Ab initio calculations of ionic hydrocarbon compounds with heptacoordinate carbon
Ionic hydrocarbon compounds that contain hypercarbon atoms, which bond to five or more atoms, are important intermediates in chemical synthesis and may also find applications in hydrogen storage. Extensive investigations have identified hydrocarbon compounds that contain a five- or six-coordinated hypercarbon atom, such as the pentagonal-pyramidal hexamethylbenzene, C6(CH3)62+, in which a hexacoordinate carbon atom is involved. It remains challenging to search for further higher-coordinated carbon in ionic hydrocarbon compounds, such as seven- and eight-coordinated carbon. Here, we report ab initio density functional calculations that show a stable 3D hexagonal-pyramidal configuration of tropylium trication, (C7H7)3+, in which a heptacoordinate carbon atom is involved. We show that this tropylium trication is stable against deprotonation, dissociation, and structural deformation. In contrast, the pyramidal configurations of ionic C8H8 compounds, which would contain an octacoordinate carbon atom, are unstable. These results provide insights for developing new molecular structures containing hypercarbon atoms, which may have potential applications in chemical synthesis and in hydrogen storage.
KeywordsHeptacoordinate hypercarbon Density functional theory Ionic hydrocarbon compounds Tropylium trication Ab initio electronic structure calculations
Neutral carbon compounds involve carbon with the coordination number up to four (tetravalency). Ionic hydrocarbon compounds that contain hypercarbon (or hypercoordiated carbon) atoms, which bond to five or more other atoms, and the related species are a significant feature and important intermediates in various branches of chemistry [1, 2]. Since the 1950s, it has been shown that ionic carbon compounds may contain five- and six-coordinated carbon atoms . These hypercoordiated carbon structures may find valuable applications in hydrogen storage due to a large hydrogen/carbon ratio [3, 4].
Among the ionic hydrocarbons, the methanium ion CH5+, pyramidal (CH)5+, and (CH3)2C5H3+ involve a pentacoordinate carbon atom. These monocations have been observed experimentally [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The dications CH62+ and pyramidal (C6H6)2+ contain a hexacoordinate carbon atom, with the latter one recently being confirmed experimentally [1, 5, 15, 16, 17]. The six-coordinated carbocation, diprotonated methane (CH62+), were investigated with ab initio calculations, which showed, however, contradictory results — the structure was predicted to be either stable [18, 19] or unstable . In addition, the pentagonal-pyramidal hexamethylbenzene, C6(CH3)62+, in which a carbon atom is six-coordinated, was first synthesized in highly acidic conditions at low temperature  and recently confirmed with the determination of the corresponding crystal structure [21, 22]. The trication, triprotonated ethane (C2H93+), and the tetracation, tetraprotonated ethane (C2H104+), were also studied with ab initio calculations . The results showed that the stable configurations involve five- and six-coordinated carbon atoms, however, neither structure has been verified experimentally.
The search for ionic hydrocarbon compounds that contain a heptacoordinate or octacoordinate carbon has not yet resulted in any structures confirmed by experiments. Earlier ab initio calculations for the proposed triprotonated methane, the parent heptacoordinate carboncation, (CH7)3+, showed that the trication was a local minimum-energy configuration and its deprotonation was highly exothermic, making it difficult to be prepared experimentally . Similar calculations further suggested that the structure was unstable . In addition, Hogeveen and Kwant suggested a pyramidal structure of the trication C7(CH3)73+ involving seven-coordinated carbon several decades ago , but no further theoretical and experimental studies have been done since then, and the possibility of formation of heptacoordinate carbon in C7(CH3)73+ still remains open.
Motivated by possible applications in chemical synthesis and hydrogen storage as well as by the scientific curiosity of the possibility of seven or eight chemical bonds of carbon, we performed ab initio density functional theory (DFT) calculations, through which we explore possible heptacoordinate carbon and octacoordinate carbon in ionic hydrocarbon compounds of C7H7, C8H8, and C7(CH3)7. In particular, we report the identification of a stable three-dimensional pyramidal configuration of (C7H7)3+ that involves a seven-coordinate carbon, suggesting the possibility of heptacoordinate carbon in ionic hydrocarbon compounds. We show that this tropylium trication is stable against deprotonation and dissociation. Our calculations also show that a previously proposed pyramidal trication, C7(CH3)73+, which would involve heptacoordinate carbon, is an unstable configuration. In addition, we find that the pyramidal configurations of ionic C8H8 compounds, which would contain an octacoordinate carbon atom, are unstable.
