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Xavier Andrade renamed Future.tex to Conclusions1.tex
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\section{Conclusions}
Electronic strucuture methods face several challenges.
The main limitation of real-space electronic structure calculations is that in general the number of grid points, equivalent to the number of expansion coefficients in a basis set method, that are required for each calculation is large (in the range of \(10^4\) to \(10^6\)). In standard DFT and TDDFT the amount of work and memory scales linearly with the number of grid points, and the required amount of work per grid point is small so the total cost is competitive with atomic orbital methods that require considerably less coefficients. However, there are some methods that require the calculation of objects that depend on two, or more, coordinates. For these systems, real-space methods become impractical even for moderately sized systems.
Another disadvantage is the cost of the calculation of two-body Coulumb integrals that are quite common in quantum chemistry methods, in particular in the Hartree-Fock exchange term that is used by hybrid XC functionals. In real-space these integrals can be calculated in linear or quasi-linear time by considering them as a Poisson problem that can be solved using fast Fourier transforms, fast multipole methods or multigrid~\cite{Garc_a_Risue_o_2013}. However the prefactor of the numerical cost is considerable in comparison with pure DFT methods.
The efficiency of the methods and the advancement in computational power have made electronic structure calculations cheap enough to be used in high-throughput studies where thousands or even millions of simulations are performed~\cite{Hachmann_2014}. For these of studies the most important factor is the robustness of the methods, since individual tuning of each calculation becomes impractical.
Current and future high-performance computing platforms present a significant challenge to electronic structure methods. In our order to reach exaflop computing, the trend is to move towards massively parallel processors that provide significant computation throughput in comparison with traditional CPU architectures, examples of these processors are GPUs from Nvidia and AMD, and the Intel MIC architecture. Due to the nature of this processors, the code must be parallelized and highly optimized.
