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n the last two decades, colloidal semiconductor nanocrystals have emerged as a phenomenal research topic due to their size-dependent optoelectronic properties and to their outstanding versatility in many technological applications. In this review, we provide an historical account of the most relevant computational works that have been carried out to understand atomistically the electronic structure of these materials, including the main requirements needed for the preparation of nanocrystal models that align well with the experiments. We further discuss how the advancement of these computational tools has affected the analysis of these nanomaterials over the years. We focus our review on the three main families of colloidal semiconductor nanocrystals: group II-VI and IV-VI metal chalcogenides, group III-V metal pnictogenides and metal halides, in particular lead-based halide perovskites. We discuss the most recent research frontiers and outline the future outlooks expected in this field from a computational perspective.

We use the dimer (HF???HF) as a model system to understand the dynamics in hydrogen-bonded systems. This particularly simple system has been widely used both in experimental and theoretical studies. Here we focus on the remarkable mode selectivity in vibrational predissociation processes which occur on time scales of picoseconds to nanoseconds. We have performed classical molecular dynamics (MD) calculations on the six-dimensional SO-3 potential energy surface (PES) of (HF)2[1] to estimate absorption spectra and predissociation lifetimes ?PD for various initial vibrational excitations involving HF stretching. Our calculations can qualitatively reproduce the mode selectivity in ?PD observed experimentally: Excitations involving the 'hydrogen-bonded' HF stretching mode give rise to shorter ?PD than those involving the 'free' HF stretching mode. Besides results concerning the HF dimer, this study offers the opportunity to check to what extent classical MD calculations on an accurate and realistic potential are suitable to study dynamical properties in such a molecular system.