Derivation of interionic potentials using embedded quantum-mechanical clusters: Cation and anion impurities in MgO
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I. INTRODUCTION
There is significant interest in developing reliable interionic potentials for ionic systems, most importantly the oxides and related ceramic materials. Magnesium oxide (MgO) is such a technologically important ceramic with applications ranging from catalysis to microelectronics. It is a simple oxide of the NaCl structure and has therefore been considered as the prototypical oxide for both experimental and theoretical studies of defect properties of ceramic materials. Interionic potentials of ionic crystals are generally derived from empirical fittings to perfect lattice properties, such as cohesive energies, elastic and dielectric constants, ensuring that the potentials are compatible with lattice stability.1 This approach, however, does not provide impurity ionic potentials directly since it relies heavily on the availability of experimental data. One therefore uses an arbitrary averaging method to extract impurity potentials from host lattice potentials. An alternative, nonempirical approach is to obtain the potentials by using electron gas methods. Here the interaction between charge densities representing the interacting ions is calculated, the densities being obtained by calculating the wave function of the isolated ion.1 This method, however, approximates the exchange and correlation potentials and does not allow the distortion of the charge densities which is expected for the cases of highly polarizable anions. Thus, the derivation of reliable impurity potentials has so far proved to be a difficult task. With the availability of the ICECAP program package,2 we have undertaken a study to derive reliable impurity interionic potentials in ionic crystals. In earlier works, we derived the potentials for the impurities, namely Cu+ and Ag+ in some alkali halides, concluding that a more accurate derivation would require a larger distortion of the embedded cluster.3'4 In the present work, we derive interionic potentials for impurities using large distortions (typically about 25%) in the cluster and
then use them to obtain defect energies in MgO. The impurities considered here are Li+, Na+, K+, Be2+, H~, and S2", substituting the host cation/anion in MgO. Our approach has been to dilate and compress the quantum-mechanical cluster containing the impurity. Interionic potentials are then determined such that the same sequence of distortions, applied to a shell-model lattice containing the impurity, produces the same energy variation. In all cases, the embedding lattice is fully relaxed. In Sec. II we will give a brief description of this method of deriving impurity potentials. In Sec. Ill we will present and discuss our results, including the derived potentials, defect energies, and impurity diffusion in MgO. II. METHOD
We simulate impurity-doped MgO in ICECAP calculations as a molecular cluster consisting of the substitutional impurity, its nearest-neighbors, and/or secondnearest neighbors embedded in the lattice represented by the shell model.5 ICECAP combines electronic structure calculations with
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