Focal point analysis of the reaction energies (in kcal mol−1) for the pericyclic reactions of Scheme 1a.
| Basis set | ΔEe(HF) | +δ[MP2] | +δ[CCSD] | +δ[CCSD(T)] | +δ[CCSDT(Q)] | NET |
|---|---|---|---|---|---|---|
| Diels-Alder reaction | ||||||
| cc-pVDZ (134) | −42.71 | −11.94 | 5.26 | 0.45 | 0.14 + 0.35 | −48.46 |
| aug′-cc-pVDZ (188) | −42.22 | −11.66 | 4.64 | 0.50 | [0.49] | [−48.25] |
| aug′-cc-pVTZ (416) | −38.82 | −13.94 | 4.44 | 0.46 | [0.49] | [−47.36] |
| aug′-cc-pVQZ (780) | −38.64 | −13.97 | 4.36 | 0.44 | [0.49] | [−47.33] |
| aug′-cc-pV5Z (1312) | −38.58 | −14.10 | [4.33] | [0.43] | [0.49] | [−47.44] |
| CBS LIMIT | [−38.56] | [−14.24] | [4.30] | [0.42] | [0.49] | [−47.59] |
| ΔEfinal = ΔEe(NET/CBS) + Δ(DBOC) + Δ(rel) + Δ(core) = −47.59 + 0.02 + 0.13 − 0.21 = −47.65 kcal mol−1 ΔE0 = ΔEfinal + Δ(ZPVE) = −47.65 + 6.75 = −40.90 kcal mol−1 | ||||||
| 1,3-Dipolar cycloaddition | ||||||
| cc-pVDZ (119) | −30.34 | 6.08 | −5.92 | 1.85 | 0.11 + 0.65 | −27.56 |
| aug′-cc-pVDZ (173) | −31.13 | 3.51 | −5.70 | 1.38 | [0.76] | [−31.17] |
| aug′-cc-pVTZ (374) | −26.94 | 1.68 | −5.67 | 1.55 | [0.76] | [−28.61] |
| aug′-cc-pVQZ (690) | −26.75 | 1.48 | −5.69 | 1.51 | [0.76] | [−28.68] |
| aug′-cc-pV5Z (1147) | −26.65 | 1.24 | [−5.70] | [1.50] | [0.76] | [−28.83] |
| CBS LIMIT | [−26.60] | [1.00] | [−5.70] | [1.49] | [0.76] | [−29.05] |
| ΔEfinal = ΔEe(NET/CBS) + Δ(DBOC) + Δ(rel) + Δ(core) = −29.05 − 0.02 + 0.17 + 0.04 = −28.86 kcal mol−1 | ||||||
| ΔE0 = ΔEfinal + Δ(ZPVE) = −28.86 + 5.28 = −23.58 kcal mol−1 | ||||||
| Electrocyclic rearrangement | ||||||
| cc-pVDZ (86) | 10.78 | −5.07 | 2.15 | 0.32 | 0.19 + 0.03 | 8.40 |
| aug′-cc-pVDZ (122) | 10.91 | −3.99 | 1.61 | 0.38 | [0.22] | [9.13] |
| aug′-cc-pVTZ (268) | 11.98 | −5.39 | 1.74 | 0.31 | [0.22] | [8.86] |
| aug′-cc-pVQZ (500) | 12.01 | −5.64 | 1.75 | 0.28 | [0.22] | [8.62] |
| aug′-cc-pV5Z (838) | 12.02 | −5.77 | [1.76] | [0.27] | [0.22] | [8.50] |
| CBS LIMIT | [12.03] | [−5.91] | [1.76] | [0.26] | [0.22] | [8.36] |
| ΔEfinal = ΔEe(NET/CBS) + Δ(DBOC) + Δ(rel) + Δ(core) = 8.36 + 0.01 + 0.05 + 0.03 = 8.45 kcal mol−1 | ||||||
| ΔE0 = ΔEfinal + Δ(ZPVE) = 8.45 + 1.07 = 9.52 kcal mol−1 | ||||||
The symbol δ denotes the increment in the relative energy with respect to the preceding level of theory in the hierarchy RHF → MP2 → CCSD → CCSD(T) → CCSDT(Q). The total number of contracted Gaussian functions in each basis set is given in parentheses. Square brackets signify results obtained from basis set extrapolations or additivity assumptions, as detailed in the Theoretical methods section. The bracketed CCSD increments are based on differences of corresponding aug′-cc-pV{T,Q}Z extrapolations of MP2 and CCSD correlation energies. The CCSDT(Q) increment is separated into its CCSD(T) → CCSDT and CCSDT → CCSDT(Q) components for the cc-pVDZ basis but entered as a single, bracketed correction in the remaining rows. The sum across each row comprises the NET column entry. Beneath each FPA grid, auxiliary terms (Δ) for the diagonal Born-Oppenheimer correction (DBOC), scalar relativistic effects (rel), and core electron correlation (core) are added to NET/CBS LIMIT to arrive at the final, vibrationless result (ΔEfinal; boldfaced) used to calibrate the DFT methods. For completeness, CCSD(T)/cc-pVTZ zero-point vibrational corrections are then appended to obtain ΔE0 values.