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Treatment of the Coulomb long-range interaction

Coulomb long-range makes the real-space summation of forces very slow because of the $\frac{1}{r}$ behaviour. On the other hand in reciprocal spaces Colomb interaction behaves as $\frac{1}{k^2}$ for a point charge. Convergence at high $K$ can be accelerated by gaussian-spreading the point charges, and introducing thus a gaussian factor in the Coulomb interaction. This spreading changes the dynamical matrix, by a little amount if the spreading is small, and the correct result can be recovered by subtracting the difference between the field of a gaussian charge and the field of a point charge. This difference tends to zero very rapidly for distances bigger than the charge spreading and thus the real-space summation converges vary fast. The Coulomb contribution to the dynamical matric is thus made of two contribution : a reciprocal space summation for spreaded charges, and a real space summation for the difference between a point charges and the spreaded charges.



Subsections

Alessandro Mirone 2003-11-17