Real-time approaches are becoming increasingly important in understanding dynamical properties and excitations in condensed matter due to the increasing availability of high performance computational facilities.Here we discuss two such real-time approaches. I. The first approach is based on real-time simulations of the dynamic structure of nano-scale materials base on finite-temperature density functional theory/molecular dynamics and x-ray spectroscopy theory. This approach is illustrated for the case of nanoclusters of Pt metal supported on gamma-alumina which are used as catalysts. The simulations reveal a complex dynamical structure on multiple-time scales including, hindered Brownian-like librational motion of the center of mass and fluctuating bonding, which explain many of their unusual properties. II. The second is a real-time, time-dependent density functional theory (RT-TDDFT) approach for ab-initio calculations of frequency-dependent linear and non-linear optical response. This method is an extension to hyperpolarizabilities of an approach based on calculations of the time-evolution operator using the electronic structure program SIESTA. Instead of calculating excited quantum states, which can be a bottleneck in frequency-space calculations, the response of large molecular systems to time-varying electric fields is calculated in real-time. To speed the calculations of non-linear response, our approach uses Gaussian enveloped quasi-monochromatic external fields. With this approach we obtain frequency dependent second harmonic generation (SHG), DC nonlinear rectification, and the electro-optic effect (EOE), which are important in photonics. The method is illustrated with calculations for nano-scale, photonic nonlinear optical (NLO) molecules, and yields results in good agreement with experiment.

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