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Xavier Andrade edited Introduction.tex
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For the simulations of electrons however, other discretization methods have become more popular, in particular the use of basis sets that have a physical foundation. In chemistry the most popular approach is to use atomic orbitals as a basis, usually expanded in terms of Gaussian functions, for the orbitals and density of a molecule. In condensed matter physics the basis is a set plane waves, the eigenvectors of the electron gas.
These physics-inspired bases however have limitations. For example, it is not trivial to simulate crystalline systems using atomic
orbitals~ orbitals~\cite{Dovesi_2014}, and, on the other hand, in plane wave approaches finite systems must be simulated as periodic super cells.
Real-space approaches do not benefit from this physical connection to the system being simulated, however they are flexible enough to simulate different kinds of systems.
A real-space grid has been the traditional way of solving the electronic problem on a grid for atomic systems. In this case, radial grids with a non-uniform distribution of points are used.