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| Reaction | Ref. Barrier Height | PM7 | Error in PM7 | |Error in PM7| | Ref. Barrier Height | PM7-TS | Error in PM7-TS | |Error in PM7-TS| | Ref. Barrier Height | PM6 | Error in PM6 | |Error in PM6| | ||
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Ess & Houk |
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| hc1 - Cyclobutene → butadiene | 31.9 | 33.6 | 1.7 | 1.7 | 31.9 | 32.2 | 0.3 | 0.3 | 31.9 | 39.8 | 7.9 | 7.9 | ||
| hc2 - Hexatriene → cycloheadiene | 29.8 | 27.3 | -2.5 | 2.5 | 29.8 | 21.5 | -8.3 | 8.3 | 29.8 | 30.1 | 0.3 | 0.3 | ||
| hc3 - Dimethylene → cyclobuta - benzene | 28.3 | 34.8 | 6.5 | 6.5 | 28.3 | 26.8 | -1.5 | 1.5 | 28.3 | 38.2 | 9.9 | 9.9 | ||
| hc4 - Pentadiene → Pentadiene | 35.4 | 42.8 | 7.4 | 7.4 | 35.4 | 32.1 | -3.3 | 3.3 | 35.4 | 40.4 | 5.0 | 5.0 | ||
| hc5 - Cyclobutadiene → cyclobutadiene | 23.6 | 39.2 | 15.6 | 15.6 | 23.6 | 23.8 | 0.2 | 0.2 | 23.6 | 38.4 | 14.8 | 14.8 | ||
| hc6 - 1,5 Hexadiene → 1,5 hexadiene | 33.5 | 60.6 | 27.1 | 27.1 | 33.5 | 44.5 | 11.0 | 11.0 | 33.5 | 59.4 | 25.9 | 25.9 | ||
| hc7 - Ethylene + butadiene → cyclohexene | 22.0 | 20.6 | -1.4 | 1.4 | 22.0 | 16.8 | -5.2 | 5.2 | 22.0 | 26.5 | 4.5 | 4.5 | ||
| hc8 - Cyclobutadiene + ethylene, Diels Alder | 22.6 | 25.2 | 2.6 | 2.6 | 22.6 | 21.4 | -1.2 | 1.2 | 22.6 | 30.6 | 8.0 | 8.0 | ||
| hc9 - Two cyclopentadiene, Diels Alder | 15.2 | 28.7 | 13.5 | 13.5 | 15.2 | 24.2 | 9.0 | 9.0 | 15.2 | 33.5 | 18.3 | 18.3 | ||
| hc10 - Cyclonona-1,4,7-triene, Ring opening | 24.6 | 30.2 | 5.6 | 5.6 | 24.6 | 28.6 | 4.0 | 4.0 | 24.6 | 38.7 | 14.1 | 14.1 | ||
| hc11 - Cycloduodeca-1,5,9-triene, Ring opening | 52.5 | 55.9 | 3.4 | 3.4 | 52.5 | 49.2 | -3.3 | 3.3 | 52.5 | 74.7 | 22.2 | 22.2 | ||
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Ess & Houk |
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| N2O + C2H4 → Heterocycle | 27.9 | 26.5 | -1.4 | 1.4 | 27.9 | 24.7 | -3.2 | 3.2 | 27.9 | 27.2 | -0.7 | 0.7 | ||
| N2O + C2H2 → Heterocycle | 27.9 | 32.7 | 4.8 | 4.8 | 27.9 | 30.5 | 2.6 | 2.6 | 27.9 | 34.1 | 6.2 | 6.2 | ||
| N3H + C2H4 → Heterocycle | 20.3 | 51.5 | 31.2 | 31.2 | 20.3 | 21.5 | 1.2 | 1.2 | 20.3 | 46.1 | 25.8 | 25.8 | ||
| N3H + C2H2 → Heterocycle | 20.1 | 24.3 | 4.2 | 4.2 | 20.1 | 20.3 | 0.2 | 0.2 | 20.1 | 26.1 | 6.0 | 6.0 | ||
| N2CH2 + C2H4 → Heterocycle | 14.6 | 22.8 | 8.2 | 8.2 | 14.6 | 14.9 | 0.3 | 0.3 | 14.6 | 25.9 | 11.3 | 11.3 | ||
| N2CH2 + C2H2 → Heterocycle | 15.2 | 27.9 | 12.7 | 12.7 | 15.2 | 16.4 | 1.2 | 1.2 | 15.2 | 31.4 | 16.2 | 16.2 | ||
| H−C≡N+−O- + C2H4 → Heterocycle | 13.0 | 21.6 | 8.6 | 8.6 | 13.0 | 12.6 | -0.4 | 0.4 | 13.0 | 23.2 | 10.2 | 10.2 | ||
| H−C≡N+−O- + C2H2 → Heterocycle | 14.1 | 26.9 | 12.8 | 12.8 | 14.1 | 13.8 | -0.3 | 0.3 | 14.1 | 29.6 | 15.5 | 15.5 | ||
| H−C≡N+−N-H + C2H4 → Heterocycle | 7.2 | 16.7 | 9.5 | 9.5 | 7.2 | 2.9 | -4.3 | 4.3 | 7.2 | 20.2 | 13.0 | 13.0 | ||
| H−C≡N+−N-H + C2H2 → Heterocycle | 8.5 | 21.6 | 13.1 | 13.1 | 8.5 | 4.6 | -3.9 | 3.9 | 8.5 | 24.5 | 16.0 | 16.0 | ||
| H−C≡N+−C-H2 + C2H4 → Heterocycle | 5.9 | 16.4 | 10.5 | 10.5 | 5.9 | 0.6 | -5.3 | 5.3 | 5.9 | 21.9 | 16.0 | 16.0 | ||
| H−C≡N+−C-H2 + C2H2 → Heterocycle | 7.4 | 21.2 | 13.8 | 13.8 | 7.4 | 2.8 | -4.6 | 4.6 | 7.4 | 27.3 | 19.9 | 19.9 | ||
| H2C=N+H−O- + C2H4 → Heterocycle | 13.8 | 18.9 | 5.1 | 5.1 | 13.8 | 19.7 | 5.9 | 5.9 | 13.8 | 17.3 | 3.5 | 3.5 | ||
| H2C=N+H−O- + C2H2 → Heterocycle | 14.0 | 23.8 | 9.8 | 9.8 | 14.0 | 19.0 | 5.0 | 5.0 | 14.0 | 22.9 | 8.9 | 8.9 | ||
| H2C=N+H−N-H + C2H4 → Heterocycle | 6.6 | 21.0 | 14.4 | 14.4 | 6.6 | 12.7 | 6.1 | 6.1 | 6.6 | 23.5 | 16.9 | 16.9 | ||
| H2C=N+H−N-H + C2H2 → Heterocycle | 8.1 | 25.1 | 17.0 | 17.0 | 8.1 | 13.3 | 5.2 | 5.2 | 8.1 | 26.7 | 18.6 | 18.6 | ||
| H2C=N+H−C-H2 + C2H4 → Heterocycle | 0.9 | 12.6 | 11.7 | 11.7 | 0.9 | 3.3 | 2.4 | 2.4 | 0.9 | 18.9 | 18.0 | 18.0 | ||
| H2C=N+H−C-H2 + C2H2 → Heterocycle | 1.5 | 16.3 | 14.8 | 14.8 | 1.5 | 2.3 | 0.8 | 0.8 | 1.5 | 23.0 | 21.5 | 21.5 | ||
| Heterocycle → N2O + C2H4 | 31.8 | 52.6 | 20.8 | 20.8 | 31.8 | 35.9 | 4.1 | 4.1 | 31.8 | 53.9 | 22.1 | 22.1 | ||
| Heterocycle → N2O + C2H2 | 65.0 | 80.0 | 15.0 | 15.0 | 65.0 | 67.2 | 2.2 | 2.2 | 65.0 | 80.2 | 15.2 | 15.2 | ||
| Heterocycle → N3H + C2H4 | 40.0 | 87.4 | 47.4 | 47.4 | 40.0 | 43.8 | 3.8 | 3.8 | 40.0 | 85.1 | 45.1 | 45.1 | ||
| Heterocycle → N3H + C2H2 | 81.6 | 93.5 | 11.9 | 11.9 | 81.6 | 77.8 | -3.8 | 3.8 | 81.6 | 95.5 | 13.9 | 13.9 | ||
| Heterocycle → N2CH2 + C2H4 | 46.3 | 59.7 | 13.4 | 13.4 | 46.3 | 47.7 | 1.4 | 1.4 | 46.3 | 67.5 | 21.2 | 21.2 | ||
