Global structure of C₂B₄H₄: hypercloso or not

Abstract

Due to their fantastic structures and reactivity, carbon–boron mixed cluster hydrides have aroused increasing attention both experimentally and theoretically. Generally, n-vertex borane and carborane containing equal to or more than (n + 1) polyhedral skeletal electron pairs (PSEPs) present similar structural characteristics. However, for the n-PSEP boranes and carboranes, whether their structural pattern is similar or not is still uncertain. In this work, we report a particular example, C₂B₄H₄, the global minimum of which does not conform to the well-known polyhedral skeletal electron pair theory (PSEPT). Through extensive isomeric searching, the global minimum structure of C₂B₄H₄ is addressed to exhibit a ribbon-like structure at the aug-cc-pVTZ-CCSD(T)//B3LYP level. However, the hypercloso structure predicted by PSEPT lies 16.0 kcal mol⁻¹ higher. Our results are also different from a recent theoretical study. These findings are believed to enrich the understanding of hypercloso chemistry of carbon-substituted borane derivatives.

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1. Introduction

Studies on compounds that are composed of carbon, boron and hydrogen atoms have been an active area of research owing to their wide applications in supramolecular design, catalysts, medicines and novel materials.¹ In particular, carboranes are one of the most studied hydrogenated carbon–boron mixed clusters due to their unique molecular architectures and chemical reactivity.² In order to explain the general bonding of polyhedral boranes and carboranes, Wade, Mingos and co-workers developed an effective method, i.e., the polyhedral skeletal electron pair theory (PSEPT), to rationalize their molecular architecture by simply counting the number of polyhedral skeletal electron pairs (PSEPs).³ In their original papers,^3a,3b the n-vertex boranes and carboranes with equal to or more than (n + 1) PSEPs should have good structural similarity, i.e., the n-vertex clusters with (n + 1), (n + 2) and (n + 3) PSEPs prefer to be arranged into closo, nido, and arachno polyhedra, respectively.

Afterwards, Wade and co-workers found that beyond these definitions, there exists a special kind of n-vertex borane species that exhibit capped closo or distorted closo polyhedral structures with n-PSEPs.⁴ The term hypercloso has been used to describe these apparent closed borane species with two electrons less than the closo boranes. As reported in the available literatures, the first neutral boron hydride in the B_nH_n series whose global structure could be predicted by PSEPT is B₆H₆.^5,6 These hypercloso B_nH_n (n ≥ 6) species have uncompleted electron shells or unpaired electrons, and thus adopt distorted structures to remove the orbital degeneracy.

Can the isoelectronic boron-rich species with n-PSEPs show similar hypercloso structure to B_nH_n? Here, through extensive isomeric searching, we report an abnormal example C₂B₄H₄, whose global minimum is a ribbon-like isomer at the CCSD(T) aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level, instead of the octahedral-like hypercloso species that was revealed in a recent theoretical study.⁷ The detailed calculation strategy, results and discussions can be found in the following sections.

2. Calculation methods

To find the global structure efficiently, we applied our locally developed “skeleton-ligand cluster-growth” method⁸ by considering C₂B₄H₄ as a “skeleton-ligand” type molecule, i.e., hydrogen atoms are “ligands” surrounding the C₂B₄-skeleton. To determine all possible structural forms of the skeleton C₂B₄, we applied a “grid-based comprehensive isomeric strategy”, as illustrated in our previous work,⁹ to yield the possible structures of the C₂B₄ core. In this strategy, we first built up a three-dimensional box containing 6 × 6 × 6 grid points. The distance between the neighboring grid points was set to the averaged value of C–C, C–B and B–B single bonds. The two C-atoms and four B-atoms were placed onto these grid sites. If no atoms or groups are completely separated from the remaining parts, the structure can be considered as an effective starting structure for the C₂B₄-optimization at the B3LYP/6-31G(d) level. Subsequently, via the “cluster-growth pattern”, the hydrogen atoms were added to the optimized-C₂B₄ core one by one in an octahedral model, i.e., the H atom could occupy any of the six vertices of an octahedron whose body center is located at any atom of the core. Note that each hydrogenated structure was subject to the structural optimization at the B3LYP/6-31G(d) level before the next hydrogenation. The key local minima, which were located within 40 kcal mol⁻¹ in energy with respect to the global minimum, were re-optimized at the B3LYP/aug-cc-pVTZ level. All minima were confirmed to have no imaginary frequencies using harmonic vibrational frequency analysis. Single-point energy calculations were conducted at the CCSD(T)/aug-cc-pVTZ level with the zero point energy correction (ZPEC) at the B3LYP/aug-cc-pVTZ level. All calculations were performed using the commercial Gaussian 03 (ref. 10) and Gaussian 09 (ref. 11) suites of package.

