deletions | additions       diff --git a/Conclusions1.tex b/Conclusions1.tex  index 7c857f6..534afbf 100644  --- a/Conclusions1.tex  +++ b/Conclusions1.tex 
...
\section{Conclusions}  We have shown several recent developments in the realm of electronic structure theory. All these developments are theory that have been  based on the Octopus real-space code. They go beyond a mere implementation of existing theory, aiming to develop new ideas to advance the field. We have show that real-space grids when combined with an advances implementation can be a tool to develop new ideas that allows to advance the field of theoretical   There are however some limitations that need to be considered. In general the number of grid points required for each calculation is large (in the range of \(10^4\) to \(10^6\)) in comparison with the number of expansion coefficients in localized basis set method. This is usually not an issue, since for DFT/TDDFT the amount of work per coefficient is small and scales linearly with the number of grid points. However, some methods 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. Alternative In this case, alternative  discretizations are required. For example, by using a spectral decomposition to represent two body object~\cite{Nguyen_2012}.  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. However the prefactor of the numerical cost can be quite large in comparison with pure DFT methods.