The local atomic and electronic structures of the Na and K impurities and the vacancy at the Ca site ͑Na Ca , K Ca , and V Ca ͒, and their induced electrostatic potentials in Ca 2 CuO 2 Cl 2 have been investigated by using the GGA+ U approach. It is found that Na Ca and K Ca are markedly relaxed toward the Cl plane from the original Ca site. When V Ca exists, its neighboring Ca approaches the vacancy site, and Cl and O are relaxed outwardly. From the analyses of the local electrostatic

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... s at the Cu and O sites, we found that the Na Ca -induced potential is almost the same as the K Ca -induced potential, and the V Ca -induced potential is about twice as large. The defect-induced potentials are modeled by point charges under a dielectric medium. The atomic relaxation is found to increase the effective dielectric constants approximately threefold, indicating the importance of its contribution to the screening of the potential. The stabilization energies of small polarons obtained by the total energy differences are close to the potential energies. These results suggest that the interaction between the polaron and defects is well described by a positive charge of the polaron under the defect-induced electrostatic potential.