Density functional theory (DFT) calculations in CP2K employ the Gaussian and plane waves (GPW) method. In GPW, the description of the total density on realspace grids is typically the computationally most expensive part. By introducing a local resolution-of-the-identity (LRI) approach, the linear scaling of the GPW approach can be retained, while reducing the prefactor for the grid operations. The combined approach, LRIGPW, is comprehensively described in J. Chem. Theory Comput., 2017.
In LRIGPW, the atomic pair densities $\rho_{\mathrm{AB}}$ are approximated by an expansion in a set of fit functions centered at atom A $\{f_i^{\mathrm{A}}(\mathbf{r})\}$ and atom B $\{f_j^{\mathrm{B}}(\mathbf{r})\}$,

\begin{equation} \rho_{\mathrm{AB}}\approx \sum_i{a_i^{\mathrm{A},(\mathrm{AB})}f_i^{\mathrm{A}}}(\mathbf{r}) + \sum_j{a_j^{\mathrm{B},(\mathrm{AB})}f_j^{\mathrm{B}}}(\mathbf{r}). \end{equation} The fit functions are also Gaussian-type functions and provided as auxiliary basis set.

[inp>FORCE_EVAL/DFT|DFT]] section.

&QS
  METHOD LRIGPW
  &LRIGPW
     LRI_OVERLAP_MATRIX INVERSE
     SHG_LRI_INTEGRALS
  &END
&END QS

• Ice XV: ice_lrigpw.tar.gz