Figure 1: First 13 excited states of Hydrogen atom by using CIS theoretical method with different basis sets
Table 1: First 13 singlet excited states of Hydrogen atom by using the CIS theoretical method with different basis sets (unit: eV):
| excited states (eV) | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ | Exp(eV) | |
| 2S | 1 | 14.3 | 10.2 | 10.2 | 10.2 |
| 2P | 2 | 21.7 | 11.2 | 10.2 | |
| 3 | 21.7 | 11.2 | 10.2 | ||
| 4 | 21.7 | 11.2 | 10.2 | ||
| 3S | 5 | 64.9 | 17.4 | 12.2 | 12.1 |
| 3P | 6 | 90.5 | 25.5 | 14.2 | |
| 7 | 90.5 | 25.5 | 14.2 | ||
| 8 | 90.5 | 25.5 | 14.2 | ||
| 9 | 90.5 | 25.5 | 14.2 | ||
| 10 | 90.5 | 25.5 | 14.2 | ||
| 3D | 11 | 100.7 | 28.8 | 14.7 | |
| 12 | 100.7 | 28.8 | 14.7 | ||
| 13 | 100.7 | 28.8 | 14.7 |
Table 2: Mean absolute error of different basis sets
| MAE(eV) | cc-pVTZ | aug-cc-pVTZ | d-aug-cc-pVTZ |
| 47.1 | 7.3 | 1.0 |
According to the results of MAE, we can see that using d-aug-cc-pVTZ is the best among these three basis sets.
Table 3: First 5 singlet excited states of Helium by using the CIS、CIS(D) theoretical method with different basis sets. (a) CIS with two basis sets. (b) CIS(D) with two basis sets.
(a)一個電子固定在1S，另一個被激發到不同激發態
| CIS | |||
| excited states (eV) | aug-cc-pVTZ | d-aug-cc-pVTZ | Exp(eV)a |
| 2S | 21.6 | 21.1 | 19.8 |
| 2P | 26.1 | 22.1 | |
| 26.1 | 22.1 | ||
| 26.1 | 22.1 | ||
| 3S | 28.4 | 24.2 | 20.6 |
| MAE(eV) | 5.3 | 2.4 |
(b)一個電子固定在1S，另一個被激發到不同激發態
| CIS(D) | |||
| singlet excited states (eV) | aug-cc-pVTZ | d-aug-cc-pVTZ | Exp(eV)a |
| 2S | 21.1 | 20.7 | 19.8 |
| 2P | 25.6 | 21.7 | |
| 25.6 | 21.7 | ||
| 25.6 | 21.7 | ||
| 3S | 38.0 | 23.8 | 20.6 |
| MAE(eV) | 8.2 | 2.0 |
a: https://assets.researchsquare.com/files/rs-1734907/v1_covered.pdf?c=1655226880
1. When we use the CIS method, the MAE results show that using d-aug-cc-pVTZ is much better at reducing errors compared to aug-cc-pVTZ—it's more than twice as effective!
2.In the CIS(D) method, using d-aug-cc-pVTZ can reduce the MAE by four times.
Therefore, we prefer using d-aug-cc-pVTZ.