Abstract
Electronic correlation energies from the random-phase approximation converge slowly with respect to the plane wave basis set size. We study the conditions under which a short-range local density functional can be used to account for the basis set incompleteness error. Furthermore, we propose a one-shot extrapolation scheme based on the Lindhard response function of the homogeneous electron gas. The different basis set correction methods are used to calculate equilibrium lattice constants for prototypical solids of different bonding types.
Highlights
The random-phase approximation (RPA) for the electronic correlation energy was developed during the beginning of manybody perturbation theory in the 1950s
In the 1970s, the RPA was formulated in the framework of density functional theory (DFT)2,3 by Langreth and Perdew via the adiabatic connection formalism
This is the appropriate behavior for any reasonable local density approximation (LDA) functional, since (i) εRc,HPAE,GLR vanishes for rs → 0 and (ii) the RPA becomes exact in this limit
Summary
The random-phase approximation (RPA) for the electronic correlation energy was developed during the beginning of manybody perturbation theory in the 1950s. In the 1970s, the RPA was formulated in the framework of density functional theory (DFT) by Langreth and Perdew via the adiabatic connection formalism.. One limiting factor of the RPA, like for other methods based on many-body perturbation theory, is the slow convergence of the correlation energy with respect to the basis set size. The basis set incompleteness error decays only as 1 NPW.9,16,17 The reason for this slow convergence is connected to the electronic cusp condition, which states that the exact many-body wave function has a kink at electron coalescence. This (integrable) UV-divergence is caused by the 1 r-singularity of the Coulomb potential or, equivalently, by its 1 q2-high momentum behavior. Hartree units are used throughout the work
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