CCSDT(Q)/CBS thermochemistry for the D5h → D10h isomerization in the C10 carbon cluster: Getting the right answer for the right reason

Endocircular Li Carbon Rings

“…Thef ormer satisfies Hückelsr ule and may possess aromaticity. [47,48] Aromatic C n rings exhibit D nh symmetry,while the nonaromatic C n rings have alternating bonds which appear in three versions [45,46] in which (i)only the bond angles alternate (D n 2 h symmetry), (ii)only the bond lengths alternate (D n 2 h symmetry) and (iii)both bond lengths and bond angles alternate (C n 2 h symmetry). Bartlett and co-workers reported based on coupled-cluster calculations [49] that the equilibrium geometry of the ground state of the neutral C 20 ring belongs to class (ii), i.e., D 10h symmetry,a nd similar findings can be expected for the other C n rings we investigate here,a s discussed in the literature.…”

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface

“…Similarly, employing Δ-learning, which can normally reduce the number of expensive high-level data by a significant factor, is still computationally impractical within any reasonable time window, cf. the discussion in the preceding work . Yet, noticing that CPMD, a pseudopotential-based nongradient-corrected functional, appears to recover the D 5h –D 10h barrier very close to the “exact” value, even if fortuitously, hints at certain solutions.…”

“…The authors also found that the addition of the ZPVE at the harmonic level, albeit with B3LYP/cc-pVTZ, resulted in a negative barrier to pseudoinversion and, therefore, asserted that the effective C 10 structure was a regular decagon at 0 K. 17,18 The conclusions based on the results of the above CCSD(T) studies were rigorously questioned in a more recent and detailed investigation of the electronic structure of the cyclic C 10 that included correlation of the 1s electrons, the full triple excitations with estimated perturbative quadruples, the CBS limit, and relativistic effects. 16 The authors showed that by far the most important contribution to the D 5h −D 10h energy difference is the inclusion of full triples in the CCSD procedure. Employing a CBS extrapolation scheme 25 and correlating all electrons, the authors determined the D 5h −D 10h electronic energy difference to be 812 cm −1 , a benchmark to be considered definitive.…”

“…Any of the above functionals can be used to train the model with appropriately applied scaling, as has been done in the past. − Here, we have found it most practical to use τHCTH/cc-pVQZ as the source of training the PES, considering that its barrier is closest to the CCSDT(Q)/CBS benchmark value of 812 cm –1 , and then “gently” morph the energies in the vicinity of the D 5h minimum to bring the D 10h –D 5h difference exactly to the benchmark value. We refer to this level of theory by τHCTH-CC and use the following morphing function V τ HCTH − CC = w normalΔ E CC + [ 1 − w ] normalΔ E τ HCTH normalΔ E τ HCTH V τ HCTH where the zero of the V τHCTH energy is set at the D 10h transition state, Δ E CC is the benchmark (CC = CCSDT(Q)/CBS) barrier height, Δ E τHCTH is the τHCTH barrier height, and the energy-dependent weight factor is w = exp [ − ( V τ HCTH + Δ E τ HCTH Δ E C C ) 3 ] For the geometries where V τHCTH is slightly above the minimum, that is, where V τHCTH ≈ −Δ E τHCTH , we have w ≈ 1, and therefore V τHCTH‑CC ≈ (Δ E CC /Δ E τHCTH ) V τHCTH , a simple scalar modification of the original τHCTH data. At moderate and much higher energies, w → 0 very rapidly, given the cubed exponential, and V τHCTH→CC ≈ V τHCTH , i.e., it remains unmodified from the τHCTH data.…”

On the alternating structure of cyclo[18]carbon

“…In order to explain the alternating structure of C18, density functional theory (DFT) study has been performed and second-order Jahn-Teller effect (SOJTE) has been accounted for the structural distortion based on the coherent change on orbital energies 8 . Nevertheless, high-level calculations suggest that DFT is unable to predict the correct geometry of C18, except for a few carefully selected ones [9][10][11][12][13] .…”