Nonlinear response theories and effective pair potentials

Abstract

We present a general method based on nonlinear response theory to obtain effective interactions between ions in an interacting 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 into 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 proton-proton pair potentials in metallic environments.

The equation of state for hydrogen at high densities

“…An improved treatment including the fully nonlin- ear response (see, e.g., Refs. [54][55][56] ) is beyond the scope of this paper. Here, we estimate nonlinear effects in the electron-ion interaction by applying the nonlinear Hulthén potential 57 v H ii (r) = e 2 κ e e κer − 1 (13) as an ad-hoc model for the effective ion-ion interaction.…”

Kinetic energy density of nearly free electrons. I. Response functionals of the external potential

“…. We begin with a coupling constant integral for the system energy, 4,19,[37][38][39][40][41] , (20) in which is the total energy, is the energy of a free-electron system with the same number of electrons per unit volume, and is the deviation from the free-electron density that would be generated by the scaled perturbation . The expression in Eq.…”

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

“…Further applications of the LFCs for current warm dense matter (WDM, see below) research include the calculation of the dynamic structure factor [27][28][29][30] as it can be obtained with X-ray Thomson scattering from a variety of systems, energy transfer rates [31,32], the electrical and optical conductivity [33,34], and equation of state models of ionized plasmas [35][36][37]. Finally, we mention the construction of effective potentials both for WDM [38,39] and beyond [40,41]. In the ground state, Moroni et al [42] obtained accurate QMC results for the static response function [i.e., ω → 0, see Eq.…”