HW6
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Use Gaussian or WebMO to calculate the Electron Affinity of Helium、Neon、Argon, by using B3LYP、MP2 and M062X theoretical methods with cc-pVTZ、aug-cc-pVTZ、d-aug-cc-pVTZ basis set, and do some simple statistical analysis.(check your unit、analysis tools)
Table 1
| EA | MP2 | |||
| (unit:kcal/mol) | Exp | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ |
| He | -5 | -394.5 | -68.3 | -13.2 |
| Ne | -6.9 | -672.0 | -141.3 | -33.4 |
| Ar | -8.4 | -330.7 | -77.8 | -77.8 |
Figure 1
Table 2
| EA | B3LYP | |||
| (unit:kcal/mol) | Exp | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ |
| He | -5 | -376.8 | -61.9 | -10.1 |
| Ne | -6.9 | -630.0 | -130.2 | -28.4 |
| Ar | -8.4 | -302.7 | -72.2 | -72.2 |
Figure 2
Table 3
| EA | M062X | |||
| (unit:kcal/mol) | Exp | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ |
| He | -5 | -367.4 | -62.7 | X |
| Ne | -6.9 | -634.6 | -131.7 | -31.8 |
| Ar | -8.4 | -301.1 | -72.8 | -72.8 |
Figure 3
Table 4
| Absolute Error | MP2/cc-pVTZ | MP2/aug-cc-pVTZ | MP2/d-aug-cc-pVTZ | B3LYP/cc-pVTZ | B3LYP/aug-cc-pVTZ | B3LYP/d-aug-cc-pVTZ | M062X/cc-pVTZ | M062X/aug-cc-pVTZ | M062X/d-aug-cc-pVTZ |
| He | 389.5 | 63.3 | 8.2 | 371.8 | 56.9 | 5.1 | 362.4 | 57.7 | |
| Ne | 665.1 | 134.4 | 26.5 | 623.1 | 123.3 | 21.5 | 627.7 | 124.8 | 24.9 |
| Ar | 322.3 | 69.4 | 69.4 | 294.3 | 63.8 | 63.8 | 292.7 | 64.4 | 64.4 |
| MAE | 459.0 | 89.1 | 34.7 | 429.7 | 81.3 | 30.1 | 427.6 | 82.3 | 44.7 |
| RMSE | 476.6 | 93.3 | 41.2 | 446.6 | 85.3 | 37.0 | 445.5 | 86.3 | 47.5 |
Table 5
| MAE | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ | Average |
| MP2 | 459.0 | 89.1 | 34.7 | 194.2 |
| B3LYP | 429.7 | 81.3 | 30.1 | 180.4 |
| M062X | 427.6 | 82.3 | 44.7 | 184.9 |
Table 6
| RMSE | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ | Average |
| MP2 | 476.6 | 93.3 | 41.2 | 203.7 |
| B3LYP | 446.6 | 85.3 | 37.0 | 189.6 |
| M062X | 445.5 | 86.3 | 47.5 | 193.1 |
Try to add an additional set of diffuse functions for the s orbital of He, and the s and p orbitals of Ne and Ar. ( in the 6-31G basis set )
Table 7
| EA | (kcal/mol) | He | Ne | Ar |
| MP2 | 6-31G(+) | 860.3 | 1080.9 | 382.1 |
| 6-31+G(+) | 133.6 | 44.7 | 20.0 | |
| 6-31++G(+) | 30.9 | 44.7 | 20.0 | |
| 6-31++G(++) | 23.0 | 42.0 | 20.0 | |
| B3LYP | 6-31G(+) | 829.9 | 1009.4 | 343.5 |
| 6-31+G(+) | 122.4 | 37.0 | 14.5 | |
| 6-31++G(+) | 95.3 | 37.0 | 14.5 | |
| 6-31++G(++) | 18.9 | 34.6 | 14.5 | |
| M062X | 6-31G(+) | 827.9 | 1011.2 | 341.3 |
| 6-31+G(+) | 119.2 | 41.7 | 17.2 | |
| 6-31++G(+) | 94.8 | 41.7 | 17.2 | |
| 6-31++G(++) | 21.9 | 39.3 | 17.2 |
Figure 4
Figure 5
Figure 6
Table 8
| 絕對誤差 | He | Ne | Ar | MAE | |
| MP2 | 6-31G(+) | -865.3 | -1087.8 | -390.5 | 781.2 |
| 6-31+G(+) | -138.6 | -51.6 | -28.4 | 72.8 | |
| 6-31++G(+) | -35.9 | -51.6 | -28.4 | 38.6 | |
| 6-31++G(++) | -28.0 | -48.9 | -28.4 | 35.1 | |
| B3LYP | 6-31G(+) | -834.9 | -1016.3 | -351.9 | 734.4 |
| 6-31+G(+) | -127.4 | -43.9 | -22.9 | 64.7 | |
| 6-31++G(+) | -100.3 | -43.9 | -22.9 | 55.7 | |
| 6-31++G(++) | -23.9 | -41.5 | -22.9 | 29.4 | |
| M062X | 6-31G(+) | -832.9 | -1018.1 | -349.7 | 733.6 |
| 6-31+G(+) | -124.2 | -48.6 | -25.6 | 66.1 | |
| 6-31++G(+) | -99.8 | -48.6 | -25.6 | 58.0 | |
| 6-31++G(++) | -26.9 | -46.2 | -25.6 | 32.9 |
Try to use Gaussian or WebMO to optimize the H₃⁺ molecule and calculate the linear dissociation energy according to the formula provided in the PDF lecture.
H3+ → 2H + H+
H3+ →H2 + H+
H3+ →H2+ + H
Table 9
| unit:kca/mol | |||
| H3+ | 2H, H+ | H2, H+ | H2+, H |
| -801.4 | -627.3 | -735.8 | -691.6 |
| dissociation energy | 174.1 | 65.6 | 109.8 |