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The electronic structures of cerium-based ternary 122 compoundsCe$M_{2}$Si$_{2}$, where $M =$ Ru, Rh, Pd, and Ag, are investigatedsystematically by using the density functional theory in combination with thesingle-site dynamical mean-field theory. The momentum-resolved spectralfunctions, total and 4$f$ partial density of states, self-energy functions, andvalence state fluctuations are calculated. The obtained results are in goodaccord with the available experimental data. It is suggested that, uponincreasing atomic number from Ru to Ag, the 4$f$ electrons should becomeincreasingly localized. An itinerant-localized crossover for 4$f$ electronsdriven by chemical pressure may emerge when $M$ changes from Pd to Ag.Particularly, according to the low-frequency behaviors of 4$f$ self-energyfunctions, we identify an orbital selective 4$f$ insulating state inCeAg$_{2}$Si$_{2}$, which is totally unexpected.

Itinerant-localized crossover and orbital dependent correlations for 4$f$ electrons in cerium-based ternary 122 compounds