Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
This work addresses the computational bottleneck of RPA correlation calculations in quantum chemistry, enabling applications to larger systems.
The authors present a cubic scaling algorithm for calculating the RPA correlation energy, achieving reduced computational cost compared to previous methods. They use Cauchy's integral formula and interpolative separable density fitting to split orbital dependencies and improve efficiency.
We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $χ^0$ by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.