Mean error (ME), mean absolute error (MAE), maximum unsigned error (MUE) and standard deviation (SD) of reaction barriers and energies (kcal mol−1) for the various pericyclic reactions, computed using various density functional approximations at XC/QZ4P//CCSD(T)/cc-pVTZ compared to FPA methods targeting CCSDT(Q)/CBS//CCSD(T)/cc-pVTZ.
| XC | ΔE‡ | ΔErxn | Total | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ME | MAE | MUE | SD | ME | MAE | MUE | SD | ME | MAE | MUE | SD | |
| LDA | ||||||||||||
| VWN | −17.3 | 17.3 | 28.3 | 6.9 | −12.4 | 12.4 | 17.8 | 4.8 | −15.5 | 15.5 | 28.3 | 6.7 |
| GGAs | ||||||||||||
| BP86 | −6.5 | 6.5 | 12.1 | 3.5 | 4.5 | 4.7 | 8.5 | 3.4 | −2.3 | 5.8 | 12.1 | 3.5 |
| BLYP | −1.5 | 2.8 | 5.1 | 1.8 | 13.7 | 13.7 | 18.3 | 6.0 | 4.2 | 6.9 | 18.3 | 6.6 |
| BEE | −6.0 | 6.0 | 11.8 | 3.9 | 3.9 | 5.4 | 9.3 | 2.9 | −2.3 | 5.8 | 11.8 | 3.6 |
| PW91 | −8.1 | 8.1 | 14.5 | 3.7 | 1.8 | 2.5 | 5.1 | 1.8 | −4.4 | 6.0 | 14.5 | 4.1 |
| PBE | −8.0 | 8.0 | 14.4 | 3.7 | 1.6 | 2.9 | 5.5 | 1.9 | −4.4 | 6.0 | 14.4 | 4.0 |
| PBEsol | −13.1 | 13.1 | 21.9 | 5.1 | −6.4 | 6.4 | 9.4 | 2.1 | −10.6 | 10.6 | 21.9 | 5.3 |
| RPBE | −3.8 | 4.3 | 8.5 | 3.1 | 7.6 | 7.8 | 13.6 | 5.5 | 0.5 | 5.6 | 13.6 | 4.5 |
| revPBE | −4.1 | 4.5 | 9.0 | 3.2 | 7.0 | 7.5 | 13.0 | 5.1 | 0.1 | 5.6 | 13.0 | 4.3 |
| mPBE | −6.8 | 6.8 | 12.8 | 3.6 | 3.3 | 4.2 | 7.7 | 2.6 | −3.0 | 5.8 | 12.8 | 3.5 |
| mPW | −5.9 | 5.9 | 11.3 | 3.4 | 5.0 | 5.2 | 9.5 | 3.8 | −1.8 | 5.6 | 11.3 | 3.6 |
| HTBS | −8.2 | 8.2 | 14.7 | 4.2 | 0.6 | 3.2 | 5.2 | 2.0 | −4.9 | 6.3 | 14.7 | 4.3 |
| OLYP | −0.8 | 4.9 | 6.2 | 1.1 | 8.6 | 9.6 | 15.7 | 6.0 | 2.7 | 6.6 | 15.7 | 4.4 |
| OPBE | −5.1 | 6.6 | 11.4 | 3.9 | −0.9 | 5.5 | 8.6 | 3.2 | −3.6 | 6.2 | 11.4 | 3.7 |
| XLYP | −1.0 | 2.5 | 4.4 | 1.5 | 14.7 | 14.7 | 19.2 | 6.1 | 4.8 | 7.1 | 19.2 | 7.0 |
| Meta-GGAs | ||||||||||||
| M06-L | −1.4 | 2.4 | 4.3 | 1.3 | 3.6 | 5.3 | 12.0 | 4.7 | 0.5 | 3.5 | 12.0 | 3.4 |
| MVS | −6.0 | 6.1 | 13.6 | 5.1 | −1.8 | 4.5 | 6.9 | 1.8 | −4.4 | 5.5 | 13.6 | 4.2 |
