---
res:
bibo_abstract:
- We derive formulas for the Coulomb matrix within the full-potential linearized
augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central ingredient
in implementations of many-body perturbation theory, such as the Hartree–Fock
and GW approximations for the electronic self-energy or the random-phase approximation
for the dielectric function. It is represented in the mixed product basis, which
combines numerical muffin-tin functions and interstitial plane waves constructed
from products of FLAPW basis functions. The interstitial plane waves are here
expanded with the Rayleigh formula. The resulting algorithm is very efficient
in terms of both computational cost and accuracy and is superior to an implementation
with the Fourier transform of the step function. In order to allow an analytic
treatment of the divergence at k=0 in reciprocal space, we expand the Coulomb
matrix analytically around this point without resorting to a projection onto plane
waves. Without additional approximations, we then apply a basis transformation
that diagonalizes the Coulomb matrix and confines the divergence to a single eigenvalue.
At the same time, response matrices like the dielectric function separate into
head, wings, and body with the same mathematical properties as in a plane-wave
basis. As an illustration we apply the formulas to electron-energy-loss spectra
(EELS) for nickel at different k vectors including k=0. The convergence of the
spectra towards the result at k=0 is clearly seen. Our all-electron treatment
also allows to include transitions from 3s and 3p core states in the EELS spectrum
that give rise to a shallow peak at high energies and lead to good agreement with
experiment.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Christoph
foaf_name: Friedrich, Christoph
foaf_surname: Friedrich
- foaf_Person:
foaf_givenName: Arno
foaf_name: Schindlmayr, Arno
foaf_surname: Schindlmayr
foaf_workInfoHomepage: http://www.librecat.org/personId=458
orcid: 0000-0002-4855-071X
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Blügel, Stefan
foaf_surname: Blügel
bibo_doi: 10.1016/j.cpc.2008.10.009
bibo_issue: '3'
bibo_volume: 180
dct_date: 2009^xs_gYear
dct_identifier:
- UT:000264735800002
dct_isPartOf:
- http://id.crossref.org/issn/0010-4655
dct_language: eng
dct_publisher: Elsevier@
dct_title: Efficient calculation of the Coulomb matrix and its expansion around
k=0 within the FLAPW method@
...