Explicitly correlated benchmark calculations on C ₈H ₈ isomer energy separations: How accurate are DFT, double-hybrid, and composite ab initio procedures?

Accurate isomerization energies are obtained for a set of 45 C ₈H ₈ isomers by means of the high-level, ab initio W1-F12 thermochemical protocol. The 45 isomers involve a range of hydrocarbon functional groups, including (linear and cyclic) polyacetylene, polyyne, and cumulene moieties, as well as aromatic, anti-aromatic, and highly-strained rings. Performance of a variety of DFT functionals for the isomerization energies is evaluated. This proves to be a challenging test: only six of the 56 tested functionals attain root mean square deviations (RMSDs) below 3kcalmol ¹ (the performance of MP2), namely: 2.9 (B972-D), 2.8 (PW6B95), 2.7 (B3PW91-D), 2.2 (PWPB95-D3), 2.1 (B97X-D), and 1.2 (DSD-PBEP86) kcalmol ¹. Isomers involving highly-strained fused rings or long cumulenic chains provide a torture test for most functionals. Finally, we evaluate the performance of composite procedures (e.g. G4, G4(MP2), CBS-QB3, and CBS-APNO), as well as that of standard ab initio procedures (e.g. MP2, SCS-MP2, MP4, CCSD, and SCS-CCSD). Both connected triples and post-MP4 singles and doubles are important for accurate results. SCS-MP2 actually outperforms MP4(SDQ) for this problem, while SCS-MP3 yields similar performance as CCSD and slightly bests MP4. All the tested empirical composite procedures show excellent performance with RMSDs below 1kcalmol ¹.