Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.

1.
J.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
2.
M.
Dion
,
H.
Rydberg
,
E.
Schr
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
92
,
246401
(
2004
).
3.
I.
Daubechies
,
Ten Lectures on Wavelets
(
SIAM
,
Philadelphia
,
1992
).
4.
X.
Gonze
,
J. -M.
Beuken
,
R.
Caracas
,
F.
Detraux
,
M.
Fuchs
,
G. -M.
Rignanese
,
L.
Sindic
,
M.
Verstraete
,
G.
Zerah
,
F.
Jollet
,
M.
Torrent
,
A.
Roy
,
M.
Mikami
,
Ph.
Ghosez
,
J. -Y.
Raty
, and
D. C.
Allan
,
Comput. Mater. Sci.
25
,
478
(
2002
);
see website: http://www.abinit.org
6.
T. L.
Beck
,
Rev. Mod. Phys.
72
,
1041
(
2000
).
7.
J. E.
Pask
,
B. M.
Klein
,
C. Y.
Fong
, and
P. A.
Sterne
,
Phys. Rev. B
59
,
12352
(
1999
).
8.
J. J.
Mortensen
,
L. B.
Hansen
, and
K. W.
Jacobsen
,
Phys. Rev. B
71
,
035109
(
2005
).
9.
J. R.
Chelikowsky
,
N.
Troullier
, and
Y.
Saad
,
Phys. Rev. Lett.
72
,
1240
(
1994
).
10.
S.
Goedecker
,
Rev. Mod. Phys.
71
,
1085
(
1999
).
11.
T. A.
Arias
,
Rev. Mod. Phys.
71
,
267
(
1999
).
12.
T.
Yanai
,
G. I.
Fann
,
Z.
Gan
,
R. J.
Harrison
, and
G.
Beylkin
,
J. Chem. Phys.
121
,
6680
(
2004
).
13.
S.
Goedecker
,
Wavelets and their Application for the Solution of Partial Differential Equations
(
Polytechniques Universitaires Romandes
,
Lausanne
,
1998
).
14.
G.
Beylkin
,
R.
Coifman
, and
V.
Rokhlin
,
Commun. Pure Appl. Math.
44
,
141
(
1991
).
15.
S.
Goedecker
,
M.
Teter
, and
J.
Hutter
,
Phys. Rev. B
54
,
1703
(
1996
).
16.
C.
Hartwigsen
,
S.
Goedecker
, and
J.
Hutter
,
Phys. Rev. B
58
,
3641
(
1998
).
17.
M.
Krack
,
Theor. Chem. Acc.
114
,
145
(
2005
).
18.
M.
Payne
,
M.
Teter
,
D.
Allan
,
T.
Arias
, and
J.
Joannopoulos
,
Rev. Mod. Phys.
64
,
1045
(
1992
).
19.
G.
Beylkin
,
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
29
,
1716
(
1992
).
20.
J.
Strang
and
G. J.
Fix
,
An analysis of the Finite Element Method
(
Cambridge
,
Wellesley
,
1988
).
21.
C. J.
Tymczak
and
X. -Q.
Wang
,
Phys. Rev. Lett.
78
,
3654
(
1997
).
22.
A. I.
Neelov
and
S.
Goedecker
J. Comput. Phys.
217
,
312
(
2006
).
23.
K. -S.
Lau
and
Q.
Sun
,
Proc. Am. Math. Soc.
128
,
1087
(
2000
).
24.
L.
Genovese
,
T.
Deutsch
,
A.
Neelov
,
S.
Goedecker
, and
G.
Beylkin
,
J. Chem. Phys.
125
,
074105
(
2006
).
25.
L.
Genovese
,
T.
Deutsch
, and
S.
Goedecker
,
J. Chem. Phys.
127
,
054704
(
2007
).
26.
J. A.
White
and
D. M.
Bird
,
Phys. Rev. B
50
,
4954
(
1994
).
27.
B. R.
Johnson
,
J. P.
Modisette
,
P. J.
Nordlander
, and
J. L.
Kinsey
,
J. Chem. Phys.
110
,
8309
(
1999
).
28.
29.
J.
Hutter
,
H. P.
Lüthi
, and
M.
Parrinello
,
Comput. Mater. Sci.
2
,
244
(
1994
).
30.
P.
Pulay
, in
Modern Theoretical Chemistry
, edited by
H. F.
Schaefer
(
Plenum
,
New York
,
1977
).
32.
M. M.
Morrell
,
R. G.
Parr
, and
M.
Levy
,
J. Chem. Phys.
62
,
549
(
1975
).
33.
S.
Goedecker
and
A.
Hoisie
,
Performance Optimization of Numerically Intensive Codes
(
SIAM
,
Philadelphia
,
2001
).
34.
E. R.
Davidson
,
J. Comput. Phys.
17
,
87
(
1975
).
35.
J.
Hutter
,
A.
Alavi
,
T.
Deutsch
,
M.
Bernasconi
,
S.
Goedecker
,
D.
Marx
,
M.
Tuckerman
, and
M.
Parrinello
, CPMD, Version 3.8,
Max-Planck-Institut für Festkörperforschung and IBM Zürich Research Laboratory
,
1995–1999
.
36.
E.
Anderson
,
Z.
Bai
,
C.
Bischof
,
S.
Blackford
,
J.
Demmel
,
J.
Dongarra
,
J.
Du Croz
,
A.
Greenbaum
,
S.
Hammarling
,
A.
McKenney
, and
D.
Sorensen
,
LAPACK Users’ Guide
(
SIAM
,
Philadelphia
,
1999
).
You do not currently have access to this content.