Comparative study of $\mathrm{Si}-2p$ core-excitation spectra in the tetrahedral molecules $\mathrm{Si}{X}_4$ (with $X$=H, D, F, Cl, Br, ${\mathrm{CH}}_3$)

High-resolution $\mathrm{Si}-2p$ photoabsorption spectra of $\mathrm{Si}{X}_4$ molecules $(X$=H, D, F, Cl, Br, ${\mathrm{CH}}_3)$ are presented. High-resolution spectra were obtained for ${\mathrm{SiBr}}_4$ and ${\mathrm{S}\mathrm{i}(\mathrm{C}\mathrm{H}}_3{)}_4,$ and they are compared to the $\mathrm{Si}-2p$ spectra of the other $\mathrm{Si}{X}_4$ molecules studied before. In all cases, vibrational fine structure of the Rydberg states could be resolved, allowing a derivation of vibrational energies and intramolecular distances of the core-excited molecules from Franck-Condon analyses. The results obtained for the various ligand atoms are compared with each other, and are discussed in the context of the equivalent-cores approximation. A detailed analysis of the core-to-valence excitations in all $\mathrm{Si}{X}_4$ molecules studied is also given.