Stabilization of beryllium-containing planar pentacoordinate carbon species through attaching hydrogen atoms

Abstract

The diagonal relationship between beryllium and aluminum and the isoelectronic relationship between BeH unit and Al atom were utilized to design nine new planar and quasi-planar pentacoordinate carbon (ppC) species CAl_nBe_mH_x^q (n + m = 5, q = 0, ±1, x = q + m − 1) (1a–9a) by attaching H atoms onto the Be atoms in CAl₄Be, CAl₃Be₂⁻, CAl₂Be₃²⁻, and CAlBe₄³⁻. These ppC species are σ and π double aromatic. In comparison with their parents, these H-attached molecules are more stable electronically, as can be reflected by the more favourable alternative negative–positive–negative charge-arranging pattern and the less dispersed peripheral orbitals. Remarkably, seven of these nine molecules are global energy minima, in which four of them are kinetically stable, including CAl₃Be₂H (2a), CAl₂Be₃H⁻ (4a), CAl₂Be₃H₂ (5a), and CAlBe₄H₄⁺ (9a). They are the promising target for the experimental realization of species with a ppC.

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Planar hypercoordinate carbon chemistry can be dated back to 1968 when Monkhorst proposed the first planar tetracoordinate carbon (ptC) in a transition state structure.¹ In 1970, Hoffmann and co-workers sponsored the project of stabilizing the ptC in equilibrium structure.² After the proposal of first ptC energy minimum 1,1-dilithiocyclopropane (C₃H₄Li₂) by Schleyer and Pople group in 1976,³ the most significant advance has been the conceptual extension of ptC to planar pentacoordinate or hexacoordinate carbon (ppC or phC),⁴ which promoted the extension of the number of planar coordination to values as high as ten and the central planar hypercoordinate atom from carbon to other main group elements or even transition metals.⁵ Nevertheless, the ppC are the most witnessed in all these extended type of structures,⁶ possibly due to the geometrically nice fit between the peripheral ligand atoms and center carbon and the electronically easy satisfaction of the 18 electron (18e) rule.

In 2001, Wang and Schleyer reported a family of ppC-containing molecules, i.e. the milestone “hyparenes”, which were designed by substituting the –(CH)_n– moieties in aromatic or even anti-aromatic hydrocarbons with ppC building blocks –C₃B₃–, –C₂B₄–, and –CB₅–.^4b Subsequently, ppC species such as CCu₅H₅,⁷ CBe₅ and CBe₅⁴⁻,⁸ wheel-like C₂B₈, C₃B₉³⁺ and C₅B₁₁^+ 9 were also proposed. However, it is still unknown to date whether these small ppC clusters are global minima on their potential energy surfaces. Hence, people cannot evaluate their experimental viability. Nonetheless, situation changed when Zeng and Schleyer group reported the first ppC global minimum D_5h CAl₅⁺ in 2008, which features not only the 18e structure, but also the σ and π double aromaticity.¹⁰ Taking CAl₅⁺ as the seed structure and considering the periodicity as well as the diagonal relationship, etc., people had designed a series isoelectronic ppC structures, including CAl_nBe_m^1−m (m = 1–3),¹¹ CAl₄E⁺ (E = Al, Ga, In, Tl),¹² CBe₅E⁻ (E = Al, Ga, In, Tl),¹³ CAl₄TmX₂ (Tm = Ti, Zr, Hf; X = F, Cl, Br, I, and cyclopentadienyl anion),¹⁴ and CGa_nBe_m^1−m (n + m = 5, m = 1–4).¹⁵

