The Random Phase Approximation: A Practical Method Beyond DFT

The random phase approximation (RPA) to the correlation energy and the related GW approximation are among the most promising methods to obtain accurate correlation energy differences and QP energies from diagrammatic perturbation theory at reasonable computational cost, in particular, for solid state systems. The calculations are, however, usually two to three orders of magnitude more demanding than conventional density functional theory calculations.

Here, we show that a cubic system size scaling can be readily obtained reducing the computational time by typically one to two orders of magnitude for large systems [1, 2, 3]. Furthermore, the scaling with respect to the number of k points used to sample the Brillouin zone can be reduced to linear order.


In combination, this allows accurate and very well-converged single-point RPA and GW calculations, with a time complexity that is roughly on par to self-consistent Hartree-Fock and hybrid functional calculations. Furthermore, the talk discusses the relation between the RPA correlation energy and the GW approximation. It is shown that the GW selfenergy is the derivative of the RPA correlation energy with respect to the Green’s function. The calculated self-energy can be used to compute QP-energies in the GW approximation as well as any first derivative of the total energy including interatomic forces. This means that we can now relax atoms and perform molecular dynamics using the RPA and VASP, in the same way as for density functional theory, opening the field of materials simulations to methods beyond density functional theory. Recent advances such as a finite temperature RPA implementation which allows to treat metals using the RPA are also briefly discussed.


Finally, applications of the RPA to materials sciences problems are presented.


[1] M. Kaltak, J. Klimés, and G. Kresse, J. Chem. Theory Comput. 10, 2498 (2014).

[2] M. Kaltak, J. Klimés, and G. Kresse, Phys. Rev. B 90, 054115 (2014).

[3] P. Liu, M. Kaltak, J. Klimés, and G. Kresse, Phys. Rev. B 94, 165109 (2016).

[4] J. Klimés, M. Kaltak, E. Maggio, and G. Kresse, J. Chem. Phys. 140, 084502 (2015).

[5] B. Ramberger, T. Schäfer, and G. Kresse, Phys. Rev. Lett. 118 106403 (2017).

[6] M. Kaltak and G. Kresse, Phys. Rev. B 101, 205145 (2020).

Presented by Professor Georg Kresse

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