3. Results and discussions

Based on the present “skeleton-ligand” cluster-growth strategy, a total of 1282C₂B₄H₄ isomers are found to be local minima at the B3LYP/6-31G(d) level after thousands of computations. The huge isomeric number seems surprising yet should be reasonable if the possible bonding types of all the involved elements are considered, i.e., the C/B-atoms can form the single, double and triple bonding, while the H-atoms can form the terminal, side-bridging and face-bridging bonds. For simplicity, we present the eleven low-energy isomers lying within 25 kcal mol⁻¹ with respect to the global minimum at the aug-cc-pVTZ-CCSD(T)//B3LYP level (see Fig. 1). We can easily find that the C₂B₄H₄ system shows great preferences to be arranged into the planar pattern in the isomers 01, 02, 03, 05, 07, 08, 09 and 11. The first non-planar structure is the fourth C₂B₄H₄ in energetics (labeled as 04) that lies as high as at 16.0 kcal mol⁻¹. The lowest-energy isomer 01 in C_2h-symmetry exhibits a planar “ribbon-like” structure with two hydrogen atoms positioned on each end. In Fig. 2, we show the representative molecular orbitals of 01 at the B3LYP/aug-cc-pVTZ level. Clearly, both the peripheral σ-bonding (HOMO − 1, HOMO − 2, HOMO − 3) and the planar delocalized π-bonding orbitals (HOMO, HOMO − 4) exist in isomer 01. In HOMO − 2, the π-bonding within two CB₂ rings is delocalized, whereas it is π-anti-bonding between the edge of two rings. The HOMO − 4 π-bonding orbital is delocalized over the whole molecular plane of 01. To better illustrate the electron delocalization and aromaticity in 01, we adopted the widely-used and efficient method, i.e., nucleus-independent chemical shifts (NICS) method by setting NMR = GIAO (Gauge-Independent Atomic Orbital¹²) at the B3LYP/aug-cc-pVTZ level in the Gaussian input file, which calculates the absolute magnetic shielding at the center of ring. In this method, negative NICS values (ppm) suggest aromaticity and positive values antiaromaticity for a ring molecule. For isomer 01, the magnetic tensor Bq atom is placed right above the center of the two kinds of three member rings in consideration of the molecular symmetry. The values of NICS and NICS_zz, when Bq atom is placed at 0, 0.5 and 1.0 Å right above the ring plane, are listed in Table 1. The two outer CB₂ rings are much more aromatic (−31.1 ppm) than the two inner B₃ rings (−20.7 ppm) according to the NICS (0) values. Clearly, the whole ribbon-like structure should be considered as aromatic. This is quite interesting since the molecule only bears two π-orbitals, which usually indicate an anti-aromatic system.

Fig. 1 Top eleven isomers of C₂B₄H₄ including relative energy (ΔE < 25 kcal mol⁻¹) at CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ + ZPEC level.

Fig. 2 The top and side views of representative molecular orbitals of isomers 01 and 04. The unit of orbital energy is eV.

Table 1 Computed NICS (in ppm) and NICS_zz values of isomers 01 and 04

	Point	D (Å)	NICS	NICSzz
	11	0	−31.05	−39.42
	12	0.5	−29.26	−34.76
	13	1.0	−15.31	−24.83
	14	0	−20.74	−37.47
	15	0.5	−17.17	−26.66
	16	1.0	−9.27	−16.05
	11		D2d −75.24	−47.70
			D4h −76.31	−49.29

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Among the ribbon-like isomers, there are two interesting structural types, i.e., the planar tetra-coordinate carbon (ptC) and tetra-coordinate boron (ptB). We can see that the most-stable ptC isomer 07 lies by 18.4 kcal mol⁻¹ higher than 01. Note that in 01, there are four ptB units and the two carbon atoms are both tri-coordinate, being positioned at the edge site. Such a discrepancy in the preference between ptC and ptB could be explained that (1) carbon has larger electronegativity than boron, and (2) carbon tends to form the 2c–2e bonding, while boron prefers to form the delocalized bonding. Our results are well consistent with the previous results on binary carbon–boron clusters,¹³ which have indicated that carbon atom generally prefers to avoid the central tetra-/hyper-coordination.