During the design of these species, when each Al or its heavier congeners was replaced by a Be atom, a negative charge was added to maintain the isoelectronic relationship. However, it would be hard to experimentally realize such ppC structures due to the high molecular charges and the exposure of the electron deficient metal atoms. As a result, people had tried to stabilize the highly negatively charged ppC ions through attaching the certain number of auxiliary atoms. For example, H atoms had been attached to CAl₄⁻ and CAl₄²⁻ in a joint experimental-theoretical study, leading to the new ptC species CAl₄H and CAl₄H⁻.¹⁶ For ppC species, the most studied seed structure should be CBe₅⁴⁻,⁸ which is even not an eligible minimum.¹⁷ Nevertheless, through attaching the auxiliary atoms, like alkali metals, hydrogen, halogens, and even transition metal gold, a family of ppC species can be designed, including CBe₅Li_nⁿ⁻⁴ (n = 1–5),^17a CBe₅H_nⁿ⁻⁴ (n = 2, 3, 5),^17b CBe₅E₅⁺ (E = F, Cl, Br, Li, Na, K),¹⁸ and CBe₅Au_nⁿ⁻⁴ (n = 2–5).¹⁹ In these ppC species, the auxiliary atoms play the roles of both compensating the deficient electrons and reducing the high negatively charges. Remarkably, H atoms were also employed to stabilize the ppC-containing C–Be double chain nanoribbon, where its CBe₅H₂ ppC unit possesses the similar electronic structures to that of CAl₅⁺.²⁰

Very recently, using Li atoms to balance the high negative charge of Be-doped ppC structures results in neutral or mono-anionic species [(CAl₂Be₃)Li]^− 11b and CGa_nBe_mLi_m−1 (n + m = 5, m = 1–4),¹⁵ where Li atoms generally show high affinity to Be atoms. In addition, our recent study revealed that Be and H can be bounded together through favourable covalent and ionic bonding,^5c,21 thus H should be a better choice than Li as the auxiliary atoms around CBe₅ ppC core.^17b Herein, we wonder whether H atoms can be attached onto the Be-doped ppC structures to design the new ppC molecules possessing the molecular charges with ±1|e|, which facilitates the experimental generation and accurate calculation. The answer is positive and presented in this computational study, which designed nine new ppC molecules (see Fig. 1), in which four of them are kinetically stable global minima, thereby providing promising targets for experimental realization.

Fig. 1 Optimized structures 1a–9a at the B3LYP/aug-cc-pVTZ level. Bond distances and NBO charges are given in black and italic blue fonts, respectively.

Computational methods

The ppC species designed in this work were optimized and harmonic vibrational frequencies analyzed at the B3LYP/aug-cc-pVTZ level, which predicted these ppC structures to be true energy minima. The vibrations obtained using B3LYP functional was calibrated by the calculations using double hybrid functional B2PLYP²² with D3 empirical dispersion correction (B2PLYP-D3),²³ which gave the similar results to those obtained at the B3LYP level. So B3LYP functional should be reliable for current ppC molecules. The thermodynamic stability of designed ppC species was studied using a stochastic search algorithm.²⁴ Two sets of explorations were run for singlet potential energy surfaces until they converged. The triplet potential energy surfaces were examined by another two sets of explorations as well. The randomly generated initial structures were optimized at the B3LYP/6-31G(d) level and 20 lowest isomers were recalculated at the B3LYP/aug-cc-pVTZ level, then ten lowest isomers were refined at the B2PLYP-D3/aug-cc-pVTZ level. Finally, the energies of the five lowest isomers were improved at the CCSD(T)/aug-cc-pVTZ level. The relative energies were compared using CCSD(T)/aug-cc-pVTZ electronic energies plus B2PLYP-D3/aug-cc-pVTZ Gibbs free energy corrections. The wave function stability, natural bond orbital (NBO)²⁵ analyses and the nucleus-independent chemical shifts (NICS)²⁶ analyses were performed at B3LYP/aug-cc-pVTZ. Adaptive nature density partitioning (AdNDP)²⁷ was carried out at B3LYP/6-31G(d) level. Born–Oppenheimer molecular dynamic (BOMD)²⁸ simulations were run at the B3LYP/6-31g(d) level and 298 K. The stochastic search algorithm was realized using GXYZ 2.0 program,²⁹ the AdNDP analysis was performed using AdNDP program, the CCSD(T) calculations were carried out using MolPro 2012.1,³⁰ the NBO analyses were performed using NBO 3.1,³¹ and all other calculations were performed using the Gaussian 09 package.³²

Results and discussion

Design of CAl_nBe_mH_x^q (n + m = 5, q = ±1, x = q + m − 1)

