  The electronic structures of cerium-based ternary 122 compounds
Ce$M_{2}$Si$_{2}$, where $M =$ Ru, Rh, Pd, and Ag, are investigated
systematically by using the density functional theory in combination with the
single-site dynamical mean-field theory. The momentum-resolved spectral
functions, total and 4$f$ partial density of states, self-energy functions, and
valence state fluctuations are calculated. The obtained results are in good
accord with the available experimental data. It is suggested that, upon
increasing atomic number from Ru to Ag, the 4$f$ electrons should become
increasingly localized. An itinerant-localized crossover for 4$f$ electrons
driven by chemical pressure may emerge when $M$ changes from Pd to Ag.
Particularly, according to the low-frequency behaviors of 4$f$ self-energy
functions, we identify an orbital selective 4$f$ insulating state in
CeAg$_{2}$Si$_{2}$, which is totally unexpected.
