1202.4990 (James J. Shepherd et al.)

Convergence of many-body wavefunction expansions using a plane wave
basis: from the homogeneous electron gas to the solid state    [PDF]

James J. Shepherd, Andreas Grüneis, George H. Booth, Georg Kresse, Ali Alavi

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 utilising plane-wave wavefunction expansions. Simple
analytic and numerical results from second-order M{\o}ller-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 wavefunctions 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 wavefunction methods, from MP2 to coupled-cluster doubles theory
(CCD) and the random-phase approximation plus second-order screened exchange
(RPA+SOSEX). 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.

View original: http://arxiv.org/abs/1202.4990