The riper module is an implementation of Kohn–Sham DFT with Gaussian-type orbitals (GTO) as basis functions that treats molecular and periodic systems of any dimensionality on an equal footing. Its key component is a combination of resolution of identity (RI) approximation and continuous fast multipole method (CFMM) applied for the electronic Coulomb term [107,108]. This RI-CFMM scheme operates entirely in the direct space and partitions Coulomb interactions into far-field part evaluated using multipole expansions and near-field contribution calculated employing density fitting. Evaluation of the exchange-correlation term is performed using an octree-based adaptive numerical integration scheme . riper offers computational efficiency and favorable scaling behavior approaching O(N) for the formation of Kohn–Sham matrix  and gradient calculation . In addition, for calculations on very large molecular systems a low-memory modification of the RI approximation has been implemented . This low-memory iterative density fitting (LMIDF) scheme is based on a combination of CFMM and a preconditioned conjugate gradient (CG) solver. Compared with the standard RI implementation, up to 15-fold reduction of the memory requirements is achieved at a cost of only slight increase in computational time.
Functionalities of riper:
Limitations of riper: