W9
•Find the transition state and calculate the barrier height (ΔV≠) for the following reaction.
reaction：HNC → HCN
methods : MP2/aug-cc-pVTZ、MP2/6-31+G**
Table1.Calculate the born oppenheimer energy
| (unit: Hartress) | (unit: kcal/mol) | ||
| HNC → HCN | HNC | TS | ΔV≠ |
| MP2/6-31+G** | -93.14306 | -93.08701 | 35.2 |
| MP2/aug-cc-pVTZ | -93.23130 | -93.17648 | 34.4 |
Calculated the barrier energy by aug-cc-pVTZ has lower than 6-31+G** 0.8 kcal/mol
•Calculate the k(rate constant) in different temperatures (at least 3 different temperatures) for the following reaction and plot of ln(k) versus 1000/T then compare with the experimental values.
reaction：CH4 +OH․→ H2O + CH3․
Reference: https://doi.org/10.1016/S0082-0784(85)80560-9
| H | |||||||||
| Gibbs free Energies in MP2/aug-cc-pVTZ level | MP2/aug-cc-pVTZ | ||||||||
| T(K) | CH4 | OH | TS | ΔG‡ | 1000/T | VR (cm3 mol-1) | k | lnk | EXP(kcal/mol) |
| 100 | -40.37349 | -75.62215 | -115.98312 | 7.9 | 10.0 | 8205.7 | 1.9E-25 | -56.9 | -43.9 |
| 200 | -40.37966 | -75.62815 | -115.99246 | 9.6 | 5.0 | 16411.5 | 3.4E-18 | -40.2 | -35.4 |
| 300 | -40.38650 | -75.63473 | -116.00286 | 11.5 | 3.3 | 24617.2 | 1.0E-15 | -34.5 | -32.6 |
| 400 | -40.39380 | -75.64169 | -116.01406 | 13.4 | 2.5 | 32822.9 | 2.0E-14 | -31.5 | -31 |
| 500 | -40.40148 | -75.64893 | -116.02595 | 15.3 | 2.0 | 41028.7 | 1.4E-13 | -29.6 | -29.9 |
| 600 | -40.40951 | -75.65638 | -116.03846 | 17.2 | 1.7 | 49234.4 | 5.5E-13 | -28.2 | -29 |
| hartrees | kcal/mol | MAE | 3.6 | ||||||
| Gibbs free Energies in MP2/6-31+G** level | MP2/6-31+G** | ||||||||
| T(K) | CH4 | OH | TS | ΔG‡ | 1000/T | VR (cm3 mol-1) | k | lnk | EXP(kcal/mol) |
| 100 | -40.32489 | -75.53680 | -115.84422 | 11.0 | 10.0 | 8205.7 | 3.1E-32 | -72.6 | -43.9 |
| 200 | -40.33185 | -75.54280 | -115.85333 | 13.4 | 5.0 | 16411.5 | 2.7E-22 | -49.7 | -35.4 |
| 300 | -40.33948 | -75.54938 | -115.86350 | 15.9 | 3.3 | 24617.2 | 6.5E-19 | -41.9 | -32.6 |
| 400 | -40.34757 | -75.55634 | -115.87447 | 18.5 | 2.5 | 32822.9 | 3.7E-17 | -37.8 | -31 |
| 500 | -40.35603 | -75.56358 | -115.88614 | 21.0 | 2.0 | 41028.7 | 4.7E-16 | -35.3 | -29.9 |
| 600 | -40.36483 | -75.57104 | -115.89841 | 23.5 | 1.7 | 49234.4 | 2.8E-15 | -33.5 | -29 |
| hartrees | kcal/mol | MAE | 11.5 | ||||||
Table2.Calculate the thermal free energy
| unit(kcal/mol) | CH4+OH→CH3+H2O | ||
| T(K) | MP2/aug-cc-pVTZ | MP2/6-31+G** | EXP |
| 100 | -56.9 | -72.6 | -43.9 |
| 200 | -40.2 | -49.7 | -35.4 |
| 300 | -34.5 | -41.9 | -32.6 |
| 400 | -31.5 | -37.8 | -31 |
| 500 | -29.6 | -35.3 | -29.9 |
| 600 | -28.2 | -33.5 | -29 |
| unit:kcal/mol | MP2/aug-cc-pVTZ | MP2/6-31+G** | |
| MAE | 3.6 | 11.5 | |
reaction：CD4 +OH․→ H2O(1 H will replace by D) + CD3․
| D | ||||||||
| Gibbs free Energies in MP2/aug-cc-pVTZ level | MP2/aug-cc-pVTZ | |||||||
| T(K) | CD4 | OH | TS | ΔG‡ | 1000/T | VR (cm3 mol-1) | k | lnk |
| 100 | -40.38602 | -75.62215 | -115.99397 | 8.9 | 10.0 | 8205.7 | 9.3E-28 | -62.2 |
| 200 | -40.39263 | -75.62815 | -116.00363 | 10.8 | 5.0 | 16411.5 | 2.0E-19 | -43.1 |
| 300 | -40.39993 | -75.63473 | -116.01444 | 12.7 | 3.3 | 24617.2 | 1.4E-16 | -36.5 |
| 400 | -40.40775 | -75.64169 | -116.02614 | 14.6 | 2.5 | 32822.9 | 4.7E-15 | -33.0 |
| 500 | -40.41602 | -75.64893 | -116.03862 | 16.5 | 2.0 | 41028.7 | 4.3E-14 | -30.8 |
| 600 | -75.65638 | -116.05179 | -25348.5 | 1.7 | 49234.4 | #NUM! | #NUM! | |
| hartrees | kcal/mol | |||||||
| Gibbs free Energies in MP2/6-31+G** level | MP2/6-31+G** | |||||||
| T(K) | CD4 | OH | TS | ΔG‡ | 1000/T | VR (cm3 mol-1) | k | lnk |
| 100 | -40.33766 | -75.53680 | -115.85518 | 12.1 | 10.0 | 8205.7 | 1.0E-34 | -78.3 |
| 200 | -40.34506 | -75.54280 | -115.86461 | 14.6 | 5.0 | 16411.5 | 1.3E-23 | -52.7 |
| 300 | -40.35315 | -75.54938 | -115.87518 | 17.2 | 3.3 | 24617.2 | 8.0E-20 | -44.0 |
| 400 | -40.36174 | -75.55634 | -115.88664 | 19.7 | 2.5 | 32822.9 | 7.6E-18 | -39.4 |
| 500 | -40.37079 | -75.56358 | -115.89888 | 22.3 | 2.0 | 41028.7 | 1.3E-16 | -36.6 |
| 600 | -40.38025 | -75.57104 | -115.91182 | 24.8 | 1.7 | 49234.4 | 9.7E-16 | -34.6 |
| hartrees | kcal/mol | |||||||
Table3.Calculate the thermal free energy
| unit(kcal/mol) | CD4+OH→CD3+DOH | |
| T(K) | MP2/aug-cc-pVTZ | MP2/6-31+G** |
| 100 | -62.2 | -78.3 |
| 200 | -43.1 | -52.7 |
| 300 | -36.5 | -44.0 |
| 400 | -33.0 | -39.4 |
| 500 | -30.8 | -36.6 |
| 600 | #NUM! | -34.6 |
