Kinetic Stability of Si 2 C 5 H 2 Isomer with a Planar Tetracoordinate Carbon Atom

: Dissociation pathways of the global minimum geometry of Si 2 C 5 H 2 with a planar tetracoordinate carbon (ptC) atom, 2,7-disilatricyclo[4.1.0.0 1,3 ]hept-2,4,6-trien-2,7-diyl ( 1 ), have been theoretically investigated using density functional theory and coupled-cluster (CC) methods. Dissociation of Si-C bond connected to the ptC atom leads to the formation of 4,7-disilabicyclo[4.1.0]hept-1(6),4(5)-dien-2-yn-7-ylidene ( 4 ) through a single transition state. Dissociation of C-C bond connected to the ptC atom leads to an intermediate with two identical transition states and leads back to 1 itself. Simultaneous breaking of both Si-C and C-C bonds leads to an acyclic transition state, which forms an acyclic product, cis-1,7-disilahept-1,2,3,5,6-pentaen-1,7-diylidene ( 19 ). Overall, two different products, four transition states, and an intermediate have been identiﬁed at the B3LYP/6-311++G(2d,2p) level of theory. Intrinsic reaction coordinate calculations have also been done at the latter level to conﬁrm the isomerization pathways. CC calculations have been done at the CCSD(T)/cc-pVTZ level of theory for all minima. Importantly, all reaction proﬁles for 1 are found be endothermic in Si 2 C 5 H 2 . These results are in stark contrast compared to the structurally similar and isovalent lowest-energy isomer of C 7 H 2 with a ptC atom as the overall reaction proﬁles there have been found to be exothermic. The activation energies for Si-C, C-C, and Si-C/C-C breaking are found to be 30.51, 64.05, and 61.85 kcal mol − 1 , respectively. Thus, it is emphasized here that 1 is a kinetically stable molecule. However, it remains elusive in the laboratory to date. Therefore, energetic and spectroscopic parameters have been documented here, which may be of relevance to molecular spectroscopists in identifying this key anti-van’t-Hoff-Le Bel molecule.


Computational Details
The geometries of all Si 2 C 5 H 2 isomers reported here have been optimized using DFT with the B3LYP hybrid-functional [65][66][67][68] and the 6-311++G(2d,2p) basis set [69,70]. All the transition states corresponding to the dissociation of C-C/Si-C bonds connected to the ptC atom, the intrinsic reaction coordinate (IRC) calculations [71,72], and the nucleus independent chemical shift (NICS) values [73][74][75] have been calculated at the latter level. It is also noted here that wavefunction stability analysis has been done for all minima  obtained at the B3LYP/6-311++G(2d,2p) level and no instabilities have been found [76]. All these DFT calculations have been carried out with the Gaussian suite of programs [77]. All the low-lying isomers (minima) obtained from the DFT calculations, which lie within 40 kcal mol −1 , have been reoptimized with CC methods. All these CC calculations with single and double excitations (CCSD) [78] including a quasiperturbative triple excitations (CCSD(T)) [79,80] have been done with correlation-consistent polarized valence triple zeta (cc-pVTZ) basis set of Dunning's [81]. The latter basis set consists of 246 basis functions for Si 2 C 5 H 2 . The frozen-core (fc) approximation is used for isomers 1-18 initially in the fc-CCSD(T)/cc-pVTZ calculations. For the global minimum geometry alone (1), all-electron (ae) calculations at the ae-CCSD(T)/cc-pwCVTZ [82] level of theory have also been done. This basis set consists of 361 basis functions for Si 2 C 5 H 2 and therefore these calculations have not been done for other isomers considering their expensive nature. All these calculations have been done with the CFOUR (2.00 beta version) program package [83]. We note that for all the stationary points obtained, harmonic vibrational frequencies have been calculated by analytic calculation of second derivatives [84].

