Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid,
combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrodinger equation for low-dimensionality systems.
Absorbing boundaries are frequently employed in real-time propagation of the Schrodinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an implicit descr
iption of observables involving infinitely extended continuum states. In the literature, several boundary absorbers have been proposed. They mostly fall into three main families: mask function absorbers, complex absorbing potentials, and exterior complex-scaled potentials. To date none of the proposed absorbers is perfect, and all present a certain degree of reflections. Characterization of such reflections is thus a critical task with strong implications for time-dependent simulations of atoms and molecules. We introduce a method to evaluate the reflection properties of a given absorber and present a comparison of selected samples for each family of absorbers. Further, we discuss the connections between members of each family and show how the same reflection curves can be obtained with very different absorption schemes.
We demonstrate the capabilities of time-dependent density functional theory (TDDFT) for strong-field, short wavelength (soft X-ray) physics, as compared to a formalism based on rate equations. We find that TDDFT provides a very good description of th
e total and individual ionization yields for Ne and Ar atoms exposed to strong laser pulses. We assess the reliability of different adiabatic density functionals and conclude that an accurate description of long-range interactions by the exchange and correlation potential is crucial for obtaining the correct ionization yield over a wide range of intensities ($10^{13}$ -- $5 times 10^{15}$ W/cm$^2$). Our TDDFT calculations disentangle the contribution from each ionization channel based on the Kohn-Sham wavefunctions.
Using time dependent density functional theory (TDDFT) we examine the energy, angular and time-resolved photoelectron spectra (TRPES) of ethylene in a pump-probe setup. To simulate TRPES we expose ethylene to an ultraviolet (UV) femtosecond pump puls
e, followed by a time delayed extreme ultraviolet (XUV) probe pulse. Studying the photoemission spectra as a function of this delay provides us direct access to the dynamic evolution of the molecules electronic levels. Further, by including the nucleis motion, we provide direct chemical insight into the chemical reactivity of ethylene. These results show how angular and energy resolved TRPES could be used to directly probe electron and nucleus dynamics in molecules.
Molecular absorption and photo-electron spectra can be efficiently predicted with real-time time-dependent density-functional theory (TDDFT). We show here how these techniques can be easily extended to study time-resolved pump-probe experiments in wh
ich a system response (absorption or electron emission) to a probe pulse, is measured in an excited state. This simulation tool helps to interpret the fast evolving attosecond time-resolved spectroscopic experiments, where the electronic motion must be followed at its natural time-scale. We show how the extra degrees of freedom (pump pulse duration, intensity, frequency, and time-delay), which are absent in a conventional steady state experiment, provide additional information about electronic structure and dynamics that improve a system characterization. As an extension of this approach, time-dependent 2D spectroscopies can also be simulated, in principle, for large-scale structures and extended systems.
