We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.

1.
J. N.
Anker
,
W. P.
Hall
,
O.
Lyandres
,
N. C.
Shah
,
J.
Zhao
, and
R. P. V.
Duyne
,
Nat. Mater.
7
,
442
(
2008
).
2.
J. A.
Schuller
,
E. S.
Barnard
,
W.
Cai
,
Y. C.
Jun
,
J. S.
White
, and
M. L.
Brongersma
,
Nat. Mater.
9
,
193
(
2010
).
3.
H. A.
Atwater
and
A.
Polman
,
Nat. Mater.
9
,
205
(
2010
).
4.
N. J.
Halas
,
S.
Lal
,
W.-S.
Chang
,
S.
Link
, and
P.
Nordlander
,
Chem. Rev.
111
,
3913
(
2011
).
5.
K. J.
Savage
,
M. M.
Hawkeye
,
R.
Esteban
,
A. G.
Borisov
,
J.
Aizpurua
, and
J. J.
Baumberg
,
Nature
491
,
574
(
2012
).
6.
J. A.
Scholl
,
A. L.
Koh
, and
J. A.
Dionne
,
Nature
483
,
421
(
2012
).
8.
J. A.
Scholl
,
A.
García-Etxarri
,
A. L.
Koh
, and
J. A.
Dionne
,
Nano Lett.
13
,
564
(
2013
).
9.
S. F.
Tan
,
L.
Wu
,
J. K.
Yang
,
P.
Bai
,
M.
Bosman
, and
C. A.
Nijhuis
,
Science
343
,
1496
(
2014
).
10.
E.
Runge
and
E. K. U.
Gross
,
Phys. Rev. Lett.
52
,
997
(
1984
).
11.
W.
Ekardt
,
Phys. Rev. Lett.
52
,
1925
(
1984
).
12.
M. J.
Puska
,
R. M.
Nieminen
, and
M.
Manninen
,
Phys. Rev. B
31
,
3486
(
1985
).
13.
J.
Zuloaga
,
E.
Prodan
, and
P.
Nordlander
,
Nano Lett.
9
,
887
(
2009
).
14.
J.
Zuloaga
,
E.
Prodan
, and
P.
Nordlander
,
ACS Nano
4
,
5269
(
2010
).
15.
P.
Zhang
,
J.
Feist
,
A.
Rubio
,
P.
García-González
, and
F. J.
García-Vidal
,
Phys. Rev. B
90
,
161407
(
2014
).
16.
C.
Kumara
and
A.
Dass
,
Nanoscale
3
,
3064
(
2011
).
17.
A. C.
Dharmaratne
and
A.
Dass
,
Chem. Commun.
50
,
1722
(
2014
).
18.
L.
Serra
and
A.
Rubio
,
Phys. Rev. Lett.
78
,
1428
(
1997
).
19.
C. M.
Aikens
,
S.
Li
, and
G. C.
Schatz
,
J. Phys. Chem. C
112
,
11272
(
2008
).
20.
M.
Stener
,
A.
Nardelli
,
R. D.
Francesco
, and
G.
Fronzoni
,
J. Phys. Chem. C
111
,
11862
(
2007
).
21.
E. B.
Guidez
and
C. M.
Aikens
,
J. Phys. Chem. C
117
,
12325
(
2013
).
22.
G.
Piccini
,
R. W. A.
Havenith
,
R.
Broer
, and
M.
Stener
,
J. Phys. Chem. C
117
,
17196
(
2013
).
23.
G.-T.
Bae
and
C. M.
Aikens
,
J. Phys. Chem. C
116
,
10356
(
2012
).
24.
G.
Barcaro
,
L.
Sementa
,
A.
Fortunelli
, and
M.
Stener
,
J. Phys. Chem. C
118
,
12450
(
2014
).
25.
M.
Kuisma
,
A.
Sakko
,
T. P.
Rossi
,
A. H.
Larsen
,
J.
Enkovaara
,
L.
Lehtovaara
, and
T. T.
Rantala
, “
Localized surface plasmon resonance in silver nanoparticles: Atomistic first-principles time-dependent density-functional theory calculations
” (unpublished).
26.
X.
López-Lozano
,
H.
Barron
,
C.
Mottet
, and
H.-C.
Weissker
,
Phys. Chem. Chem. Phys.
16
,
1820
(
2014
).
27.
H.-C.
Weissker
and
C.
Mottet
,
Phys. Rev. B
84
,
165443
(
2011
).
28.
X.
López-Lozano
,
C.
Mottet
, and
H.-C.
Weissker
,
J. Phys. Chem. C
117
,
3062
(
2013
