Xavier Andrade edited Introduction.tex  over 9 years ago

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The development of theoretical methods for the simulation of electronic system is an active area of study. This interest has been fueled, on one hand, by the development of theoretical tools, like density functional theory (DFT)~\cite{Hohenberg_1964,Kohn_1965}, that can predict many properties with good accuracy at a relatively modest computational cost. And other hand, because these same tools are not good enough for many applications, and better methods in terms of accuracy or numerical cost are required.  These advances are research is  targeted on a broad range of aspects of electronic structure simulations. They involve simulations:  the development of new theoretical frameworks, new or improved methods to calculate properties within existing theories, or even new algorithms. In most cases, this theoretical work requires the development of test implementations to assess its properties. Whilewith in  the implementation of established methods are targeted is focused  towards robustness, efficiency and generality. Given the experimentative nature of this work, the target is fast translation to code of new theory needs to be easy to implement  and flexible implementations. to modify.  When simulating electrons using some level of approximation to quantum mechanics, like Hartree-Fock or density functional theory, different fields needs to be represented numerically: the ionic potential, the single-particle orbitals or states, and the electronic density. The most popular representations methods are based on the use of basis sets that have a certain physical connection to the system being simulated. In chemistry the method of choice is to use atomic orbitals as a basis to describe the orbitals of a molecule. When these atomic orbitals are expanded in Gaussian functions, it leads to a very efficient method as many integrals can be calculated from analytical formulae~\cite{szabo1996modern}. In condensed matter physics, on the other hand, the traditional basis is a set of plane waves, the eigenstates of the homogeneous electron gas. These physics-inspired basis sets have, however, some limitations. For example, it is not trivial to simulate crystalline systems using atomic orbitals~\cite{Dovesi_2014}, and, on the other hand, in plane wave approaches finite systems must be approximated as periodic system using a super cell approach.