Configuration-interaction many-body-perturbation-theory energy levels of four-valent Si i

The mixed configuration-interaction (CI) many-body-perturbation-theory method is accurate in divalent atoms. In more complex atoms, with the number of valence electrons it becomes progressively more difficult to saturate CI space. Here, a four-valence electron atom, Si i, is considered. It is found that by using a relatively small cavity of 30 a.u. and by choosing carefully configuration space, it is possible to obtain quite accurate agreement between the theory and experiment. After subtraction of systematic shifts of 481 and $-426$ ${\mathrm{cm}}^{-1}$ for the lowest even and odd states, respectively, the deviation between theory and experiment becomes at the level of 100 ${\mathrm{cm}}^{-1}$. This agreement is comparable to that in divalent atoms where the CI saturation has been achieved. It is anticipated that the approach can also give good results for atoms with more valence electrons to be considered in the future.