A method for studying electron-density-based dynamics of many-electron systems in scaled cylindrical coordinates

Abstract

The combination of quantum fluid dynamics and density functional theory had led to the formulation of a single time-dependent equation, the generalized nonlinear Schrödinger equation (GNLSE). In this paper, the above GNLSE is written as a nonlinear diffusion-type equation in appropriately scaled cylindrical coordinates and evolved in imaginary time to obtain the electronic energies, densities and other properties of all the noble gas atoms. The close agreement of the values obtained with those from the literature implies that the same method can be used in real time to study the density-based dynamics of many-electron systems in axially symmetric external fields such as intense laser fields, with relatively less computational effort.