| TPSS | −4.6 | 4.6 | 7.2 | 1.8 | 5.3 | 5.8 | 9.4 | 3.7 | −0.9 | 5.0 | 9.4 | 2.7 |
| revTPSS | −4.6 | 4.6 | 5.4 | 0.9 | 3.0 | 4.6 | 6.2 | 1.6 | −1.7 | 4.6 | 6.2 | 1.2 |
| Hybrids | ||||||||||||
| B3LYP | 1.2 | 2.1 | 3.7 | 1.2 | 7.9 | 7.9 | 10.3 | 3.3 | 3.7 | 4.3 | 10.3 | 3.5 |
| B3LYP* | −0.7 | 2.0 | 3.5 | 1.3 | 7.4 | 7.4 | 9.9 | 3.1 | 2.3 | 4.0 | 9.9 | 3.4 |
| B1LYP | 2.7 | 2.8 | 5.0 | 1.8 | 7.9 | 7.9 | 10.4 | 3.1 | 4.6 | 4.7 | 10.4 | 3.4 |
| B1PW91 | −1.3 | 2.4 | 4.1 | 1.5 | −0.5 | 2.0 | 2.8 | 0.7 | −1.0 | 2.3 | 4.1 | 1.3 |
| BHandH | −4.2 | 4.5 | 7.8 | 2.7 | −14.5 | 14.5 | 19.5 | 6.8 | −8.1 | 8.3 | 19.5 | 6.7 |
| BHandHLYP | 6.8 | 6.8 | 8.3 | 1.6 | 2.0 | 2.0 | 3.1 | 0.8 | 5.0 | 5.0 | 8.3 | 2.7 |
| KMLYP | 1.2 | 1.4 | 3.1 | 1.1 | −9.9 | 9.9 | 13.5 | 4.6 | −3.0 | 4.6 | 13.5 | 5.1 |
| O3LYP | −17.9 | 17.9 | 28.7 | 7.7 | −20.4 | 20.4 | 28.5 | 8.8 | −18.9 | 18.9 | 28.7 | 8.2 |
| OPBE0 | −1.4 | 4.1 | 5.9 | 1.8 | −5.5 | 5.5 | 8.8 | 3.3 | −3.0 | 4.7 | 8.8 | 2.6 |
| PBE0 | −3.4 | 3.4 | 7.3 | 2.5 | −3.6 | 3.6 | 5.2 | 1.3 | −3.5 | 3.5 | 7.3 | 2.1 |
| mPW1PW | −1.7 | 2.4 | 4.6 | 1.5 | −0.8 | 1.7 | 2.3 | 0.4 | −1.3 | 2.1 | 4.6 | 1.2 |
| mPW1K | 1.3 | 1.4 | 4.4 | 1.6 | −5.0 | 5.0 | 6.6 | 1.2 | −1.1 | 2.7 | 6.6 | 2.3 |
| S12H | −2.4 | 2.8 | 6.2 | 2.0 | −3.3 | 3.3 | 5.8 | 2.3 | −2.8 | 3.0 | 6.2 | 2.1 |
| X3LYP | 0.8 | 1.9 | 3.0 | 0.7 | 6.6 | 6.6 | 8.5 | 2.5 | 3.0 | 3.7 | 8.5 | 2.8 |
| Meta-hybrids | ||||||||||||
| M06 | 0.1 | 1.7 | 4.4 | 1.6 | 1.5 | 2.6 | 6.2 | 2.6 | 0.6 | 2.0 | 6.2 | 2.1 |
| M06-2X | 0.1 | 1.3 | 2.4 | 0.7 | −0.8 | 0.8 | 1.2 | 0.2 | −0.3 | 1.1 | 2.4 | 0.6 |
| M06-HF | −1.2 | 1.8 | 5.8 | 2.0 | −3.8 | 4.5 | 11.8 | 5.2 | −2.2 | 2.8 | 11.8 | 3.8 |
| TPSSH | −3.0 | 3.0 | 5.0 | 1.6 | 3.0 | 4.1 | 6.3 | 1.9 | −0.8 | 3.4 | 6.3 | 1.8 |
| Double-hybrids | ||||||||||||
| B2K-PLYP | −0.8 | 1.3 | 3.6 | 1.1 | 0.5 | 1.6 | 3.1 | 1.2 | −0.3 | 1.4 | 3.6 | 1.2 |
| B2T-PLYP | −0.4 | 0.8 | 1.9 | 0.6 | 2.9 | 2.9 | 5.7 | 2.0 | 0.8 | 1.6 | 5.7 | 1.7 |