The ab initio density functional theory (DFT) calculations were performed using the Vienna Ab Initio Simulation Package . Each hydrocarbon compound under this investigation was placed into a large supercell with the size of 20 × 20 × 20 Å to simulate isolated compounds . Convergence was checked with a larger supercell, 30 × 30 × 30 Å, which showed insignificant changes in results. The Perdew-Burke-Ernzerhof generalized gradient approximations  for the exchange-correlation functionals were employed in the DFT calculations, and the electron-core interactions were treated with the projector augmented wave (PAW) method [28, 29]. Plane-wave basis sets with a cut-off energy of 500 eV and one sampling k point at Gamma in the three-dimensional Brillouin zone of the supercell were used in the calculations. Convergence check was performed with higher cut-off energies (up to 600 eV) and more k points (up to 8 k points). Optimization of the structure was performed for each supercell via a conjugate-gradient technique using the total energy and the Hellmann-Feynman forces on the atoms , and all configurations were optimized until the forces on each atom were smaller than 0.03 eV/Å. DFT calculations, with the climbing image nudged elastic band method , were used to determine the energy barriers when structural transformations were considered. Charges of individual atoms were quantitatively determined using Bader charge analysis [31, 32].
Results and discussion
The corresponding 3D configuration, as shown in Fig. 1c and d, was obtained after optimization of the initial pyramidal configuration. We find that the pyramidal structure for (C7H7)+ is not a stable configuration, and optimization of the pyramidal structure leads to the local minimum-energy 3D configuration shown in Fig. 1c and d. However, the six-membered carbon ring does not hold on a 2D plane, resulting in the configuration with a pentacoordinated carbon atom. This 3D (C7H7)+ configuration is much higher in total energy, by 546 kJ mol-1, than planar (C7H7)+, indicating that the 3D structure with pentacoordinate carbon is very unlikely to occur.
Similar to (C7H7)+, the pyramidal structure of tropylium dication, (C7H7)2+ is unstable. The optimized 3D configuration from the initial pyramidal structure is very similar to that of (C7H7)+ and involves pentacoordinate carbon (not shown here). The planar configuration of (C7H7)2+ was also optimized, and the 2D ring structure was found to be stable. The geometry of the 2D ring structure of (C7H7)2+ is almost the same as that of (C7H7)+ (Fig. 1a and b), but the C-C and C-H bond lengths of 1.42 Å and 1.10 Å for (C7H7)2+ are slightly longer than the corresponding bond lengths for (C7H7)+. The 3D configuration is much higher in total energy than the planar structure (by 284 kJ mol-1).
The base of the pyramidal configuration is formed by a six-membered carbon ring with each carbon bonded to a hydrogen atom. The C-C and C-H bond lengths are determined to be 1.44 Å and 1.11 Å, respectively. The carbon atom at the top vertex of the hexagonal pyramid is bonded to all six carbons on the base, forming six C-C bonds each with a bond length of approximately 1.82 Å. The apical carbon is also bonded to a hydrogen atom, and the C-H bond length is 1.12 Å. Therefore, the apical carbon is bonded to seven neighboring atoms, making it heptacoordinated.
As a comparison, the optimized structure of the two-dimensional ring configuration of (C7H7)3+ was also determined. The configuration is almost the same as those for the monocation (C7H7)+ (Fig. 1a and b) and dication (C7H7)2+, except for the fact that the C-C bonds (with bond lengths of 1.45 Å) in planar (C7H7)3+ are longer than those in planar (C7H7)+ and (C7H7)2+.
As the 3D pyramidal configuration that involves heptacoordinate carbon is energetically metastable, we further investigated its stability against the structural transformation to the off-ring configuration. We determined the optimal transition pathway and the corresponding energy barrier for this structural transformation. Figure S1 shows the configuration for the transition state, in which the CH species being transferred from the top of the pyramidal configuration is located almost on the top of the bridge site of two carbon atoms in the carbon ring.
