郭騰予 第十週作業
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Calculate the first 13 excited states of Hydrogen atom by using the CIS theoretical method with appropriate basis sets ( need to include diffuse functions or other elements ) then compare with the experimental values.
Table1 Calculate the excited states from different basis sets
| unit : eV | 2S | 2P | 3S | 3D | 3P | ||||||||
| excited states | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| aug-cc-pVQZ | 10.2 | 10.9 | 10.9 | 10.9 | 15.9 | 21.3 | 21.3 | 21.3 | 21.3 | 21.3 | 23.5 | 23.5 | 23.5 |
| d-aug-cc-pVQZ | 10.2 | 10.2 | 10.2 | 10.2 | 12.1 | 13.5 | 13.5 | 13.5 | 13.8 | 13.8 | 13.8 | 13.8 | 13.8 |
| (+)d-aug-cc-pVQZ | 10.2 | 10.2 | 10.2 | 10.2 | 12.1 | 12.2 | 12.2 | 12.2 | 12.2 | 12.2 | 13.2 | 13.2 | 13.2 |
| Experimental values | 10.2 | 10.2 | 12.1 | 12.1 | 12.1 | ||||||||
Figure 1 Energy v.s. Excited states
Table 3 The absolute error of different basis sets
| Absolute error | 2S | 2P | 3S | 3D | 3P | ||||||||
| aug-cc-pVQZ | 0.0 | -0.7 | -0.7 | -0.7 | -3.8 | -9.2 | -9.2 | -9.2 | -9.2 | -9.2 | -11.4 | -11.4 | -11.4 |
| d-aug-cc-pVQZ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -1.4 | -1.4 | -1.4 | -1.7 | -1.7 | -1.7 | -1.7 | -1.7 |
| (+)d-aug-cc-pVQZ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.1 | -0.1 | -0.1 | -0.1 | -0.1 | -1.1 | -1.1 |
-1.1 |
unit:eV
Table 4 Mean Unsigned Error of different basis sets
| MUE | aug-cc-pVQZ | d-aug-cc-pVQZ | (+)d-aug-cc-pVQZ |
| 6.6 | 1.0 | 0.3 |
unit:eV
Calculate the first 5 excited states of Helium by using the CIS、CIS(D) theoretical method with appropriate basis sets then compare with the experimental values.
| CIS | |||||
| Unit:eV | 2S | 2P | 3S | ||
| excited states | 1 | 2 | 3 | 4 | 5 |
| aug-cc-pVQZ | 21.4 | 24.7 | 24.7 | 24.7 | 34.9 |
| d-aug-cc-pVQZ | 21.1 | 21.9 | 21.9 | 21.9 | 24.0 |
| experimental value | 19.8 | 21.0 | 21.0 | 21.0 | 22.7 |
| Absolute error CIS | |||||
| Unit:eV | 2S | 2P | 3S | ||
| excited states | 1 | 2 | 3 | 4 | 5 |
| aug-cc-pVQZ | -1.6 | -4.9 | -4.9 | -4.9 | -12.1 |
| d-aug-cc-pVQZ | -1.3 | -2.1 | -2.1 | -2.1 | -1.3 |
unit:eV
| CIS(D) | |||||
| Unit:eV | 2S | 2P | 3S | ||
| excited states | 1 | 2 | 3 | 4 | 5 |
| aug-cc-pVQZ | 21.1 | 24.3 | 24.3 | 24.3 | 34.5 |
| d-aug-cc-pVQZ | 20.8 | 21.6 | 21.6 | 21.6 | 23.6 |
| experimental value | 19.8 | 21.0 | 21.0 | 21.0 | 22.7 |
| Absolute error CIS(D) | |||||
| Unit:eV | 2S | 2P | 3S | ||
| excited states | 1 | 2 | 3 | 4 | 5 |
| aug-cc-pVQZ | -1.2 | -4.5 | -4.5 | -4.5 | -11.8 |
| d-aug-cc-pVQZ | -0.9 | -1.7 | -1.7 | -1.7 | -0.9 |
unit:eV
| CIS | ||
| Unit:eV | aug-cc-pVQZ | d-aug-cc-pVQZ |
| MUE | 5.7 | 1.8 |
unit:eV
| CIS(D) | ||
| Unit:eV | aug-cc-pVQZ | d-aug-cc-pVQZ |
| MUE | 5.3 | 1.4 |
unit:eV
Reference
Zadeh, D. H. (2022). Atomic excited states and the related energy levels. Journal of Molecular Modeling, 28(9), 282. https://doi.org/10.1007/s00894-022-05257-x