).
29.
G.
Barcaro
,
M.
Broyer
,
N.
Durante
,
A.
Fortunelli
, and
M.
Stener
,
J. Phys. Chem. C
115
,
24085
(
2011
).
30.
E. B.
Guidez
and
C. M.
Aikens
,
Nanoscale
4
,
4190
(
2012
).
31.
M.-S.
Liao
,
P.
Bonifassi
,
J.
Leszczynski
,
P. C.
Ray
,
M.-J.
Huang
, and
J. D.
Watts
,
J. Phys. Chem. A
114
,
12701
(
2010
).
32.
E. B.
Guidez
,
V.
Mäkinen
,
H.
Häkkinen
, and
C. M.
Aikens
,
J. Phys. Chem. C
116
,
20617
(
2012
).
33.
H.-C.
Weissker
,
H. B.
Escobar
,
V. D.
Thanthirige
,
K.
Kwak
,
D.
Lee
,
G.
Ramakrishna
,
R. L.
Whetten
, and
X.
López-Lozano
,
Nat. Commun.
5
,
3785
(
2014
).
34.
S.
Malola
,
L.
Lehtovaara
,
J.
Enkovaara
, and
H.
Häkkinen
,
ACS Nano
7
,
10263
(
2013
).
35.
S.
Malola
,
L.
Lehtovaara
, and
H.
Häkkinen
,
J. Phys. Chem. C
118
,
20002
(
2014
).
36.
L.
Gell
,
L.
Lehtovaara
, and
H.
Häkkinen
,
J. Phys. Chem. A
118
,
8351
(
2014
).
37.
G.-T.
Bae
and
C. M.
Aikens
,
J. Phys. Chem. A
116
,
8260
(
2012
).
38.
F.
Jensen
,
WIREs Comput. Mol. Sci.
3
,
273
(
2013
).
39.
M.
Miura
,
Y.
Aoki
, and
B.
Champagne
,
J. Chem. Phys.
127
,
084103
(
2007
).
40.
D. P.
Chong
,
Can. J. Chem.
73
,
79
(
1995
).
41.
P.
Manninen
and
J.
Vaara
,
J. Comput. Chem.
27
,
434
(
2006
).
42.
J.
Lehtola
,
P.
Manninen
,
M.
Hakala
, and
K.
Hämäläinen
,
J. Chem. Phys.
137
,
104105
(
2012
).
43.
S.
Lehtola
,
J. Comput. Chem.
36
,
335
(
2015
).
44.
A.
Tsolakidis
,
D.
Sánchez-Portal
, and
R. M.
Martin
,
Phys. Rev. B
66
,
235416
(
2002
).
45.
S.
Ikäläinen
,
P.
Lantto
,
P.
Manninen
, and
J.
Vaara
,
Phys. Chem. Chem. Phys.
11
,
11404
(
2009
).
46.
P.
Lantto
,
K.
Jackowski
,
W.
Makulski
,
M.
Olejniczak
, and
M.
Jaszuński
,
J. Phys. Chem. A
115
,
10617
(
2011
).
47.
J.
Vähäkangas
,
S.
Ikäläinen
,
P.
Lantto
, and
J.
Vaara
,
Phys. Chem. Chem. Phys.
15
,
4634
(
2013
).
48.
N.
Abuzaid
,
A. M.
Kantola
, and
J.
Vaara
,
Mol. Phys.
111
,
1390
(
2013
).
49.
M.
Jaszuński
and
M.
Olejniczak
,
Mol. Phys.
111
,
1355
(
2013
).
50.
J.
Vaara
,
M.
Hanni
, and
J.
Jokisaari
,
J. Chem. Phys.
138
,
104313
(
2013
).
51.
S.
Ikäläinen
,
P.
Lantto
,
P.
Manninen
, and
J.
Vaara
,
J. Chem. Phys.
129
,
124102
(
2008
).
52.
S.
Ikäläinen
,
M. V.
Romalis
,
P.
Lantto
, and
J.
Vaara
,
Phys. Rev. Lett.
105
,
153001
(
2010
).
53.
S.
Ikäläinen
,
P.
Lantto
, and
J.
Vaara
,
J. Chem. Theory Comput.
8
,
91
(
2012
).
54.
T. S.
Pennanen
,
S.
Ikaäläinen
,
P.
Lantto
, and
J.
Vaara
,
J. Chem. Phys.
136
,
184502
(
2012
).
55.
J.
Shi
,
S.
Ikäläinen
,
J.
Vaara
, and
M. V.
Romalis
,
J. Phys. Chem. Lett.
4
,
437
(
2013
).
56.
L.-J.
Fu
and
J.
Vaara
,
J. Chem. Phys.
138
,
204110
(
2013
).
57.
J.
Vähäkangas
,
P.
Lantto
, and
J.
Vaara
,
J. Phys. Chem. C
118
,
23996
(
2014
).
