sung, Y. M. et al. Reversal of Hückel (anti)aromaticity in the lowest triplet states of hexaphyrins and spectroscopic evidence for Baird's rule. Nat. Chem. 7, 418–422 (2015).
Sung, Y. M. et al. Switching between aromatic and antiaromatic 1,3-phenylene-strapped - and hexaphyrins upon passage to the singlet excited state. J. Am. Chem. Soc. 137, 11856–11859 (2015).
Cha, W. -Y. et al. Multifaceted octaphyrin(22.214.171.124.126.96.36.199): deprotonation-induced switching among nonaromatic, Möbius aromatic, and Hückel antiaromatic species. Chem. Commun. 52, 6076–6078 (2016).
Oh, J. et al. Aromaticity reversal in the lowest excited triplet state of archetypical mobius heteroannulenic systems. Angew. Chem. Int. Ed. 55, 6487–6491 (2016).
Sung, Y. M. et al. A description of vibrational modes in hexaphyrins: Understanding the aromaticity reversal in the lowest triplet state. Angew. Chem. Int. Ed. 55, 11930–11934 (2016).
Hong, Y. et al. The extension of Baird's rule to twisted heteroannulenes: Aromaticity reversal of singly and doubly twisted molecular systems in the lowest triplet state. Angew. Chem. Int. Ed. 56, 2932–2936 (2017).
Möllerstedt, H., Piqueras, M. C., Crespo, R. & Ottosson, H. Fulvenes, fulvalenes, and azulene: Are they aromatic chameleons? J. Am. Chem. Soc. 126, 13938–13939 (2004).
Ottosson, H. et al. Scope and limitations of Baird's theory on triplet state aromaticity: application to the tuning of singlet-triplet energy gaps in fulvenes. Chem. -Eur. J. 13, 6998–7005 (2007).
Rosenberg, M., Ottosson, H. & Kilså, K. Influence of excited state aromaticity in the lowest excited singlet states of fulvene derivatives. Phys. Chem. Chem. Phys. 13, 12912–12919 (2011).
Jorner, K. et al. Impact of ground- and excited-state aromaticity on cyclopentadiene and silole excitation energies and excited-state polarities. Chem. -Eur. J. 20, 9295–9303 (2014).
Ayub, R., Bakouri, O. E., Jorner, K., Solà, M. & Ottosson, H. Can Baird's and Clar's rules combined explain triplet state energies of polycyclic conjugated hydrocarbons with fused 4nπ- and (4n + 2)π-rings? J. Org. Chem. 82, 6327–6340 (2017).
Fratev, F., Monev, V. & Janoschek, R. Ab initio study of cyclobutadiene in excited states: optimized geometries, electronic transitions and aromaticities. Tetrahedron 38, 2929–2932 (1982).
Karadakov, P. B. Ground- and excited-state aromaticity and antiaromaticity in benzene and cyclobutadiene. J. Phys. Chem. A 112, 7303–7309 (2008).
Feixas, F., Vandenbussche, J., Bultinck, P., Matito, E. & Solà, M. Electron delocalization and aromaticity in low-lying excited states of archetypal organic compounds. Phys. Chem. Chem. Phys. 13, 20690–20703 (2011).
Zhu, C. et al. Stabilization of anti-aromatic and strained five-membered rings with a transition metal. Nat. Chem. 5, 698–703 (2013).
Zhu, C. et al. Planar Mobius aromatic pentalenes incorporating 16 and 18 valence electron osmiums. Nat. Commun. 5, 3265 (2014).
Mauksch, M. & Tsogoeva, S. B. Demonstration of "Möbius" aromaticity in planar metallacycles. Chem. -Eur. J. 16, 7843–7851 (2010).
Wang, X., Zhu, C., Xia, H. & Zhu, J. Theoretical study on the stability and aromaticity of metallasilapentalynes. Organometallics 33, 1845–1850 (2014).