| B2-PLYP | −0.8 | 0.9 | 1.7 | 0.7 | 4.3 | 4.3 | 7.7 | 2.5 | 1.1 | 2.2 | 7.7 | 2.3 |
| LS1-TPSS | −3.9 | 3.9 | 9.0 | 2.9 | −4.7 | 4.7 | 9.1 | 3.2 | −4.2 | 4.2 | 9.1 | 3.1 |
| mPW2K-PLYP | −0.9 | 1.5 | 3.9 | 1.2 | 0.4 | 1.6 | 2.8 | 1.0 | −0.4 | 1.5 | 3.9 | 1.1 |
| mPW2-PLYP | 0.0 | 0.7 | 1.2 | 0.4 | 3.5 | 3.5 | 5.8 | 1.7 | 1.3 | 1.7 | 5.8 | 1.7 |
| PBE0-DH | −2.0 | 2.2 | 4.3 | 1.6 | −6.2 | 6.2 | 9.2 | 2.1 | −3.6 | 3.7 | 9.2 | 2.6 |
| revDSD-BLYP | −0.8 | 1.8 | 4.4 | 1.4 | 0.7 | 1.8 | 3.1 | 1.0 | −0.3 | 1.8 | 4.4 | 1.2 |
| revDSD-PBE | −1.8 | 2.0 | 5.1 | 1.7 | −1.6 | 2.6 | 4.5 | 1.3 | −1.7 | 2.2 | 5.1 | 1.6 |
| revDSD-PBEP86 | −0.1 | 1.1 | 2.8 | 1.0 | 0.4 | 2.1 | 3.7 | 1.2 | 0.1 | 1.5 | 3.7 | 1.2 |
| Range-separated hybrids | ||||||||||||
| CAM-B3LYP | 2.5 | 2.5 | 4.1 | 1.4 | 1.4 | 1.4 | 2.3 | 0.6 | 2.1 | 2.1 | 4.1 | 1.3 |
| CAMY-B3LYP | 1.0 | 1.5 | 2.4 | 0.8 | 2.4 | 2.4 | 3.2 | 0.7 | 1.5 | 1.8 | 3.2 | 0.9 |
| ωB97 | 3.6 | 3.6 | 4.3 | 0.6 | −6.7 | 6.7 | 8.5 | 1.3 | −0.3 | 4.7 | 8.5 | 1.8 |
| ωB97X | 2.7 | 2.7 | 3.9 | 0.9 | −3.7 | 3.7 | 4.7 | 0.7 | 0.3 | 3.1 | 4.7 | 1.0 |
| ωB97X-D | 1.8 | 2.0 | 4.7 | 1.8 | −0.4 | 1.1 | 2.2 | 0.9 | 1.0 | 1.6 | 4.7 | 1.6 |
| Dispersion-corrected | ||||||||||||
| BP86-D3(BJ) | −9.4 | 9.4 | 15.5 | 3.8 | 1.6 | 1.7 | 4.5 | 2.0 | −5.3 | 6.5 | 15.5 | 5.0 |
| BLYP-D3(BJ) | −5.4 | 5.4 | 9.2 | 2.6 | 9.8 | 9.8 | 13.0 | 3.2 | 0.3 | 7.0 | 13.0 | 3.6 |
| PBE-D3(BJ) | −9.9 | 9.9 | 16.7 | 4.1 | −0.2 | 2.2 | 2.9 | 0.5 | −6.3 | 7.0 | 16.7 | 4.9 |
| OLYP-D3(BJ) | −9.4 | 9.4 | 14.1 | 3.6 | −0.5 | 2.5 | 3.1 | 0.6 | −6.1 | 6.8 | 14.1 | 4.4 |
| OPBE-D3(BJ) | −13.5 | 13.5 | 20.5 | 5.0 | −9.6 | 9.6 | 15.0 | 4.0 | −12.0 | 12.0 | 20.5 | 5.0 |
| B3LYP-D3(BJ) | −2.0 | 2.4 | 4.2 | 1.3 | 4.7 | 4.7 | 6.0 | 1.1 | 0.5 | 3.3 | 6.0 | 1.7 |
| PBE0-D3(BJ) | −5.1 | 5.1 | 9.3 | 2.8 | −5.2 | 5.2 | 7.9 | 1.9 | −5.2 | 5.2 | 9.3 | 2.5 |
| M06-2X-D3 | 0.0 | 1.4 | 2.3 | 0.7 | −0.9 | 0.9 | 1.3 | 0.3 | −0.3 | 1.2 | 2.3 | 0.7 |