Dynamic exchange-correlation potentials for the 2D electron gas

Recent progress in the formulation of a fully dynamical local approximation to time-dependent density functional theory (TD-DFT) appeals to the longitudinal and transverse components of the long-wavelength exchange and correlation kernel in the homogeneous electron gas, . We extend to the two-dimensional longitudinal and transverse case our work on the 3D J. Phys.: Condens. Matter 9 (1997) 475], which accounts for two-pair excitations through an approximate decoupling of the equation of motion for the current–current response function. We present numerical results and compare with asymptotic behaviours and previous approximations.