Linear and non-linear response phenomena of molecular systems within time-dependent density functional theory

Abstract

In this thesis we develop, implement and apply the formalism of time-dependent density functional theory (TDDFT) to the description of non-linear electronic and ionic phenomena of complex structures. This is framed in the general context of having an e cient formalism able to describe both the electronic and magnetic dynamical response properties of nanoscopic systems beyond the linear regime, including time-resolved spectroscopies. As we are focusing on the modelling of realistic systems, emphasis is placed on developing formalisms that are suitable for e cient numerical implementation. Two novel basic formulations are considered in this work: propagation in real-time of the TDDFT equations for arbitrary external perturbation and the frequency-dependent Sternheimer equation for linear and non-linear dynamical susceptibilities. The real-time TDDFT formulation, already a popular method for the calculation of optical absorption spectra, is extended in the present work to deal with other responses like the chiro-optical activity. A particular fundamental contribution in the thesis is the realisation of modi ed Ehrenfest dynamics, a mixed classical-quantum dynamics where the ions are treated as classical particles. In the adiabatic regime this new ab-initio molecular dynamics approach becomes competitive with the widely used Car-Parrinello and Born-Oppenheimer methods. The scheme is ideally suited for massive parallel implementations and allows handling of thousands of atoms. The Sternheimer equation is an alternative method for linear response in the frequency domain that, as the previous time-propagation scheme, does not need unoccupied states or response functions. It is based on the solution of a self-consistent set of linear equations for each frequency. In this work we present a dynamic version of the Sternheimer formalism that can be used to calculate response in the resonant and non-resonant regimes. We apply this formalism to calculate di erent properties, including the magnetic response and the non-linear optical response. This thesis has a major component in algorithm development and code implementation to reach the goal of handling, from rst principles, the nonequilibrium properties of systems with a large number of active particles, electrons and/or ions. This numerical implementation phase of the work is also discussed in detail, including the aspects required for e cient simulations: the discretization of the problem based on a real-space grid, the algorithms used to solve the di erent equations and the optimization and parallelization of the code. Finally, some examples of applications are shown, where the methods are used to calculate di erent properties of physical systems of interest, including small molecules and nano-clusters, highlighting the impact of the present work for future applications in nano and bio-sciences.