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Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems
Journal article   Peer reviewed

Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems

James J Shepherd, Andreas Grüneis, George H Booth, Ali Alavi and Georg Kresse
Physical Review B - Condensed Matter and Materials Physics, Vol.86(3)
2012
DOI: 10.1103/PhysRevB.86.035111
url
https://arxiv.org/pdf/1202.4990View
Open Access

Abstract

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Moller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.

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