We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear contributions to the interatomic potential are expressed in terms of physically meaningful quantities, giving insight in the physical properties of the system. The method is applied to various test cases and is found to improve the standard linear and quadratic response approaches. It also reduces the discrepancies previously observed between perturbation theory and density-functional theory results for the proton-proton pair potentials in metallic environments.
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