Quantum-chemistry methods for materials science
Analytic gradients for the RPA: using the relation between total energies and self-energiesGeorg Kresse
University of Vienna, Austria
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 computation time by
typically one order 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, any first derivative of the total
energy including forces, as well as corrections to the correlation energy from the changes of the
charge density when switching from DFT to a many-body body description (GW singles energy
contribution) . First applications of RPA forces to systems with mixed covalent and vdW
bonding are discussed. These applications include phonons, relaxation of structures, as well as
molecular dynamics simulations .
 M. Kaltak, J. Klimés, and G. Kresse, J. Chem. Theory Comput., 10, 2498 (2014).
 M. Kaltak, J. Klimés, and G. Kresse, Phys. Rev. B 90, 054115 (2014).
 P. Liu, M. Kaltak, J. Klimés, and G. Kresse, Phys. Rev. B 94, 165109 (2016).
 J. Klimés, M. Kaltak, E. Maggio, and G. Kresse, J. Chem. Phys. 140, 084502 (2015).
 B. Ramberger, T. Schäfer, G. Kresse, Phys. Rev. Lett. 118 106403 (2017).