We present ONETEP (order-N electronic total energy package), a density functional program for parallel computers whose computational cost scales linearly with the number of atoms and the number of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theoretical developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a physical way of dividing the computational effort among many processors to allow calculations to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing numbers of processors and confirm that the time taken by ONETEP as a function of increasing number of atoms for a given number of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and mathematically consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calculations with ONETEP have the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.

1.
A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, 1st ed. (McGraw-Hill, New York, 1989).
2.
R. M. Martin, Electronic Structure. Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004).
3.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
4.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
5.
C.-K.
Skylaris
,
O.
Igglessi-Markopoulou
,
A.
Detsi
, and
J.
Markopoulos
,
Chem. Phys.
293
,
355
(
2003
).
6.
C.
Molteni
,
I.
Frank
, and
Parrinello
,
J. Am. Chem. Soc.
121
,
12177
(
1999
).
7.
E.
Artacho
,
M.
Rohlfing
,
M.
Côté
,
P. D.
Haynes
,
R. J.
Needs
, and
C.
Molteni
,
Phys. Rev. Lett.
93
,
116401
(
2004
).
8.
A. H.
Nevidomskyy
,
G.
Csányi
, and
M. C.
Payne
,
Phys. Rev. Lett.
91
,
105502
(
2003
).
9.
L.
Colombi Ciacchi
and
M. C.
Payne
,
Phys. Rev. Lett.
92
,
176104
(
2004
).
10.
R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
11.
G.
Galli
,
Curr. Opin. Solid State Mater. Sci.
1
,
864
(
1996
).
12.
S.
Goedecker
,
Rev. Mod. Phys.
71
,
1085
(
1999
).
13.
W.
Kohn
,
Phys. Rev.
115
,
809
(
1959
).
14.
W.
Kohn
,
Phys. Rev. Lett.
76
,
3168
(
1996
).
15.
E. I.
Blount
,
Solid State Phys.
13
,
305
(
1962
).
16.
N.
Marzari
and
D.
Vanderbilt
,
Phys. Rev. B
56
,
12847
(
1997
).
17.
C. M.
Goringe
,
E.
Hernández
,
M. J.
Gillan
, and
I. J.
Bush
,
Comput. Phys. Commun.
102
,
1
(
1997
).
18.
M.
Challacombe
,
Comput. Phys. Commun.
128
,
93
(
2000
).
19.
J.-L.
Fattebert
and
J.
Bernholc
,
Phys. Rev. B
62
,
1713
(
2000
).
20.
C. K.
Gan
and
M.
Challacombe
,
J. Chem. Phys.
118
,
9128
(
2003
).
21.
E. R.
Davidson
and
D.
Feller
,
Chem. Rev. (Washington, D.C.)
86
,
681
(
1986
).
22.
C. F.
Guerra
,
J. G.
Snijders
,
G.
te Velde
, and
E. J.
Baerends
,
Theor. Chem. Acc.
99
,
391
(
1998
).
23.
P. D.
Haynes
and
M. C.
Payne
,
Comput. Phys. Commun.
102
,
17
(
1997
).
24.
J.
Junquera
,
O.
Paz
,
D.
Sánchez-Portal
, and
E.
Artacho
,
Phys. Rev. B
64
,
235111
(
2001
).
25.
E.
Hernández
,
M. J.
Gillan
, and
C. M.
Goringe
,
Phys. Rev. B
55
,
13485
(
1997
).
26.
P.
Fernández
,
A.
Dal Corso
,
A.
Baldereschi
, and
F.
Mauri
,
Phys. Rev. B
55
,
R1909
(
1997
).
27.
C.-K.
Skylaris
,
A. A.
Mostofi
,
P. D.
Haynes
,
O.
Diéguez
, and
M. C.
Payne
,
Phys. Rev. B
66
,
035119
(
2002
).
28.
C.-K.
Skylaris
,
A. A.
Mostofi
,
P. D.
Haynes
,
C. J.
Pickard
, and
M. C.
Payne
,
Comput. Phys. Commun.
140
,
315
(
2001
).
29.
C.-K.
Skylaris
,
O.
Diéguez
,
P. D.
Haynes
, and
M. C.
Payne
,
Phys. Rev. B
66
,
073103
(
2002
).
30.
R.
Baer
and
M.
Head-Gordon
,
Phys. Rev. Lett.
79
,
3962
(
1997
).
31.
S.
Ismail-Beigi
and
T. A.
Arias
,
Phys. Rev. Lett.
82
,
2127
(
1999
).
32.
L.
He
and
D.
Vanderbilt
,
Phys. Rev. Lett.
86
,
5341
(
2001
).
33.
R.
McWeeny
,
Rev. Mod. Phys.
32
,
335
(
1960
).
34.
