Dynamic Response of Electronic Systems: An Implementation and Application of Time-Dependent Density-Functional-Theory

Abstract

This project consisted of the implementation of time-dependent density functional theory (TDDFT) in an electronic-structure code and the application of this code to study the dynamics of atoms, molecules and solids in the presence of particle beams or radiation. Several algorithms for expanding the time evolution operator were investigated. We concluded that for systems that are memory limited, the Chebychev method is preferred as it has the smallest memory footprint. For systems that are CPU limited, the Short Iterative Lanczos (SIL) method is preferred since it generally requires less floating point operations for a given propagation step. We applied TDDFT to study three dynamical systems: ions moving through matter, photo-absorption by atomic clusters and high-harmonic generation of light from noble gases. Prior calculations of the "stopping power" (SP) of ion beams in solids have been based on a homogeneous electron gas scattering off a static atom and entail at least one free parameter. We performed dynamical simulations of ions channeled in silicon using TDDFT. The calculated SP's are in excellent agreement with the observed oscillatory dependence on atomic number. TDDFT calculations for a homogeneous electron gas demonstrate that both dynamical response and non-uniformities in the electron density are essential to reproduce the data without free parameters. In another application, we simulated the photo-absorption of light by sodium clusters of various sizes. In this approach, the electrons are treated as a classical set of oscillators that absorb light at their natural oscillation frequencies. We conclude that the optical absorption spectrum does not, in general, correlate to the natural frequencies of an electronic system. Finally, we calculated the nonlinear optical response of noble gases to ultrashort laser pulses. The optical response is found by approximating the electronic system as a dynamic classical charge distribution. The spectrum is calculated by applying the dipole approximation in conjunction with the power spectrum method. Results indicate that this method is able to capture many of the qualitative characteristics observed in experiment but that quantitative agreement will probably require one to account for non-adiabatic exchange and correlation effects.