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# Low scaling ACFDT/RPA and GW algorithms

This category shows all tags and articles concerning low scaling GW and RPA algorithms available as of VASP.6 and newer.

## Theoretical Background

The Random Phase Approximation (RPA) is a diagrammatic method to determine the groundstate energy of interacting electrons. The computational cost of diagrammatic methods typically exceeds the one of hybrid DFT calculations, since a frequency dependent Hamiltonian is diagonalized. Conventional GW and RPA/ACFDT algorithms typically scale with the forth power of the system size and are, thus, limited to relatively small system sizes. However, by performing all calculations on the imaginary time and imaginary frequency axis one can exploit coarse Fourier transformation compatible grids and obtain a cubic scaling GW and RPA/ACFDT algorithm. These algorithms can be used to study relatively large systems with diagrammatic methods.

Please take a look on the RPA and GW pages for more information about their theoretical formulation.

## How to

The following pages contain some general recipes for

- RPA: RPA-ACFDT calculations
- GW: A practical guide to low-scaling GW calculations can be found here.