| Heterocycle → N2CH2 + C2H2 | 64.2 | 76.9 | 12.7 | 12.7 | 64.2 | 65.0 | 0.8 | 0.8 | 64.2 | 83.1 | 18.9 | 18.9 | ||
| Heterocycle → H−C≡N+−O- + C2H4 | 52.3 | 56.2 | 3.9 | 3.9 | 52.3 | 50.4 | -1.9 | 1.9 | 52.3 | 58.4 | 6.1 | 6.1 | ||
| Heterocycle → H−C≡N+−O- + C2H2 | 88.1 | 84.8 | -3.3 | 3.3 | 88.1 | 85.2 | -2.9 | 2.9 | 88.1 | 85.6 | -2.5 | 2.5 | ||
| Heterocycle → H−C≡N+−N-H + C2H4 | 64.6 | 64.1 | -0.5 | 0.5 | 64.6 | 59.8 | -4.8 | 4.8 | 64.6 | 70.5 | 5.9 | 5.9 | ||
| Heterocycle → H−C≡N+−N-H + C2H2 | 108.8 | 100.5 | -8.3 | 8.3 | 108.8 | 98.3 | -10.5 | 10.5 | 108.8 | 103.8 | -5.0 | 5.0 | ||
| Heterocycle → H2C=N+H−C-H2 + C2H4 | 73.9 | 65.1 | -8.8 | 8.8 | 73.9 | 73.1 | -0.8 | 0.8 | 73.9 | 74.4 | 0.5 | 0.5 | ||
| Heterocycle → H−C≡N+−C-H2 + C2H2 | 94.1 | 83.4 | -10.7 | 10.7 | 94.1 | 89.9 | -4.2 | 4.2 | 94.1 | 91.0 | -3.1 | 3.1 | ||
| Heterocycle → H2C=N+H−O- + C2H4 | 42.6 | 51.3 | 8.7 | 8.7 | 42.6 | 44.6 | 2.0 | 2.0 | 42.6 | 55.9 | 13.3 | 13.3 | ||
| Heterocycle → H2C=N+H−O- + C2H2 | 57.9 | 74.3 | 16.4 | 16.4 | 57.9 | 68.0 | 10.1 | 10.1 | 57.9 | 77.2 | 19.3 | 19.3 | ||
| Heterocycle → H2C=N+H−N-H + C2H4 | 49.4 | 62.8 | 13.4 | 13.4 | 49.4 | 54.1 | 4.7 | 4.7 | 49.4 | 72.7 | 23.3 | 23.3 | ||
| Heterocycle → H2C=N+H−N-H + C2H2 | 68.9 | 85.2 | 16.3 | 16.3 | 68.9 | 79.7 | 10.8 | 10.8 | 68.9 | 91.0 | 22.1 | 22.1 | ||
| Heterocycle → H2C=N+H−C-H2 + C2H4 | 63.6 | 58.9 | -4.7 | 4.7 | 63.6 | 63.6 | 0.0 | 0.0 | 63.6 | 69.9 | 6.3 | 6.3 | ||
| Heterocycle → H2C=N+H−C-H2 + C2H2 | 78.4 | 78.4 | 0.0 | 0.0 | 78.4 | 79.4 | 1.0 | 1.0 | 78.4 | 87.8 | 9.4 | 9.4 | ||
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Zhao, et. al |
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| H· + FH → HF + H· | 42.2 | 26.6 | -15.5 | 15.5 | 42.2 | 42.5 | 0.3 | 0.3 | 42.2 | 0.1 | -42.1 | 42.1 | ||
| H· + FCH3 → HF + CH3· | 30.4 | 19.6 | -10.8 | 10.8 | 30.4 | 28.7 | -1.7 | 1.7 | 30.4 | 10.0 | -20.4 | 20.4 | ||
| H· + F2 → HF + F· | 2.3 | 8.3 | 6.0 | 6.0 | 2.3 | 6.6 | 4.3 | 4.3 | 2.3 | 2.4 | 0.1 | 0.1 | ||
| CH3· + FCl → CH3F + Cl· | 7.4 | 17.5 | 10.0 | 10.0 | 7.4 | 7.1 | -0.3 | 0.3 | 7.4 | 11.4 | 4.0 | 4.0 | ||
| OH- + CH3F → HOCH3 + F- | 11.0 | 16.1 | 5.1 | 5.1 | 11.0 | 12.6 | 1.7 | 1.7 | 11.0 | 5.4 | -5.5 | 5.5 | ||
| H· + N2 → HN2· | 14.7 | 2.1 | -12.6 | 12.6 | 14.7 | 0.0 | -14.7 | 14.7 | 14.7 | 1.4 | -13.3 | 13.3 | ||
