Predicting the reflectivity and colour of metals from first principles

Gold and copper are the only two elemental metals that show a characteristic colour, due to the presence of a drop in the reflectivity curve inside the visible range. Reflectivities of all other metals are in general high and flat for all visible frequencies, making they appear shiny and silvery white. Nowadays, with state-of-the-art theoretical methods, it is possible to calculate reflectivity and colour of a material by means of first-principles simulations and, as a consequence, predict the colour of new metal alloys. The computational approach for material design can be, for example, useful for applications related to jewellery and the high-end watch industry, where there is the demand, due to market and fashion trends, for precious-metal alloys with specific optical properties. The simulations can therefore substitute or, at least, reduce the use of expensive and inefficient trial-and-error experiments, which is otherwise the common route followed by researchers and manufacturers in order to identify novel materials. Because of its unique properties (i.e. characteristic red-yellow colour, high corrosion resistance, high density and considerable malleability), since ancient times gold and, as a consequence, its alloys have been of particular interest for jewellery applications. In particular, gold alloys and intermetallics show a broad spectrum of colours (yellow, red, purple, white and others), which can be tuned by varying the alloying elements in the material. In this thesis, we first discuss the physical approach used to simulate the optical properties of metals, that is the independent particle approximation for the evaluation of the dielectric function, based on the calculation of both interband and intraband contributions from the electronic structure obtained with density-functional theory simulations. We also describe in some detail the computational approach developed to perform in practice first-principles simulations in both an efficient and automatic way. For this purpose, on one hand we have developed a code, named SIMPLE, to calculate optical properties using Shirley's interpolation method, which is an efficient and robust automatic procedure. On the other hand, in order to have reliable band structures as the starting ingredients for the evaluation of the dielectric function, we have exploited the results of a protocol, named SSSP, developed by us to test the precision and performance of pseudopotentials for all elements. Using the results above, we then show through a systematic study on elemental metals and extensive comparisons with experimental data that the chosen computational approach is able to reproduce the correct behaviour of the reflectivity curve and to capture the main differences in optical properties among several elements of the periodic table. Finally, we perform a similar study on metal alloys by considering different types of compounds, i.e. ordered intermetallics, disordered solid solutions and heterogeneous alloys. In particular, we show through a comparison with several experimental results that, if the appropriate methods are used for the simulation of the different types of compounds, (i) the simulated colours of known coloured intermetallics are often in quantitative agreement with experiments, (ii) the main mechanisms that modify the colour of bulk gold in alloys are qualitatively captured and that (iii) we manage to reproduce the main colour trends in noble-metal-based binary alloys