In this work, we focus on four components, including CAl₄Be, CAl₃Be₂⁻, CAl₂Be₃²⁻, and CAlBe₄³⁻ (see Fig. S1†), in which the global energy minima of former three components had been proved to be ppC structure previously.¹¹ We had studied CAlBe₄³⁻ and found that it is a ppC local energy minimum at the B3LYP/aug-cc-pVTZ level. However, its wavefunction is unstable, possibly due to the high negative charge, so reducing such charge is necessary. Using the four ppC species and their ppC-containing isomers as the seed structures, we try to attach H atoms onto the Be–Be or Be–Al edges. Considering molecular charges within ±1|e|, there are nine possible components, including CAl₄BeH⁺, CAl₃Be₂H, Cal₃Be₂H₂⁺, CAl₂Be₃H⁻, CAl₂Be₃H₂, CAl₂Be₃H₃⁺, CAlBe₄H₂⁻, CAlBe₄H₃, CAlBe₄H₄⁺. Fig. 1 shows the most stable ppC structures (1a–9a) for each component. At the B3LYP/aug-cc-pVTZ level, 8a adopts the quasi-planar geometry, while other species adopt the perfectly planar structures. The C–Al distances in 1a–9a range from 1.995 to 2.250 Å and the C–Be distances range from 1.641 to 1.710 Å, which are close enough to consider each of corresponding Al or Be atom as a coordination to C atom, so 1a–9a can be regarded as ppC or quasi-ppC species.

Electronic structure analyses

Orbital analysis. To better understand the chemical bonding in these ppC species, the adaptive natural density partitioning (AdNDP)²⁷ analysis was performed and the results of 4a–6a are shown in Fig. 2, while those of other species are given in Fig. S2 in the ESI.† AdNDP is an extension of natural bond orbital (NBO) analysis. It represents the electronic structure of a molecular system in terms of n-center two-electron (nc-2e) bonds, with n ranging from one to total number of atoms in the molecule. Thus, AdNDP recovers not only the Lewis elements (lone pairs and 2c-2e bonds), but also the delocalized nc-2e bonds. As the first and second columns of these figures show, for any Be–Be or Be–Al edge without bridging H atom, there is a 2c-2e σ bond with occupation numbers (ONs) ranging from 1.98 to 1.99|e|, while for that with a bridging H atom, there is a Be–H–Be or Be–H–Al three-center two-electron (3c-2e) bond (ON = 1.95–1.98|e|). We note that the 3c-2e bonds are less dispersed than 2c-2e bonds, indicating that occupying such bonds may be beneficial to the molecular stability. Consistently, as shown in Table 1, for species with the same ppC core (except for CAl₄Be core), their HOMO–LUMO gaps are enlarged with the increasing number of attached H atoms. For instance, CAl₂Be₃²⁻, 4a, 5a, and 6a have zero, one, two, and three H atoms attaching to the common CAl₂Be₃ core, their HOMO–LUMO gaps are 0.94, 2.66, 2.86, and 2.96 eV, respectively, showing the obvious increasing trend. The pictures shown in third to fifth column are the delocalized six-center two-electron (6c-2e) σ bonds (ON = 1.99–2.00|e|) and those in the last column are the 6c-2e π bonds (ON = 1.98–2.00|e|). These orbitals are essentially identical to their parent molecules, which describe the ligand-to-ppC interactions. Remarkably, three 6c-2e σ bonds and one 6c-2e π bonds fill eight electrons to the valence shell of C atoms, meeting the octet rule, which would be a reason why these ppC species can be stable.

Fig. 2 AdNDP bonding patterns of 4a, 5a and 6a with occupation numbers (ONs).

Table 1 The lowest vibrational frequencies (υ_min, in cm⁻¹), HOMO–LUMO gaps (gap, in eV), vertical detachment energies (VDE, in eV), vertical electron affinities (VEA, in eV), and the Wiberg bond indices (WBIs) for selected atom–atom interactions