| H· + CO → HCO· | 3.2 | 0.8 | -2.4 | 2.4 | 3.2 | 2.6 | -0.5 | 0.5 | 3.2 | 0.3 | -2.9 | 2.9 | ||
| H· + C2H4 → CH3CH2· | 2.1 | 0.2 | -1.9 | 1.9 | 2.1 | 0.5 | -1.6 | 1.6 | 2.1 | 0.1 | -2.0 | 2.0 | ||
| CH3· + C2H4 → CH3CH2CH2· | 6.9 | 2.2 | -4.7 | 4.7 | 6.9 | 1.0 | -5.9 | 5.9 | 6.9 | 4.4 | -2.4 | 2.4 | ||
| HCN → HNC | 48.2 | 86.1 | 37.9 | 37.9 | 48.2 | 44.6 | -3.6 | 3.6 | 48.2 | 86.0 | 37.8 | 37.8 | ||
| HF + CH3· → H· + FCH3 | 57.0 | 56.4 | -0.6 | 0.6 | 57.0 | 57.2 | 0.1 | 0.1 | 57.0 | 43.1 | -14.0 | 14.0 | ||
| CH3F + Cl· → CH3· + FCl | 60.2 | 45.4 | -14.8 | 14.8 | 60.2 | 60.8 | 0.7 | 0.7 | 60.2 | 45.6 | -14.5 | 14.5 | ||
| HOCH3 + F- → OH- + CH3F | 47.2 | 33.4 | -13.8 | 13.8 | 47.2 | 39.2 | -8.0 | 8.0 | 47.2 | 24.0 | -23.2 | 23.2 | ||
| HN2· → H· + N2 | 10.7 | 33.0 | 22.3 | 22.3 | 10.7 | 14.2 | 3.4 | 3.4 | 10.7 | 35.9 | 25.1 | 25.1 | ||
| HCO· → H· + CO | 22.7 | 36.7 | 14.1 | 14.1 | 22.7 | 25.0 | 2.3 | 2.3 | 22.7 | 42.3 | 19.6 | 19.6 | ||
| CH3CH2· → H· + C2H4 | 42.1 | 49.2 | 7.1 | 7.1 | 42.1 | 51.5 | 9.4 | 9.4 | 42.1 | 51.2 | 9.1 | 9.1 | ||
| CH3CH2CH2· → CH3· + C2H4 | 33.0 | 32.2 | -0.8 | 0.8 | 33.0 | 36.3 | 3.4 | 3.4 | 33.0 | 37.0 | 4.0 | 4.0 | ||
| HNC → HCN | 33.1 | 77.3 | 44.1 | 44.1 | 33.1 | 41.5 | 8.4 | 8.4 | 33.1 | 72.5 | 39.4 | 39.4 | ||
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Zheng, et. al. |
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| Cl- + CH3Cl → CH3Cl + Cl- | 13.4 | 6.3 | -7.1 | 7.1 | 13.4 | 13.5 | 0.1 | 0.1 | 13.4 | 7.7 | -5.7 | 5.7 | ||
| F- + CH3Cl → CH3F + Cl- | 3.4 | 5.2 | 1.8 | 1.8 | 3.4 | 6.9 | 3.5 | 3.5 | 3.4 | 2.0 | -1.5 | 1.5 | ||
| CH3F +Cl- →CH3Cl + F- | 29.4 | 37.2 | 7.8 | 7.8 | 29.4 | 27.3 | -2.1 | 2.1 | 29.4 | 37.4 | 8.0 | 8.0 | ||
| CH3F + OH- → CH3OH + F- | -2.4 | 2.3 | 4.7 | 4.7 | -2.4 | -10.2 | -7.8 | 7.8 | -2.4 | -7.4 | -5.0 | 5.0 | ||
| CH3OH + F- → CH3F + OH- | 17.7 | 26.7 | 9.0 | 9.0 | 17.7 | 24.5 | 6.9 | 6.9 | 17.7 | 16.0 | -1.7 | 1.7 | ||
| H· + HCl → H2 + Cl· | 18.0 | 6.0 | -12.0 | 12.0 | 18.0 | 18.1 | 0.1 | 0.1 | 18.0 | 2.0 | -16.0 | 16.0 | ||
| OH· + CH4 → H2O + ·CH3 | 6.7 | 3.0 | -3.7 | 3.7 | 6.7 | 0.8 | -5.9 | 5.9 | 6.7 | -1.8 | -8.5 | 8.5 | ||
| H2O + ·CH3 → OH· + CH4 | 19.6 | 26.0 | 6.4 | 6.4 | 19.6 | 24.3 | 4.7 | 4.7 | 19.6 | 25.5 | 5.9 | 5.9 | ||