58.
S.
Lehtola
,
P.
Manninen
,
M.
Hakala
, and
K.
Hämäläinen
,
J. Chem. Phys.
138
,
044109
(
2013
).
59.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
60.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
61.
Fundamentals of Time-Dependent Density Functional Theory
,
Lecture Notes in Physics
Vol.
837
, edited by
M. A. L.
Marques
,
N. T.
Maitra
,
F. M. S.
Nogueira
,
E. K. U.
Gross
, and
A.
Rubio
(
Springer
,
2012
).
62.
K.
Yabana
and
G. F.
Bertsch
,
Phys. Rev. B
54
,
4484
(
1996
).
63.
M. E.
Casida
, in
Recent Advances in Density Functional Methods, Part I
, edited by
D. P.
Chong
(
World Scientific
,
Singapore
,
1995
), p.
155
.
64.
J. J.
Mortensen
,
L. B.
Hansen
, and
K. W.
Jacobsen
,
Phys. Rev. B
71
,
035109
(
2005
).
65.
M.
Walter
,
H.
Häkkinen
,
L.
Lehtovaara
,
M.
Puska
,
J.
Enkovaara
,
C.
Rostgaard
, and
J. J.
Mortensen
,
J. Chem. Phys.
128
,
244101
(
2008
).
66.
A. H.
Larsen
,
M.
Vanin
,
J. J.
Mortensen
,
K. S.
Thygesen
, and
K. W.
Jacobsen
,
Phys. Rev. B
80
,
195112
(
2009
).
67.
See https://wiki.fysik.dtu.dk/gpaw/ for GPAW: DFT and beyond within the projector-augmented wave method.
68.
J.
Enkovaara
,
C.
Rostgaard
,
J. J.
Mortensen
,
J.
Chen
,
M.
Dułak
,
L.
Ferrighi
,
J.
Gavnholt
,
C.
Glinsvad
,
V.
Haikola
,
H. A.
Hansen
,
H. H.
Kristoffersen
,
M.
Kuisma
,
A. H.
Larsen
,
L.
Lehtovaara
,
M.
Ljungberg
,
O.
Lopez-Acevedo
,
P. G.
Moses
,
J.
Ojanen
,
T.
Olsen
,
V.
Petzold
,
N. A.
Romero
,
J.
Stausholm-Møller
,
M.
Strange
,
G. A.
Tritsaris
,
M.
Vanin
,
M.
Walter
,
B.
Hammer
,
H.
Häkkinen
,
G. K. H.
Madsen
,
R. M.
Nieminen
,
J. K.
Nørskov
,
M.
Puska
,
T. T.
Rantala
,
J.
Schiøtz
,
K. S.
Thygesen
, and
K. W.
Jacobsen
,
J. Phys.: Condens. Matter
22
,
253202
(
2010
).
69.
S.
Bahn
and
K.
Jacobsen
,
Comput. Sci. Eng.
4
,
56
(
2002
).
70.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
72.
J.
Lehtola
,
M.
Hakala
,
A.
Sakko
, and
K.
Hämäläinen
,
J. Comput. Chem.
33
,
1572
(
2012
).
73.
S.
Lehtola
, ERKALE—HF/DFT from Hel, 2014, http://erkale.googlecode.com.
74.
J. M.
Soler
,
E.
Artacho
,
J. D.
Gale
,
A.
García
,
J.
Junquera
,
P.
Ordejón
, and
D.
Sánchez-Portal
,
J. Phys.: Condens. Matter
14
,
2745
(
2002
).
75.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
,
Comput. Phys. Commun.
180
,
2175
(
2009
).
76.
X.
Ren
,
P.
Rinke
,
V.
Blum
,
J.
Wieferink
,
A.
Tkatchenko
,
A.
Sanfilippo
,
K.
Reuter
, and
M.
Scheffler
,
New J. Phys.
14
,
053020
(
2012
).
77.
I. Y.
Zhang
,
X.
Ren
,
P.
Rinke
,
V.
Blum
, and
M.
Scheffler
,
New J. Phys.
15
,
123033
(
2013
).
78.
F.
Corsetti
,
M.-V.
Fernández-Serra
,
J. M.
Soler
, and
E.
Artacho
,
J. Phys.: Condens. Matter
25
,
435504
(
2013
).
79.

