T - IfB

Long-range potentialsLong-range are potentials that decay slowerthan r -d . Examples are electrostatics, gravityand dipols. A cut-off r c is not possible since itwould be equivalent in the electrostatic case tothe introduction of a charged sphere of radius r caround the considered particle. This could becompensated by introducing a sphere withopposite charge but this corresponds to achange of the potential, i.e. a different physics.93Electrostatic problemGravitation problem analogousElectrostatic potentialbetween charges z 1 and z 2 :V()r eDramatic finite size problem.z zr2 1 2• Ewald method• Particle – Mesh methods (PM & PPPM)• Reaction field method94