C. A.
White
,
B. G.
Johnson
,
P. M. W.
Gill
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
253
,
268
(
1996
).
35.
M. C.
Strain
,
G. E.
Scuseria
, and
M. J.
Frisch
,
Science
271
,
51
(
1996
).
36.
E.
Schwegler
and
M.
Challacombe
,
J. Chem. Phys.
105
,
2726
(
1996
).
37.
J. M.
Soler
,
E.
Artacho
,
J. D.
Gale
,
A.
Garcı́a
,
J.
Junquera
,
P.
Ordejón
, and
D.
Sánchez-Portal
,
J. Phys.: Condens. Matter
14
,
2745
(
2002
).
38.
X. P.
Li
,
R. W.
Nunes
, and
D.
Vanderbilt
,
Phys. Rev. B
47
,
10891
(
1993
).
39.
J. M.
Millam
and
G. E.
Scuseria
,
J. Chem. Phys.
106
,
5569
(
1997
).
40.
P. D.
Haynes
and
M. C.
Payne
,
Phys. Rev. B
59
,
12173
(
1999
).
41.
U.
Stephan
,
Phys. Rev. B
62
,
16412
(
2000
).
42.
J.
Kim
,
F.
Mauri
, and
G.
Galli
,
Phys. Rev. B
52
,
1640
(
1995
).
43.
O. F.
Sankey
and
D. J.
Niklewski
,
Phys. Rev. B
40
,
3979
(
1989
).
44.
S. D.
Kenny
,
A. P.
Horsfield
, and
H.
Fujitani
,
Phys. Rev. B
62
,
4899
(
2000
).
45.
E.
Anglada
,
J. M.
Soler
,
J.
Junquera
, and
E.
Artacho
,
Phys. Rev. B
66
,
205101
(
2002
).
46.
M. C.
Payne
,
M. P.
Teter
,
D. C.
Allan
,
T. A.
Arias
, and
J. D.
Joannopoulos
,
Rev. Mod. Phys.
64
,
1045
(
1992
).
47.
In our earlier work (Refs. 27 and 54) we refer to these functions as “periodic bandwidth limited delta functions.”
48.
A. A.
Mostofi
,
P. D.
Haynes
,
C.-K.
Skylaris
, and
M. C.
Payne
,
J. Chem. Phys.
119
,
8842
(
2003
).
49.
E.
Artacho
and
L. M.
del Bosch
,
Phys. Rev. A
43
,
5770
(
1991
).
50.
M. D.
Segall
,
P. J. D.
Lindan
,
M. J.
Probert
,
C. J.
Pickard
,
P. J.
Hasnip
,
S. J.
Clark
, and
M. C.
Payne
,
J. Phys.: Condens. Matter
14
,
2717
(
2002
).
51.
T. P. Straatsma, E. Apra, T. L. Windus et al., NWChem, A Computational Chemistry Package for Parallel Computers, Version 4.5, Pacific Northwest National Laboratory, Richland, Washington, 2003.
52.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
53.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
54.
A. A.
Mostofi
,
C.-K.
Skylaris
,
P. D.
Haynes
, and
M. C.
Payne
,
Comput. Phys. Commun.
147
,
788
(
2002
).
55.
P.
Pulay
,
Mol. Phys.
17
,
197
(
1969
).
56.
Message Passing Interface Forum, http://www.mpi-forum.org/
57.
P. Pacheco, Parallel Programming with MPI (Morgan Kaufmann, San Fransisco, CA, 1996).
58.
S.
Baroni
,
S.
de Gironcoli
,
A.
Dal Corso
, and
P.
Giannozzi
,
Rev. Mod. Phys.
73
,
515
(
2001
).
59.
C. J.
Pickard
and
F.
Mauri
,
Phys. Rev. B
63
,
245101
(
2001
).
60.
R.
Resta
,
Int. J. Quantum Chem.
75
,
599
(
1999
).
61.
G.
Csányi
,
T.
Albaret
,
M. C.
Payne
, and
A.
De Vita
,
Phys. Rev. Lett.
93
,
175503
(
2004
).
62.
D. M.
Ceperley
and
B. J.
Alder
,
Phys. Rev. Lett.
45
,
566
(
1980
).
63.
J. P.
Perdew
and
A.
Zunger
,
Phys. Rev. B
23
,
5048
(
1981
).
64.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
65.
B.
Hammer
,
L. B.
Hansen
, and
J. K.
Nørskov
,
Phys. Rev. B
59
,
7413
(
1999
).
66.
J. P.
Perdew
,
J. A.
Chevary
,
S. H.
Vosko
,
K. A.
Jackson
,
M. R.
Pederson
,
D. J.
Singh
, and
C.
Fiolhais
,
Phys. Rev. B
46
,
6671
(
1992
).
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