Accurate theoretical evaluation of strain energy of all-carboatomic ring (cyclo[2n]carbon), boron nitride ring, and cyclic polyacetylene

Cyclocarbon fully consists of sp-hybridized carbon atoms, which shows quite unusual electronic and geometric structures compared to common molecules. In this work, we systematically studied strain energy (SE) of cyclocarbons of different sizes using regression analysis method based on electronic energies evaluated at the very accurate DLPNO-CCSD(T)/cc-pVTZ theoretical level. In addition, ring strain of two systems closely related to cyclocarbon, boron nitride (BN) ring and cyclic polyacetylene (c-PA), is also explored. Very ideal relationships between SE and number of repeat units (n) are built for cyclo[2n]carbon, BnNn, and [2n]c-PA as SE = 555.0•n^-1, 145.1•n^-1 and 629.8•n^-1 kcal•mol^-1, respectively, and the underlying reasons of the difference and similarity in their SEs are discussed from electronic structure perspective. In addition, force constant of harmonic potential of C-C-C angles in cyclocarbon is derived based on SE values, the result is found to be 56.23 kcal•mol^-1•rad^-2. The possibility of constructing homodesmotic reactions to calculate SEs of cyclocarbons is also explored in this work, although this method is far less rigorous than the regression analysis method, its result is qualitatively correct has the advantage of much lower computational cost. In addition, comparison shows that ωB97XD/def2-TZVP is a good inexpensive alternative to the DLPNO-CCSD(T)/cc-pVTZ for evaluating energies used in deriving SE, while the popular and very cheap B3LYP/6-31G(d) level should be used with caution for systems with global electron conjugation such as c-PA.