There are 5 non-planar isomers (i.e., 04, 06, 10, 12, 13) within 25 kcal mol⁻¹ (Fig. 1). In particular, 04 and 12 belong to the so-called “hypercloso” structures, in which four H-atoms are attached to the four skeletons of the C₂B₄-cage. The most stable non-planar isomer is 04 (16.0 kcal mol⁻¹) with a D_2d cage distorted from the perfect D_4h octahedron at the B3LYP/aug-cc-pVTZ level. This is consistent with the intuitive prediction from the Jahn–Teller effect,¹⁴ since 04 is one electron pair less than the perfectly caged structure with n + 1 PSEPs. To our surprise, in a recent computational study, 04 was predicted to have a perfect D_4h-cage at the BP86/def2-TZVPP level.⁷ So, we performed extra optimizations for isomer 04 using eight exchange-correlation functionals, e.g., BP86, X3LYP, M062X, WB97XD, B3PW91, PBEPBE, PBEPW91 and HSEH1PBE with aug-cc-pVTZ basis set. Table 2 lists the energy difference at the CCSD(T)/aug-cc-pVTZ + ZPEC level based on various DFT geometries between the global minimum and the hypercloso cage. B3LYP, X3LYP and WB97XD predict the D_2d distorted cage as a local minimum, whereas the D_4h perfect cage is just a first-order saddle point with one imaginary frequency corresponding to the transition to the distorted cage. The deviation dihedral angle of the cage lies in the range of 12.4–13.9°, depending on the DFT methods. Interestingly, although there seems to exist significant geometric differences between the D_2d and D_4h cage of 04, their energy differences are quite trivial (less than 1 kcal mol⁻¹). Such a tiny energy difference is also reflected in the nucleus-independent chemical shift (NICS) calculations (see Table 1), i.e., the NICS(0) and NICS_zz(0) values (−75.2 and −47.7 ppm for D_2d and −76.3 and −49.3 ppm for D_4h, respectively) differs only by ca. 1 ppm. Clearly, the significantly negative NICS(0) and NICS_zz(0) in combination with the delocalized bonding orbitals (see Fig. 2) show that 04 is a strong three-dimensional aromatic species.

Table 2 The minimum frequency (M_fq, cm⁻¹) and relative energies (R_e, kcal mol⁻¹) with respect to the global minimum of the perfect D_4h and distorted D_2d (deviation dihedral angle is available) C₂B₄H₄ cages using different DFT methods with aug-cc-pVTZ basis set. The label “i” is used to represent the imaginary nature of the obtained frequency. The energies are calculated at the CCSD(T)/aug-cc-pVTZ + ZPEC level based on the geometries obtained using different functional with aug-cc-pVTZ basis set

Functional	Perfect cage		Distorted cage
	Re	Mfq	Re	Mfq	θ
B3LYP	15.2	129.8 i	16.0	167.1	13.9
X3LYP	15.3	133.5 i	15.8	164.3	13.9
BP86	15.4	120.8	—	—	—
M062X	16.3	134.1	—	—	—
WB97XD	15.4	87.3 i	16.0	101.2	12.4
B3PW91	15.5	80.8	—	—	—
PBEPBE	15.5	163.2	—	—	—
PBEPW91	15.5	160.1	—	—	—
HSEH1PBE	15.8	114.7	—	—	—

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Clearly, the global structure of C₂B₄H₄ is quite different from the parent B₆H₆, for which a hypercloso structure is the global minimum and the planar ribbon structure lies 9.4 kcal mol⁻¹ higher.⁵ The significant energetic change caused by the isoelectronic replacement of BH → C could be ascribed to that carbon prefers to be more involved in the planar π-bonding than B. Thus, unlike the analogue between many boranes and carboranes with n + 1 PSEPs, the C₂B₄H₄ and B₆H₆ with n-PSEPs show marked structural difference.

It should be noted that the recent computational study⁷ predicted the caged 04 to be the global minimum, which surely contrasts our results. This is understandable since in that work, only the direct combination of the HBCBH monomer was considered. In our located ribbon-like 01 as the global minimum, two of the four H-atoms should have migrated from boron to the neighboring carbon. In order to testify the kinetic stability of 01 and 04, we performed the Born–Oppenheimer molecular dynamics (BOMD) simulation at 300 and 373 K at the B3LYP/6-31g(d) level for both isomers. The root mean structure deviations with respect to the optimized structures of 01 and 04 as a function of time (ps) are provided in Fig. 3. It is clearly evident that the structures of 01 and 04 have slight deviation caused by the thermal effect during the 10 ps simulation. Therefore, both the isomers 01 and 04 should be stable enough in kinetics and thermodynamics at room temperature for experimental observation.

Fig. 3 Root mean structure deviations (RMSD, nm) as a function of time (ps) along the 10 ps BOMD trajectory of isomers (a) 01 and (b) 04, respectively. Left: BOMD simulations at 300 K. Right: BOMD simulations at 373 K.

4. Conclusions

In summary, a “skeleton-ligand” cluster-growth strategy in combination with standard quantum chemical calculations was applied to extensively explore the local minimum of C₂B₄H₄. We found that the replacement of two vertexes BH group in hypercloso B₆H₆ by isoelectronic C atoms yield a planar ribbon-like species 01 with considerable aromaticity as the lowest-energy structure. This does not comply with the PSEPT predictions that the n-vertex, n-PSEPs cluster prefers to adopt a hypercloso structure. The hypercloso isomer 04 is calculated to be 16.0 kcal mol⁻¹ in energy higher than 01 at the aug-cc-pVTZ-CCSD(T)//B3LYP level. Our results are also different from a recent theoretical study. These findings could be helpful for further studies on the structures of carbon-substituted borane derivatives.

Acknowledgements

This work was funded by the National Natural Science Foundation of China (no. 21273093, 21473069, 21073074). The reviewers' helpful comments are greatly acknowledged.

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