DFT calculations of the defect structures, electronic structures, and EPR parameters for three Rh²⁺ centers in AgCl

The local structures for various Rh²⁺ centers in AgCl are theoretically studied using density functional theory (DFT) with periodic CP2K program. Through geometry optimizing, the stable ground states with minimal energies and electronic structures are obtained for the tetragonally elongated (T_E ), orthorhombically elongated (O_E ), and tetragonally compressed (T_C ) centers, and the corresponding g and hyperfine coupling tensors are calculated in ORCA level. The calculations reveal obvious Jahn-Teller elongation distortions of about 0.109 and 0.110 Å along [001] axis for T_E and O_E centers without and with 1 next nearest neighbor (nnn) cation vacancy V_Ag in [100] axis, respectively. Whereas T_C center with 1 nnn V_Ag along [001] axis exhibits moderate axial compression of about 0.066 Å due to the Jahn-Teller effect. For O_E and T_C centers with 1 nnn V_Ag , the ligand intervening in the central Rh²⁺ and the V_Ag is found to displace away from the V_Ag by about 0.028 and 0.024 Å, respectively. The present results are discussed and compared with those of the previous calculations based on the perturbation formulas by using the improved ligand field theory.