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Lopez, et. al |
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| REP (2',3'-cyclic ribose ethylene phosphate anion) + methoxide anion → Product | 82.0 | 90.2 | 8.2 | 8.2 | 82.0 | 78.6 | -3.4 | 3.4 | 82.0 | 74.1 | -7.9 | 7.9 | ||
| EP (Ethylene phosphate anion) + methoxide anion → Product | 87.2 | 98.5 | 11.3 | 11.3 | 87.2 | 86.8 | -0.4 | 0.4 | 87.2 | 83.4 | -3.8 | 3.8 | ||
| Product → REP (2',3'-cyclic ribose ethylene phosphate anion) + methoxide anion | 32.8 | 18.2 | -14.6 | 14.6 | 32.8 | 37.1 | 4.3 | 4.3 | 32.8 | 24.7 | -8.1 | 8.1 | ||
| Product → EP (Ethylene phosphate anion) + methoxide anion | 43.1 | 14.8 | -28.3 | 28.3 | 43.1 | 38.0 | -5.0 | 5.0 | 43.1 | 20.4 | -22.6 | 22.6 | ||
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Nachimuthu, et. al. |
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| H5O2+ (Ec-Eb) | 5.3 | -12.8 | -18.1 | 18.1 | 5.3 | 5.5 | 0.2 | 0.2 | 5.3 | 0.0 | -5.3 | 5.3 | ||
| H5O2+ (Ec-Ea) | 10.0 | 2.0 | -8.0 | 8.0 | 10.0 | 5.5 | -4.5 | 4.5 | 10.0 | 3.4 | -6.6 | 6.6 | ||
| H5O2+ (Eb-Ea) | 4.7 | 14.8 | 10.1 | 10.1 | 4.7 | 0.0 | -4.7 | 4.7 | 4.7 | 3.4 | -1.3 | 1.3 | ||
| CH3OH…H+…OH2 (Ec-Eb) | 9.9 | -1.7 | -11.6 | 11.6 | 9.9 | 10.2 | 0.4 | 0.4 | 9.9 | 0.9 | -9.0 | 9.0 | ||
| CH3OH…H+…OH2 (Ec-Ea) | 11.9 | 0.6 | -11.4 | 11.4 | 11.9 | 10.2 | -1.7 | 1.7 | 11.9 | 3.2 | -8.7 | 8.7 | ||
| CH3OH…H+…OH2 (Eb-Ea) | 2.1 | 2.3 | 0.2 | 0.2 | 2.1 | 0.0 | -2.1 | 2.1 | 2.1 | 2.3 | 0.3 | 0.3 | ||
| CH3COOH...OH2 DE1 | 183.4 | 169.3 | -14.2 | 14.2 | 183.4 | 178.5 | -4.9 | 4.9 | 183.4 | 160.6 | -22.8 | 22.8 | ||
| CH3COOH...OH2 DE2 | -10.6 | -9.3 | 1.3 | 1.3 | -10.6 | -2.6 | 8.0 | 8.0 | -10.6 | -8.8 | 1.8 | 1.8 | ||
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Goerigk and Grimme |
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| H + N2O → N2OH | 18.1 | -0.1 | -18.2 | 18.2 | 18.1 | 0.1 | -18.0 | 18.0 | 18.1 | 0.0 | -18.2 | 18.2 | ||
| F- + CH3F → CH3F + F- | -0.3 | 24.7 | 25.0 | 25.0 | -0.3 | 4.0 | 4.3 | 4.3 | -0.3 | 11.6 | 11.9 | 11.9 | ||
| F- ... CH3F → CH3F ... F- | 13.4 | 34.0 | 20.6 | 20.6 | 13.4 | 21.1 | 7.8 | 7.8 | 13.4 | 19.9 | 6.5 | 6.5 | ||
| Cl- + CH3Cl → CH3Cl + Cl- | 3.1 | -4.9 | -8.0 | 8.0 | 3.1 | 2.3 | -0.8 | 0.8 | 3.1 | -4.0 | -7.1 | 7.1 | ||
