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md2011-10-note_Part_4

md2011-10-note_Part_4 - This introduced charge distribution...

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I This introduced charge distribution screens the interaction between neighboring point-charges limiting them to a short range I Consequently, the sum converges rapidly I To counteract this Gaussian distribution, a second Gaussian distribution of the same sign as magnitude as the original distribution is added for each point charge I Now, the summation is carried out in reciprocal space using Fourier transforms I For a system with charges, also the surrounding medium has an effect: in a perfect conductor ( ε = ), the Ewald summation works I However, if the system is in vacuum ( ε = 1 ), a dipole layer should form at the surface I This can be taken into account by adding a dipole term in the summation I The dipole term includes the effects of the total dipole moment of the unit cell, the shape of the macroscopic lattice, and the dielectric constant of the surrounding medium I Overall, the final outcome of the potential becomes rather complicated, but luckily ready-made programs exist for Ewald summation [Anastasiou & Fincham, Comput. Phys. Commun. 25, 159 (1981)]
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