	υmin	Gap	VDE	VEA	WBI
					C–Be	C–Al	Be–H	Be–Al
CAl4Be	77	2.60	7.20	−1.21	0.64	0.40/0.47
CAl4BeH^+ (1a)	59	2.32	11.70	−5.91	0.78	0.34–0.45	0.58	0.27
CAl3Be2^−	98	2.04	2.39	2.35	0.51	0.46/0.54
CAl3Be2H (2a)	104	2.34	7.01	−1.24	0.67	0.41/0.45	0.45
CAl3Be2H2^+ (3a)	81	2.70	12.21	−5.90	0.69/0.75	0.30–0.45	0.43/0.49	0.28
CAl2Be3^2−	131	0.94	−1.34	4.03	0.52/0.56	0.49
CAl2Be3H^− (4a)	118	2.66	2.60	2.30	0.52/0.65	0.45	0.45
CAl2Be3H2 (5a)	142	2.86	7.08	−0.71	0.62/0.77	0.39	0.39/0.53
CAl2Be3H3^+ (6a)	96	2.96	12.35	−5.56	0.66–0.69	0.30/0.41	0.42–0.54	0.32
CAlBe4^3−	173	0.33	−3.71	5.13	0.59/0.61	0.42
CAlBe4H2^− (7a)	144	2.40	2.26	2.28	0.57/0.63	0.45	0.41/0.48
CAlBe4H3 (8a)	42	2.96	6.66	0.21	0.56/0.73	0.35	0.38–0.54
CAlBe4H4^+ (9a)	91	3.55	12.62	−4.96	0.78–0.83	0.35	0.54–0.64	0.28
CAl5^+	69	2.82	11.67	−5.48		0.43

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Aromaticity. In addition to offering the stable shell structure for carbon, three delocalized σ orbitals and one delocalized π orbitals in these ppC species match the 4n + 2 rule, where n = 0 and 1, respectively, so these ppC species may be σ and π aromatic, similar to their parents molecules. To verify the orbital analysis results, we further conducted the NICS analysis, a powerful tool to evaluate the aromaticity. As shown in Fig. 3 and S3,† the concerned points were chosen according to molecular symmetry and the ghost atoms were placed for these points from 0 Å (within molecular plane) up to 2 Å above the molecular plane. Similar to the situation in their parent molecules, which was previously proved to be aromatic, the NICS values for the concerned point in the ppC molecules reported in this work are all negative (shown in red balls). Therefore, the NICS analyses confirmed the orbital analysis results that the molecules were aromatic. We think the aromaticity should be another factor to stabilize these ppC species.

Fig. 3 NICS of CAl₂Be₃²⁻ and 4a–6a. Points with negative NICS values (shown in red balls) are aromatic.

Ionic and covalent bonding. We also performed the conventional NBO²⁵ analysis. The ionic bonding was evaluated by natural charge distribution. As shown in Fig. 1, the NBO charges on carbon of 1a–9a are largely negative, ranging from −1.99 to −2.58|e|, while those on beryllium (+0.29 to +0.76|e|) and aluminum (+0.37 to +1.11|e|) are positive. This suggests the obvious charge transfer from Be and Al to C, similar to the situation in their parent molecules. Nevertheless, different from them, there are peripheral hydrogen atoms in 1a–9a, which possess the small but non-negligible negative charges (−0.19 to −0.31|e|), so the ionic bonding in 1a–9a is more favourable than in CAl₅⁺ because of more efficient alternative negative–positive–negative charge distribution patterns. The covalent bonding was assessed by the Wiberg bond indices (WBI). As shown in Table 1, the WBI_C–Al and WBI_C–Be values, 0.30–0.45 and 0.50–0.83, respectively, indicate the multicenter peripheral to center covalent bonding interactions. The WBI_Al–H and WBI_Be–H values range from 0.27 to 0.64, implying the formation of Be–H–Be or Be–H–Al 3c-2e bonds. The WBI analysis results are consistent with the AdNDP analyses described above. The NBO analyses results revealed that both ionic and covalent bonding contribute significantly to the stabilization of ppC species 1a–9a.

Stability consideration

Thermodynamic and kinetic stability. The experimental viability of small clusters is closely related to their thermodynamic and kinetic stabilities. In this work, the stochastic search algorithm²⁴ was employed to explore the thermodynamic stability. As shown in Fig. S4 in ESI,† 1a and 3a are higher than their global energy minimum by 10.7 and 3.8 kcal mol⁻¹, respectively, at the final CCSD(T)/aug-cc-pVTZ level, thus 1a and 3a will not be viable experimentally and they are disregarded in the following. In contrast, 2a and 4a–9a are proved to be global energy minima on their PES, being respectively 4.6, 3.1, 4.6, 3.6, 3.7, 2.8 and 15.0 kcal mol⁻¹ lower than their corresponding second lowest isomers at the CCSD(T)/aug-cc-pVTZ level. The good thermodynamic stability will benefit their generation in the gas-phase experiment.