| Cl- ... CH3Cl → CH3Cl ... Cl- | 13.6 | 6.3 | -7.3 | 7.3 | 13.6 | 13.6 | 0.0 | 0.0 | 13.6 | 7.7 | -5.9 | 5.9 | ||
| CH3CH2 → CH2CH3 | 41.8 | 49.1 | 7.3 | 7.3 | 41.8 | 50.7 | 9.0 | 9.0 | 41.8 | 51.1 | 9.3 | 9.3 | ||
| H + HCl → HCl + H | 18.0 | 5.9 | -12.1 | 12.1 | 18.0 | 9.2 | -8.8 | 8.8 | 18.0 | 1.8 | -16.2 | 16.2 | ||
| F + HC → HF + F | 106.2 | 87.5 | -18.7 | 18.7 | 106.2 | 106.0 | -0.1 | 0.1 | 106.2 | 99.6 | -6.6 | 6.6 | ||
| F- + CH3Cl → CH3F + Cl- | -12.5 | -6.3 | 6.2 | 6.2 | -12.5 | -9.3 | 3.3 | 3.3 | -12.5 | -8.7 | 3.8 | 3.8 | ||
| Cl- + CH3F → CH3Cl + F- | 20.1 | 27.7 | 7.6 | 7.6 | 20.1 | 14.4 | -5.7 | 5.7 | 20.1 | 28.4 | 8.3 | 8.3 | ||
| F- ... CH3OH → CH3F ... OH- | 47.2 | 42.3 | -4.9 | 4.9 | 47.2 | 47.1 | -0.1 | 0.1 | 47.2 | 40.5 | -6.7 | 6.7 | ||
| OH- ... CH3F → CH3OH ... F- | 11.0 | 16.1 | 5.1 | 5.1 | 11.0 | 12.9 | 1.9 | 1.9 | 11.0 | 5.4 | -5.6 | 5.6 | ||
| Average: | 11.0 | Average: | 3.8 | Average: | 12.2 |
All values in Kcal/mol.
Ess & Houk: "Activation Energies of Pericyclic Reactions: Performance of DFT, MP2, and CBS-QB3 Methods for the Prediction of Activation Barriers and Reaction Energetics of 1,3-Dipolar Cycloadditions, and Revised Activation Enthalpies for a Standard Set of Hydrocarbon Pericyclic Reactions" D. H. Ess and K. N. Houk, J. Phys. Chem. A, 2005, 109, pp 9542–9553.
Zhao, et. al.: Yan Zhao, Núria González-García, and Donald G. Truhlar, "Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Its Use to Test Theoretical Methods" J. Phys. Chem. A 109, 2012-2018, (2005).
Zheng, et. al.: Zheng, J., Zhao, Y,Truhlar, D. G., "The DBH24/08
Database and Its Use to Assess Electronic Structure Model Chemistries for
Chemical Reaction Barrier Heights", J. Chem. Theory Comput. 5, 808–821, (2009).
Lopez, et. al.: Xabier Lopez, Annick Dejaegere, Fabrice
Leclerc, Darrin M. York, and Martin Karplus, "Nucleophilic Attack on Phosphate Diesters: A Density Functional Study of
In−Line Reactivity in Dianionic, Monoanionic, and Neutral Systems"
J. Phys. Chem. B 110, 11525–11539 (2006).
Nachimuthu, et. al.: Nachimuthu S., Gao J., Truhlar D., "A benchmark test suite for proton transfer energies and its use to test electronic structure model chemistries", Chemical Physics 400, 8-12 (2012).
Goerigk and Grimme : L. Goerigk and S. Grimme in J. Chem. Theory Comput. 2010, 6, 107-126.