Explicitly correlated benchmark calculations on C₈H₈ isomer energy separations: how accurate are DFT, double-hybrid, and composite ab initio procedures?

Abstract

Accurate isomerization energies are obtained for a set of 45 C₈H₈ 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 3 kcal mol⁻¹ (the performance of MP2), namely: 2.9 (B972-D), 2.8 (PW6B95), 2.7 (B3PW91-D), 2.2 (PWPB95-D3), 2.1 (ωB97X-D), and 1.2 (DSD-PBEP86) kcal mol⁻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 1 kcal mol⁻¹.

Keywords:

• C₈H₈
• isomerization
• unsaturated hydrocarbons
• CCSD(T)
• explicitly-correlated
• W1-F12
• DFT
• double-hybrid
• G4, and G4(MP2)

Acknowledgements

JMLM is on leave of absence as the Thatcher Professor of Chemistry at the Weizmann Institute of Science. This research was supported in part by the Weizmann AERI (Alternative Energy Research Initiative) and by a startup grant from the University of North Texas from which the Martin group Linux cluster was purchased. AK was supported by Australian Research Council Discovery Project grant DP110102336. The authors would like to thank Dr. David A. Hrovat (UNT, manager of CRUNTCh) for system administration assistance and Dr. Angela K. Wilson (UNT) and Dr. Nathan DeYonker (University of Memphis) for helpful discussions clarifying details of ccCA.

Notes

Note

1. Combines Becke88 55 exchange functional (28% HF exchange) and Becke95 correlation functional [105].