Next, we studied the kinetic stability of global energy minima 2a and 4a–9a by performing 50 pico-second (ps) Born–Oppenheimer molecular dynamic (BOMD)²⁸ simulations at the B3LYP/6-31G(d) level and 298 K. The structural evolution during the simulation was described by the root-mean-square deviation (RMSD) relative to their B3LYP/6-31G(d)-optimized structures. As shown in Fig. 4, the RMSD plots of 6a–8a show irreversible upward jumps at about 34, 32, and 9 ps, respectively. Structural sampling suggested that the upward jumps of these RMSD plots correspond to the isomerization processes, so 6a–8a are kinetically unstable. As a comparison, the RMSD values of 2a, 4a, and 5a have no upward jump and the fluctuation also relatively small, ranging from 0.06, 0.08, and 0.09 to 0.47, 0.45 and 0.48 Å. The RMSD plot of 9a shows some reversible jumps. However, the highest RMSD value is only 0.80 Å, which corresponds to the flexibility of H atoms rather than the tendency to isomerize the structure. The average RMSD values for these four molecules are also small, being 0.22, 0.24, 0.25 and 0.29 Å, respectively. The dynamic simulations suggest their structures can be well-maintained during the simulations at 298 K. Being the kinetically stable global energy minima, 2a, 4a, 5a, and 9a would be promising targets for gas phase generation and followed spectroscopic characterization.

Fig. 4 The RMSD plots for the BOMD simulations of 2a and 4a–9a at 298 K.

VDEs and VEAs. To give experimentalists the reference data, we have calculated the VDEs and VEAs of these molecules. Here, we only discuss 2a, 4a, 5a, and 9a. For mono-anionic global minimum 4a, its VDE is 2.60 eV, which reasonably high for photoelectron spectroscopy, while its VEA, 2.26 eV suggest that gaining an electron is endothermic. For neutral global minima 2a and 5a, their VDEs of 7.01 and 7.08 eV as well as the VEAs of −1.24 and −0.71 eV indicate their low tendency to lose or gain an electron. For mono-cation 9a, it VEA value of −4.96 eV ranges between that of Na⁺ (−5.14 eV) and K⁺ (−4.30 eV), so its VEA is rather low in cations. Simultaneously, its VDE of 12.62 eV indicate its low tendency to lose an electron.

Conclusion

In summary, we have designed nine ppC species with molecular charges within ±1|e| through attaching the H atoms at the Be–Be or Be–Al edge of ppC species CAl₄Be, CAl₃Be₂⁻, CAl₂Be₃²⁻, and CAlBe₄³⁻. Similar to their parent molecules, these ppC species meet the octet rule and feature the σ and π double aromaticity. The introduction of H atoms on these ppC structures does not obviously influence the ppC core structure both geometrically and electronically, but can enlarge the HOMO–LUMO gaps, convert the dispersed Be–Be or Be–Al 2c-2e σ bonds to the less dispersed Be–H–Be or Be–H–Al 3c-2e π bonds, which further stabilize the ppC structures. In these nine H-attached ppC species, four of them were confirmed to be stable both thermodynamically and kinetically, including CAl₃Be₂H (2a), CAl₂Be₃H⁻ (4a), CAl₂Be₃H₂ (5a), and CAlBe₄H₄⁺ (9a). They are the promising targets for generation and characterization in the gas phase experiments.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge support for this work from the NSFC (Grant No. 21720102006, 21273140, and 21471092), the Special Program for Applied Research on Supercomputation of the NSFC-Guangdong Joint Fund (the second phase) (Grant No. U1501501), the One Hundred-Talent Program of Shanxi Province, the Program for Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, the Shanxi 1331KIRT, the Foundation of the State Key Laboratory of Coal Conversion (Grant No. J17-018-610), and the Shanxi University supercomputing platform.

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Footnote

† Electronic supplementary information (ESI) available: The AdNDP and NICS results mentioned in the text, the structures and relative energies of isomers, as well as the necessary Cartesian coordinates. See DOI: 10.1039/c8ra07664b

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