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

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.