Furthermore, as a comparison, we calculated the energy barrier for the structural transformation of the 2D ring configuration of (C7H7)3+ to the off-ring configuration, and we obtained a value of 2 kJ mol-1 (Fig. 5). This small energy barrier suggests that, even at low temperatures, the 2D ring configuration may transfer to the off-ring configuration.
We have also calculated the change of the total energy during the process of deprotonation and dissociation of the CH+ species. The energy cost of both processes are very high: 332 kJ mol-1 when the hydrogen at the top of the pyramid is separated from the rest, 377 kJ mol-1 if a hydrogen bonded to a carbon atom at the pyramid base is separated, and 514 kJ mol-1 when the CH+ species is dissociated from the (C6H6)2+ ring, indicating that the pyramidal configuration is highly stable against deprotonation and dissociation.
Our computational results for tropylium ions are consistent with Hückel’s rule (the 4n + 2 rule) [35, 36] for 2D aromaticity and the 4n + 2 interstitial electron rule for 3D aromaticity [37, 38]. The tropylium monocation (C7H7)+ that takes a 2D ring structure is an aromatic species. There are 6 π-electrons in the ring because of the monocation nature, and Hückel’s rule is hence satisfied (4n + 2, and n = 1) [35, 36, 37]. On the other hand, the stable trication (C7H7)3+ takes the 3D pyramidal configuration. This configuration can be regarded as a combination of dication (C6H6)2+ and monocation (CH)+, which provides 4 and 2 electrons, respectively, for the bonding between them. Therefore, there are 6 valence electrons participating in the bonding between the apical carbon atom and the six carbons on the base of the pyramid, and the 4n + 2 (n = 1) interstitial electron rule for 3D aromaticity is satisfied .
It becomes intriguing to explore octacoordinate carbon using the same chemical principle. We examined possible octacoordinate carbon in the configurations of mono-, di-, tri-, and tetra-cations of C8H8, which are (C8H8)+, (C8H8)2+, (C8H8)3+, and (C8H8)4+, respectively. The optimized equilibrium configurations are shown in Figs. S3–S8.
(C8H8)+, (C8H8)2+, (C8H8)3+, and (C8H8)4+ have a stable 2D ring configuration. The pyramidal configurations of both (C8H8)+ and (C8H8)2+ are unstable, and they spontaneously transferred to the configurations that have much higher energies than the corresponding 2D ring structures, by 89 kJ mol-1 and 229 kJ mol-1, respectively, indicating that the 2D ring structures are much more likely to occur.
Instead, we find that the pyramidal configurations for (C8H8)3+ and (C8H8)4+ are stable, but both have a much higher energy than the corresponding 2D ring configurations, by 290 kJ mol-1 and 145 kJ mol-1, respectively, implying that the pyramidal configurations are unlikely to occur. In addition, the off-ring configurations for (C8H8)3+ and (C8H8)4+ have a much lower energy than the corresponding pyramidal configurations by 196 kJ mol-1 and 162 kJ mol-1, respectively. The energy barriers for the pyramidal configurations to transfer to the off-ring configurations are determined to be very small (10 kJ mol-1 and 6 kJ mol-1 for (C8H8)3+ and (C8H8)4+, respectively). Therefore, the pyramidal configurations are kinetically unstable at room temperature.
In conclusion, ab initio DFT calculations reported here demonstrate that heptacoordinate carbon is possible in the ionic hydrocarbon compound tropylium trication (C7H7)3+. The 3D hexagonal-pyramidal (C7H7)3+, which contains a heptacoordinate carbon atom, is predicted to be a metastable configuration. It is highly stable against dissociation of CH+ and deprotonation, and fairly stable against structural transformation. The result can be explained by the 4n + 2 interstitial electron rule for 3D aromaticity. On the other hand, tropylium monocation and dication, (C7H7)+ and (C7H7)2+, as well as the previously proposed hexagonal-pyramidal heptamethylbenzene, C7(CH3)73+, do not involve any heptacoordinate carbon. In addition, none of the ionic C8H8 would involve octacoordinate carbon, and the proposed heptagonal-pyramidal configurations are all shown to be unstable. These results provide insights for developing new molecular structures containing hypercarbon atoms, which may have potential applications in chemical synthesis and in hydrogen storage.
The authors would like to thank Michael Lee from the Oklahoma School of Science and Mathematics (now at the University of Oklahoma) for valuable discussions at the early stage of this work. The calculations have been performed using computational resources at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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