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ÎÄÕÂDOI:10.1103/PhysRevB.87.195430
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One subtle but essential physical ingredient which can interfere with adsorption calculations is that of electrostatic polarity under periodic boundary conditions (PBC). A wellknown difficulty which dates back to classical electrostatics is that the polarization of an ionic crystal can depend on the definition of the (neutral) bulk unit cell if no explicit reference is made to the surface conditions. This has been expressed with great clarity in the context of ab initio calculations by Makov and Payne.52 Under the constraints of PBC, the crystal is infinite so the surface is undefined. Thus,with no surface cell to cancel out the spurious potential produced from unphysical interactions between periodic images of multipole moments in neighboring supercells, the dipole moment of a neutral polar system can depend on the location of the supercell boundaries, or equivalently, on the placement of the system within the supercell. This positional dependence of the energy arises because of electron density overlapping with the cell boundary in the direction of the polarity, thus making the total cell dipole sensitive to the placement of the system. Metal adatomgraphene systems, especially adsorption configurations, tend to be polar in the vacuum direction owing to the charge transfer associated with the metal-carbon bond. Hence, it is essential that the systems are placed in the center of the vacuum slab far from the supercell boundary at each end of the vacuum so as to ensure that the charge density is zero across this boundary. Various dipole correction schemes and studies of the subject have been published.53¨C59 In this work we use the self-consistent electrostatic dipole correction scheme of Neugebaueur and Scheffler53 as implemented in CASTEP60 to ensure that our input files satisfy the condition of zero charge density at the extremities of the vacuum slab.
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