An, K., Shen, T. & Zhu, J. Craig-Type Möbius aromaticity and antiaromaticity in dimetallaannulenes: A metal-induced Yin-and-Yang pair. Organometallics 36, 3199–3204 (2017).
Schleyer, P.v. R., Maerker, C., Dransfeld, A., Jiao, H. & Hommes, N. J. R.v. E. Nucleus-independent chemical shifts: A simple and efficient aromaticity probe. J. Am. Chem. Soc. 118, 6317–6318 (1996).
Chen, Z., Wannere, C. S., Corminboeuf, C., Puchta, R. & Schleyer, P. v. R. Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. Chem. Rev. 105, 3842–3888 (2005).
Gershoni-Poranne, R. & Stanger, A. The NICS-XY-scan: identification of local and global ring currents in multi-ring systems. Chem. -Eur. J. 20, 5673–5688 (2014).
Peeks, M. D., Claridge, T. D. & Anderson, H. L. Aromatic and antiaromatic ring currents in a molecular nanoring. Nature 541, 200–203 (2017).
Fallah-Bagher-Shaidaei, H., Wannere, C. S., Corminboeuf, C., Puchta, R. & Schleyer, Pv. R. Which NICS aromaticity index for planar π rings is best? Org. Lett. 8, 863–866 (2006).
Sun, H., An, K. & Zhu, J. Triplet state aromaticity: NICS criterion, hyperconjugation, and charge effects. Chem. -Asian J. 11, 234–240 (2016).
Herges, R. & Geuenich, D. Delocalization of electrons in molecules. J. Phys. Chem. A 105, 3214–3220 (2001).
Geuenich, D., Hess, K., Köhler, F. & Herges, R. Anisotropy of the induced current density (ACID), a general method to quantify and visualize electronic delocalization. Chem. Rev. 105, 3758–3772 (2005).
Silvi, B. & Savin, A. Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371, 683–686 (1994).
Poater, J., Duran, M., Solà, M. & Silvi, B. Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches. Chem. Rev. 105, 3911–3947 (2005).
Villaume, S., Fogarty, H. A. & Ottosson, H. Triplet-state aromaticity of 4nπ-electron monocycles: analysis of bifurcation in the π contribution to the electron localization function. ChemPhysChem. 9, 257–264 (2008).
Zhu, J., Dahlstrand, C., Smith, J. R., Villaume, S. & Ottosson, H. On the importance of Clar structures of polybenzenoid hydrocarbons as revealed by the π-contribution to the electron localization function. Symmetry 2, 1653–1682 (2010).
Papadakis, R. & Ottosson, H. The excited state antiaromatic benzene ring: a molecular Mr Hyde? Chem. Soc. Rev. 44, 6472–6493 (2015).
Frisch, M. J. et al. Gaussian 03, Revision E.01. (Gaussian, Inc., Wallingford CT, 2004).
Hay, P. J. & Wadt, W. R. Ab initio effective core potentials for molecular calculations. Potentials for potassium to gold including the outermost core orbitals. J. Chem. Phys. 82, 299–310 (1985).
Huzinaga, S. Basis sets for molecular calculations. Comput. Phys. Rep. 2, 281–339 (1985).
te Velde, G. et al. Chemistry with ADF. J. Comput. Chem. 22, 931 (2001).
Fonseca Guerra, C., Snijders, J. G., te Velde, G. & Baerends, E. J. Towards an order-N DFT method. Theor. Chem. Acc. 99, 391 (1998).
Lu, T. & Chen, F. Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33, 580–592 (2012).
Financial support by the Top-Notch Young Talents Program of China, the National Science Foundation of China (21573179) and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1263) is gratefully acknowledged. We thank Prof. Henrik Ottosson at Uppsala University and Prof. Sason Shaik at the Hebrew University of Jerusalem for their suggestions and discussion.
The authors declare no competing interests.
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Chen, D., Shen, T., An, K. et al. Adaptive aromaticity in S0 and T1 states of pentalene incorporating 16 valence electron osmium. Commun Chem 1, 18 (2018). https://doi.org/10.1038/s42004-018-0018-y