Results and Discussion
Eighteen low-lying isomers of Si 2 C 5 H 2 obtained at the fc-CCSD(T)/cc-pVTZ level of theory are shown in Figure 1. Zero-point vibrational energy (ZPVE) corrected relative energies calculated with respect to 1, point group symmetry, and the absolute dipole moment value calculated for the corresponding geometry are given underneath each isomer. Optimal geometry parameters obtained at five different levels for isomer 1 are given in Table 1. Harmonic vibrational frequencies, infrared (IR) intensities, and various isotopic shifts ( 28 Si- 29 Si, 12 C-mono-substituted-13 C, Si 13 2 C 5 H 2 , 1 H-mono-substituted-2 D, and Si 2 C 5 D 2 ) in harmonic vibrational frequencies for isomer 1 are collected in Table 2. The activation energies (∆E ‡ ), reaction energies (∆E r ), and relative energies (∆E 0 ) calculated at different levels for the various dissociation pathways of 1 are given in Table 3. The atom numbering scheme, natural atomic charges, possible valence structures, and relevant occupied molecular orbitals contributing to the bonding of the ptC atom of isomer 1 are shown in Figure 2. Schematic reaction profile diagram connecting the reactant 1 and their dissociative products through appropriate transition states calculated at the B3LYP/6-311++G(2d,2p) level of theory is shown in Figure 3. Likewise, reaction profile diagram involving the isomerization of 1 to 2 is shown in Figure 4. For brevity, total electronic energies, ZPVEs, and final Cartesian coordinates of the optimized geometries of all isomers are given in the supporting information.   (4) and Si(5); C(2) and C(3); C(6) and C (7); H(8) and H(9) are equivalent.  (1) All bond lengths of isomer 1 are systematically overestimated at the CCSD/cc-pVDZ and CCSD(T)/cc-pVDZ levels (see Table 1). One could notice a contraction in bond lengths with respect to the same methods using the cc-pVTZ basis set. They are slightly contracted further if we observe the change in bond lengths from CCSD(T)/cc-pVTZ to CCSD(T)/cc-pwCVTZ levels. These results (longer bond lengths with respect to cc-pVDZ basis set) are largely due to the lack of higher angular momentum polarization functions [85][86][87][88][89][90] and consistent with our earlier observations [91][92][93][94][95][96]. Considering the double bond characteristics of C 6 C 7 , C 2 Si 4 (C 3 Si 5 ; equal due to C 2v symmetry) and single bond characteristics of C 1 C 2 (C 1 C 3 ) and C 2 C 6 (C 3 C 7 ), we have come to the conclusion that valence structure 1a shown in Figure 2 is dominant. However, based on the natural atomic charges, one could also assume an equally dominant resonance contributor where the molecule behaves like a zwitterion (Si and H atoms having a partial positive charge whereas all carbon atoms having a partial negative charge). The second most stable isomer, 2-ethynylmethylene-1,4-disilabicyclo[1.1.0]but-1(3)-en-4-ylidene (2), is 21.39 kcal mol −1 above 1 at the fc-CCSD(T)/cc-pVTZ level of theory (see Figure 1). Therefore, isomer 1 is thermodynamically well-separated from others. It is worth noting here that the singlet-triplet energy gap (∆E ST ) calculated for isomer 1 is 72.26 kcal mol −1 (positive value indicates singlet being more stable) at the (U)B3LYP/6-311++G(2d,2p) level of theory [58].
Harmonic vibrational frequencies calculated for 1 reveal that three vibrational modes (modes 4, 8, and 17) are dominant (see Table 2). One is the Si-C-Si rocking (b 2 ) calculated at 427.7 cm −1 , another is the Si-C-Si breathing motion (a 1 ) calculated at 616.0 cm −1 , and yet another is the C-C stretching motion (a 1 ) calculated at 1340.0 cm −1 at the ae-CCSD(T)/cc-pwCVTZ level of theory. Various isotopic shift values calculated by us can help in resolving potential ambiguities in assigning vibrational modes. It is also possible to identify isomer 1 and all other low-lying isomers (2-18) using Fourier transform microwave spectroscopy as the net dipole moment is non-zero (µ = 0) in all cases. The net dipole moment value calculated for isomer 1 is 0.39 Debye at the fc-CCSD(T)/cc-pVTZ level of theory. Rotational and centrifugal distortion constants of all 18 isomers are given in our previous article [58] and detailed discussion related to rotational constants are not repeated here for brevity. It is also noted here that for the low-lying C 7 H 2 isomer with a ptC atom, tricyclo[4.1.0.0 1,3 ]hept-2,4,6-trien-2,7-diyl [92], the net dipole moment value calculated at the same level of theory is 5.84 Debye. Such a large deviation is not surprising considering the fact that silicon is more electropositive than carbon and the overall charge (see Figure 2) is more balanced and thus the net dipole moment has a smaller value for isomer 1. Also, compared with the iso-valent C 7 H 2 isomer with a ptC atom, isomer 1 exhibits higher aromatic characteristic. The NICS (1 Å) value obtained for 1 is −20.28 ppm at the B3LYP/6-311++G(2d,2p) level.
At the latter level, the NICS (1 Å) value obtained for C 7 H 2 isomer with a ptC atom is −12.21 ppm. Nevertheless, both the molecules remain elusive to date. To analyze the aromatic characteristics further, we have carried out NICS calculations in 3D grid points (see supporting information). The out-of-plane NICS values are negative for all the three rings. On the other hand, the in-plane NICS value (NICS (0 Å)) is positive for the C 5 ring and negative for the SiC 2 rings. Thus, the entire molecule is π-aromatic (see the MOs in Figure 2; HOMO, HOMO-2, HOMO-6) but σ-aromaticity is not completely there in the C 5 ring (HOMO-1, HOMO-3, HOMO-4, HOMO-5). Therefore, isomer 1 of Si 2 C 5 H 2 can be characterized as a molecule, which exhibits pseudo-double aromaticity [97][98][99]. To assess the multi-reference characteristic of isomer 1, we have calculated the T 1 diagnostic value suggested elsewhere [100] and found that it is below 0.02. The value obtained for isomer 1 at the fc-CCSD/cc-pVTZ level of theory is 0.015. Thus, we have not carried out multireference CC calculations for this molecule.

