There are also numerical constraints on the wave-functions: space must be represented in a homogeneous hyper-cube, eventually allowing for different particle masses by modifying the kinetic-energy operator for the corresponding directions. All of the grid-partitioning algorithms intrinsic to octopus carry over to arbitrary dimensions, which allows for immediate parallelization of the calculations of the ground and excited states. The code can run with an arbitrary number of dimensions, however, the complexity and memory size grow exponentially with the number of particles simulated, as expected. Production runs have been executed up to 6 or 7 dimensions.

Most of the additional treatment for many-body quantities is actually post-processing of the wave-functions. For each state, the determination of the fermionic or bosonic nature by Young-tableau symmetrization is followed by the calculation and output of the density for each given particle type, if several are present. Other properties of the many-body wave-function can also be calculated. For example, Octopus can also output the one-body density matrix, provided in terms of its occupation numbers and natural orbitals.

This type of studies, even when they are limited to model systems of a few electrons, allows us to produce results that can be compared to lower levels of theory like approximate DFT or RDMFT, and to develop better approximations for the exchange and correlation term. Exact results obtained from such calculations have been used to assess the quality of a 1D LDA functional~\cite{1DLDA} and adiabatic 1D LDA and exact exchange in a TDDFT calculation calculation of photoemission spectra~\cite{1DLDA,Helbig1}. 