郭騰予 第七週作業
HW7
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Calculate the structures and atomization energies (AE) of XHn (X = H~Ne) by using B3LYP、MP2 theoretical methods with 6-31+G(d,p)、aug-cc-pVTZ then compare with the experimental values.
Table 1
| Atomization Energy | |||||
| unit(kcal/mol) | B3LYP/6-31+G(d,p) | B3LYP/aug-cc-pVTZ | MP2/6-31+G(d,p) | MP2/aug-cc-pVTZ | Exp |
| H2 | 111.7 | 110.1 | 101.1 | 103.8 | 103.3 |
| LiH | 57.0 | 58.4 | 45.1 | 51.8 | 55.7 |
| BeH2 | 153.7 | 150.7 | 138.7 | 146.0 | 149.3 |
| BH3 | 286.7 | 284.7 | 269.4 | 275.4 | 266.8 |
| CH4 | 422.8 | 420.6 | 399.3 | 411.3 | 392.4 |
| NH3 | 300.1 | 300.6 | 274.8 | 290.1 | 276.7 |
| H2O | 229.5 | 230.5 | 220.4 | 232.1 | 219.4 |
| HF | 138.2 | 138.8 | 137.0 | 143.3 | 135.4 |
Figure 1 B3LYP with different basis sets Figure 2 MP2 with different basis sets
Table 2
| Absolute Error | ||||
| unit(kcal/mol) | B3LYP/6-31+G(d,p) | B3LYP/aug-cc-pVTZ | MP2/6-31+G(d,p) | MP2/aug-cc-pVTZ |
| H2 | -8.4 | -6.9 | 2.2 | -0.5 |
| LiH | -1.3 | -2.7 | 10.6 | 3.9 |
| BeH2 | -4.4 | -1.5 | 10.6 | 3.3 |
| BH3 | -19.9 | -17.9 | -2.7 | -8.7 |
| CH4 | -30.3 | -28.2 | -6.8 | -18.9 |
| NH3 | -23.3 | -23.9 | 2.0 | -13.4 |
| H2O | -10.2 | -11.2 | -1.1 | -12.8 |
| HF | -2.7 | -3.4 | -1.6 | -7.9 |
| MAE | 12.5798154 | 11.94395218 | 4.691976633 | 8.664215046 |
| RMSE | 16.1 | 15.3 | 6.0 | 10.4 |
Figure 3
Table 3
| Bond angle ( degree ) | |||||
| B3LYP/6-31+G(d,p) | B3LYP/aug-cc-pVTZ | MP2/6-31+G(d,p) | MP2/aug-cc-pVTZ | Exp | |
| H2 | - | - | - | - | - |
| LiH | - | - | - | - | - |
| BeH2 | 180 | 180 | 180 | 180 | 180 |
| BH3 | 120 | 120 | 120 | 120 | 120 |
| CH4 | 109.5 | 109.5 | 109.5 | 109.5 | 109.5 |
| NH3 | 108.1 | 107.2 | 108.1 | 106.8 | 106.7 |
| H2O | 105.8 | 105.1 | 105.4 | 104.1 | 104.5 |
| HF | - | - | - | - | - |
Table 4
| Bond length (Å) | |||||
| B3LYP/6-31+G(d,p) | B3LYP/aug-cc-pVTZ | MP2/6-31+G(d,p) | MP2/aug-cc-pVTZ | Exp | |
| H2 | 0.743 | 0.743 | 0.734 | 0.737 | 0.741 |
| LiH | 1.614 | 1.59 | 1.623 | 1.605 | 1.595 |
| BeH2 | 1.331 | 1.325 | 1.328 | 1.33 | 1.326 |
| BH3 | 1.193 | 1.188 | 1.186 | 1.187 | 1.19 |
| CH4 | 1.093 | 1.088 | 1.087 | 1.086 | 1.087 |
| NH3 | 1.016 | 1.013 | 1.012 | 1.012 | 1.012 |
| H2O | 0.965 | 0.962 | 0.963 | 0.961 | 0.958 |
| HF | 0.928 | 0.924 | 0.926 | 0.922 | 0.917 |
Table 4
| Absolute error of bond length (Å) | |||||
| B3LYP/6-31+G(d,p) | B3LYP/aug-cc-pVTZ | MP2/6-31+G(d,p) | MP2/aug-cc-pVTZ | ||
| H2 | 0.002 | 0.002 | 0.007 | 0.004 | |
| LiH | 0.019 | 0.005 | 0.028 | 0.01 | |
| BeH2 | 0.005 | 0.001 | 0.002 | 0.004 | |
| BH3 | 0.003 | 0.002 | 0.004 | 0.003 | |
| CH4 | 0.006 | 0.001 | 0 | 0.001 | |
| NH3 | 0.004 | 0.001 | 0 | 0 | |
| H2O | 0.007 | 0.004 | 0.005 | 0.003 | |
| HF | 0.011 | 0.007 | 0.009 | 0.005 | |
| MAE | 0.007 | 0.003 | 0.007 | 0.004 | |
Reference
Enthalpy of Atomization. Experimental values