Activation and Reaction Energies
To calculate the activation and reaction energies, different bonds connected to the ptC atom of 1 were broken. Four different transition states (TS-1 to TS-4), one intermediate (20), and three different products, 1, 4,7-disilabicyclo[4.1.0]hept-1(6),4(5)-dien-2-yn-7-ylidene (4), and cis-1,7-disilahept-1,2,3,5,6-pentaen-1,7-diylidene (19), respectively, have been identified (see Figure 3) along three different dissociation pathways A, B, and C connected to the ptC atom of isomer 1. It is noted here that for pathway A, both the reactant and the product are one and the same. Breaking of C-ptC bond requires an ∆E ‡ of 64.05 kcal mol −1 at the B3LYP/6-311++G(2d,2p) level. IRC calculations through this transition state (TS-1) leads to an intermediate (20), which lies at 54.64 kcal mol −1 above 1. Another identical transition state, TS-2, which is a half-chair equivalent conformer of TS-1, has been identified along pathway A. IRC calculations along these two transition states (TS-1 and TS-2) either leads to the same non-planar intermediate (20-in one direction) or to the global minimum isomer itself (1-in the other direction). The lowest activation energy required was estimated to be 30.51 kcal mol −1 at the same level of theory, which occurs through Si-ptC bond breaking (pathway B). Along pathway C, where simultaneous breaking of both C-ptC and Si-ptC bonds has been taken into consideration, an acyclic transition state has been identified (TS-4), which requires an activation energy of 61.85 kcal mol −1 and leads to an acyclic product, 19. Overall, the reaction profiles along these three different dissociation pathways are found to be endothermic with a reaction energy of 54.64, 18.80, and 43.03 kcal mol −1 , respectively, for dissociation pathways A, B, and C. For the lowest activation energy path (B), we have also estimated rate constant values using Rice-Ramsperger-Kassel-Marcus (RRKM) theory [101]. It was estimated that the rate of the reverse reaction (4 to 1) is three orders of magnitude faster than the forward reaction. This clearly implies that 1 is kinetically stable.

Isomerization of 1 to 2
Isomerization of 1 to 2 has also been considered though 2 lies 21.39 kcal mol −1 above 1 (see Figure 4). Considering the structural similarity between 1 and 2, the Si-C double bond and the ptC-C bonds on one side are initially broken. This requires an activation energy of 71.45 kcal mol −1 at the B3LYP/6-311++G(2d,2p) level. IRC calculations from this transition state (TS-5) lead us to a new intermediate (22). Upon rotating the C-C bond, we found a new transition state (TS-6). IRC calculations from TS-6 lead to new intermediate (21), where the hydrogen atoms are in the trans position. A 1,2-H shift must happen to reach the geometry of 2. Therefore, using this new intermediate 22 and slightly elongating the C-C-C angle, we found a new transition state geometry TS-7, which requires an activation energy of 62.71 kcal mol −1 . It is noted here that the energy barrier between 21 and TS-7 is negative after ZPVE-correction at the B3LYP/6-311++G(2d,2p) level. Without ZPVEcorrections, the activation energy (∆E * ; see Figure 4) is 66.96 kcal mol −1 . It is well-known in the literature that various DFT functionals including the popular B3LYP underestimate the barrier-heights [102,103]. Doubly hybrid density functionals such as B2PLYP [104,105] and XYG3 [102] offer promising alternatives for accurate description of barrier-heights. We leave this discussion with a caveat that currently we have not tried these alternatives and in a future work we would be exploring these avenues. IRC calculations in one direction from TS-7 lead us to isomer 2, whose reaction energy is 17.53 kcal mol −1 . It is also noted here that the Gibbs free energy change is minimal for almost all stationary points.

