Category:Low-scaling GW and RPA: Difference between revisions
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This category shows all tags and articles concerning low scaling GW and RPA algorithms available as of VASP.6 and newer. | |||
== Theoretical Background == | == 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. | 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. | 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/ACFDT: Correlation energy in the Random Phase Approximation|RPA]] and [[The GW approximation of Hedin's equations|GW]] pages for more information about their theoretical formulation. | |||
== How to == | == How to == | ||
A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW|here]]. | The following pages contain some general recipes for | ||
*RPA: [[ACFDT/RPA calculations#ACFDTR/RPAR| RPA-ACFDT calculations]] | |||
*GW: A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW|here]]. | |||
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[[Category:VASP|ACFDT]][[Category:Many- | [[Category:VASP|ACFDT]][[Category:Many-body perturbation theory]] | ||
Latest revision as of 09:05, 21 February 2024
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.
Pages in category "Low-scaling GW and RPA"
The following 20 pages are in this category, out of 20 total.