Relative energies of increasingly large [n]helicenes by means of high-level quantum chemical methods

We investigate the relative stability of increasingly large helicenes at the CCSD(T) level via the high-level G4(MP2) thermochemical protocol. The relative energies of [n]helicenes (n = 4–9) are obtained via the following reaction: [n]helicene + benzene → [n + 1]helicene + ethene. This reaction conserves the number of sp²-hybridized carbons, the number of aromatic rings, and the helical structures on the two sides of the reaction. We show that the reaction energy converges to an asymptotic value of ΔH298 = + 22.4 kJ/mol for increasingly large helicenes. For comparison, for [n]acenes, the same reaction converges to a much higher asymptotic reaction enthalpy of ΔH298 = + 56.8 kJ/mol. This difference between the two asymptotic reaction enthalpies sheds light on the relative thermodynamic stability of increasingly large helicenes. We proceed to use the G4(MP2) reaction energies to evaluate the performance of dispersion-corrected density functional theory (DFT) and semiempirical molecular orbital (SMO) methods for the relative energies of [n]helicenes. Nearly all DFT methods perform poorly with root-mean-square deviations (RMSDs) above 10 kJ/mol. The best performing DFT method, BLYP-D4, attains an RMSD = 5.2 kJ/mol. Surprisingly, the advanced SMO methods, XTB and PM7, outperform the DFT methods and result in RMSDs of 3.0 and 3.1 kJ/mol, respectively.