Rate Co-Efficient for the Isomerization Reaction
The activation energies and reaction energies estimated among the low-lying isomers of Si 2 C 5 H 2 reveal that pathway B is the most feasible based on energetics. Therefore, for this isomerization process alone, we have calculated the rate coefficients for the forward (k 1 ) and reverse (k −1 ) reactions using RRKM theory [101] given by the expression where E TS is the energy of the transition state from the ground state of the isomers under consideration, E is the total energy of the isomer, N(E-E TS ) is the sum of states of the transition state that would be available for the given energy E of the isomer, c is the velocity of light, and ρ is the density of the vibrational states. The densities of the vibrational states are calculated by Beyer and Swinehart direct count algorithm [106]. The rate of forward and reverse reactions are given in Figure 5 as a function of energy. The reverse reaction is found to be around three orders of magnitude faster than the forward reaction. The equilibrium constant for the isomerization reaction is calculated using the expression K = k 1 /k −1 and it is given in Figure 6. The equilibrium constant is much below 1. This is due to the high density of vibrational states for isomer 1 (global minimum structure) compared to isomer 4 at energies above the isomerization barrier. This favors the reverse reaction than the forward reaction. Figure 6 clearly indicates that over a wide range of energies, isomer 1 is kinetically as well as energetically more stable.

Conclusions
The most stable isomer (global minimum) of Si 2 C 5 H 2 containing a ptC atom and its dissociation pathways have been theoretically characterized using DFT and CC methods. The lowest activation energy barrier for 1 has been calculated as 30.51 kcal mol −1 at the B3LYP/6-311++G(2d,2p) level of theory. Possible interconversion of 1 to 2 is highly unlikely as the initial activation energy required for this process is 71.45 kcal mol −1 at the same level. Hence, it is concluded that 1 is a kinetically stable molecule. Also, the rate co-efficient for the reverse reaction (4 to 1; exothermic) is ∼3 orders of magnitude faster than the forward reaction (1 to 4; endothermic). This clearly indicates further that isomer 1 is kinetically stable. In fact, our extensive search for various structural isomers of Si 2 C 5 H 2 indicates that there are no other isomers lying close to 1 within 20 kcal mol −1 [58] at the fc-CCSD(T)/cc-pVTZ level of theory (see Figure 1). Thus, 1 is not only the energetically most stable molecule but also thermodynamically well-separated from other isomers. Perhaps, synthetic challenges may remain as one of the potential issues in the laboratory identification of this molecule considering the pyrophoric nature of some of the precursor molecules such as SiH 4 in the preparation of this isomer or silicon-doped hydrocarbons, in general. Nevertheless, it is believed that the current theoretical efforts may motivate and assist the experimentalists in devising successful synthetic strategies and in characterizing this potential "anti-van't Hoff-Le Bel" molecule in the laboratory. The kinetic stability of 1,7-disilatricyclo[4.1.0.0 1,3 ]hept-2,4,6-trien-2,7-diyl (6), which contains a ptSi atom will be examined in a future work. Funding: Computational support provided at the SDSU by DURIP Grant W911NF-10-1-0157 from the U.S. Department of Defense and by NSF CRIF Grant CHE-0947087 is gratefully acknowledged. Additional computational support provided at the VIT, Vellore, India, through a research grant (Project. No. YSS/2014/001019) from the Science and Engineering Research Board, Department of Science and Technology, New Delhi, Government of India, is gratefully acknowledged. Computing time provided (to VST) at the National Computational Infrastructure (NCI), which is supported by the Australian Government, is also gratefully acknowledged.

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Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available in inside the article or the supplementary material.