This NGTO construction scheme is readily available in GPAW.

80.

These conditions are equivalent to restricting Gaussian exponents to following limits: s-shell: 0.0090–0.93, p-shell: 0.014–1.4, d-shell: 0.019–1.9, f-shell: 0.024–2.4.

81.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
82.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
78
,
1396
(
1997
).
83.
A.
Castro
,
A.
Rubio
, and
M. J.
Stott
,
Can. J. Phys.
81
,
1151
(
2003
).
84.
J. R.
Lombardi
and
B.
Davis
,
Chem. Rev.
102
,
2431
(
2002
).
85.
See supplementary material at http://dx.doi.org/10.1063/1.4913739 for the generated NAO-sz + NGTO basis sets and the relaxed nanoparticle geometries.
86.
P. A. M.
Dirac
,
Math. Proc. Cambridge Philos. Soc.
26
,
376
(
1930
).
87.
F.
Bloch
,
Z. Angew. Phys.
57
,
545
(
1929
).
88.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
45
,
13244
(
1992
).
89.
A. D.
Becke
,
Phys. Rev. A
38
,
3098
(
1988
).
90.
C.
Lee
,
W.
Yang
, and
R. G.
Parr
,
Phys. Rev. B
37
,
785
(
1988
).
91.
B.
Miehlich
,
A.
Savin
,
H.
Stoll
, and
H.
Preuss
,
Chem. Phys. Lett.
157
,
200
(
1989
).
92.
O.
Gritsenko
,
R.
van Leeuwen
,
E.
van Lenthe
, and
E. J.
Baerends
,
Phys. Rev. A
51
,
1944
(
1995
).
93.
M.
Kuisma
,
J.
Ojanen
,
J.
Enkovaara
, and
T. T.
Rantala
,
Phys. Rev. B
82
,
115106
(
2010
).
94.
J.
Yan
,
K. W.
Jacobsen
, and
K. S.
Thygesen
,
Phys. Rev. B
84
,
235430
(
2011
).
95.
J.
Yan
,
K. W.
Jacobsen
, and
K. S.
Thygesen
,
Phys. Rev. B
86
,
241404
(
2012
).
96.

Timings were performed on Intel Xeon E5-2680 v2 processors with FDR InfiniBand interconnect.

97.

The exact speed-up factors are likely to be affected by the choice between the different parallelization schemes.

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