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Xavier Andrade edited Conclusions1.tex
over 9 years ago
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What we have presented also shows some of the current challenges in real-space electronic strucuture. One example is the use pseudo-potentials or other form of projectors to represent the electron-ion interaction. Non-local potentials introduce additional complications on both the formulation, as show by the case of magnetic response, and the implementation. Pseudo-potentials also include an additional, and in some cases, not well controlled approximation. It would be interesting to study the possibility of developing an efficient method to perform full-potential calculations without additional computational cost, for example by using adaptive or radial grids.
Another challenge for real-space approaches is the cost of the calculation of two-body Coulumb integrals that appear in electron-hole linear
reponse, response, RDMFT or hybrid xc functionals. In real-space these integrals are calculated in linear or quasi-linear time by considering them as a Poisson problem. However the actual numerical cost can be quite large when compared with other operations. A fast approach to compute these integrals, perhaps by using an auxiliary basis, would certainly make the real-space approach more competitive for some applications.
The scalability of real-space grid methods makes them as a good candidate for electronic structure simulations in the future exaflop systems expected for the end of the decade. In this aspect, the challenge is to develop high-performance implementations that can run efficiently on these machines.