According to previous interpretations of experimental data, sodium-scandium double-cation borohydride NaSc(BH4)4 crystallizes in the crystallographic space group Cmcm where each sodium (scandium) atom is surrounded by six scandium (sodium) atoms. A careful investigation of this phase based on ab initio calculations indicates that the structure is dynamically unstable and gives rise to an energetically and dynamically more favorable phase with C2221 symmetry and nearly identical x-ray diffraction pattern. By additionally performing extensive structural searches with the minima-hopping method we discover a class of new low-energy structures exhibiting a novel structural motif in which each sodium (scandium) atom is surrounded by four scandium (sodium) atoms arranged at the corners of either a rectangle with nearly equal sides or a tetrahedron. These new phases are all predicted to be insulators with band gaps of 7.9–8.2 eV. Finally, we estimate the influence of these structures on the hydrogen-storage performance of NaSc(BH4)4.

1.
E. A.
Nickels
,
M. O.
Jones
,
W. I. F.
David
,
S. R.
Johnson
,
R. L.
Lowton
,
M.
Sommariva
, and
P. P.
Edwards
,
Angew. Chem. Int. Ed.
47
,
2817
(
2008
).
2.
Z.-Z.
Fang
,
X.-D.
Kang
,
J.-H.
Luo
,
P.
Wang
,
H.-W.
Li
, and
S.-I.
Orimo
,
J. Phys. Chem. C
114
,
22736
(
2010
).
3.
H.
Hagemann
,
M.
Longhini
,
J. W.
Kaminski
,
T. A.
Wesolowski
,
R.
Černý
,
N.
Penin
,
M. H.
Sørby
,
B. C.
Hauback
,
G.
Severa
, and
C. M.
Jensen
,
J. Phys. Chem. A
112
,
7551
(
2008
).
4.
R.
Černý
,
D. B.
Ravnsbæk
,
G.
Severa
,
Y.
Filinchuk
,
V.
D' Anna
,
H.
Hagemann
,
D.
Haase
,
J.
Skibsted
,
C. M.
Jensen
, and
T. R.
Jensen
,
J. Phys. Chem. C
114
,
19540
(
2010
).
5.
I.
Lindemann
,
R. D.
Ferrer
,
L.
Dunsch
,
R.
Černý
,
H.
Hagemann
,
V.
D'Anna
,
Y.
Filinchuk
,
L.
Schultz
, and
O.
Gutfleisch
,
Faraday Discuss.
151
,
231
(
2011
).
6.
P.
Schouwink
,
V.
D'Anna
,
M. B.
Ley
,
L. M. L.
Daku
,
B.
Richter
,
T. R.
Jensen
,
H.
Hagemann
, and
R.
Černý
,
J. Phys. Chem. C
116
,
10829
(
2012
).
7.
T.
Jarón
and
W.
Grochala
,
Dalton Trans.
40
,
12808
(
2011
).
8.
D.
Ravnsbæk
,
Y.
Filinchuk
,
Y.
Cerenius
,
H. J.
Jakobsen
,
F.
Besenbacher
,
J.
Skibsted
, and
T. R.
Jensen
,
Angew. Chem. Int. Ed.
48
,
6659
(
2009
).
9.
R.
Černý
,
K. C.
Kim
,
N.
Penin
,
V.
D'Anna
,
H.
Hagemann
, and
D. S.
Sholl
,
J. Phys. Chem. C
114
,
19127
(
2010
).
10.
D. B.
Ravnsbæk
,
C.
Frommen
,
D.
Reed
,
Y.
Filinchuk
,
M.
Sørby
,
B. C.
Hauback
,
H.
Jakobsen
,
D.
Book
,
F.
Besenbacher
,
J.
Skibsted
, and
T.
Jensen
,
J. Alloys Compd.
509
,
S698
(
2011
).
11.
L.
Schlapbach
and
A.
Züttel
,
Nature (London)
414
,
353
(
2001
).
12.
R.
Černý
,
G.
Severa
,
D. B.
Ravnsbæk
,
Y.
Filinchuk
,
V.
D'Anna
,
H.
Hagemann
,
D.
Haase
,
C. M.
Jensen
, and
T. R.
Jensen
,
J. Phys. Chem. C
114
,
1357
(
2010
).
13.
L. W.
Huang
,
O.
Elkedim
, and
X.
Li
,
J. Alloys Compd.
536
,
S546
(
2012
).
14.
K. C.
Kim
,
J. Chem. Phys.
137
,
084111
(
2012
).
15.
K. C.
Kim
,
Int. J. Quantum Chem.
113
,
119
(
2013
).
16.
S. V.
Alapati
,
J. K.
Johnson
, and
D. S.
Sholl
,
J. Phys. Chem. C
111
,
1584
(
2007
).
17.
S. V.
Alapati
,
J. K.
Johnson
, and
D. S.
Sholl
,
Phys. Chem. Chem. Phys.
9
,
1438
(
2007
).
18.
Nist database, see http://webbook.nist.gov.
19.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
20.
W.
Kohn
and
L.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
21.
S.
Goedecker
,
J. Chem. Phys.
120
,
9911
(
2004
).
22.
M.
Amsler
and
S.
Goedecker
,
J. Chem. Phys.
133
,
224104
(
2010
).
23.
P. E.
Blöchl
,
Phys. Rev. B
50
,
17953
(
1994
).
24.
G.
Kresse
and
J.
Hafner
,
Phys. Rev. B
47
,
558
(
1993
).
25.
G.
Kresse
, “
Ab initio Molekular Dynamik für flüssige Metalle
,” Ph.D. thesis,
Technische Universität Wien
,
1993
.
26.
G.
Kresse
and
J.
Furthmüller
,
J. Comput. Mater. Sci.
6
,
15
(
1996
).
27.
G.
Kresse
and
J.
Furthmüller
,
Phys. Rev. B
54
,
11169
(
1996
).
28.
H. J.
Monkhorst
and
J. D.
Pack
,
Phys. Rev. B
13
,
5188
(
1976
).
29.
W.
Hellmann
,
R. G.
Hennig
,
S.
Goedecker
,
C. J.
Umrigar
,
B.
Delley
, and
T.
Lenosky
,
Phys. Rev. B
75
,
085411
(
2007
).
30.
S.
Roy
,
S.
Goedecker
,
M. J.
Field
, and
E.
Penev
,
J. Phys. Chem. B
113
,
7315
(
2009
).
31.
K.
Bao
,
S.
Goedecker
,
K.
Koga
,
F.
Lançon
, and
A.
Neelov
,
Phys. Rev. B
79
,
041405
(
2009
).
32.
A.
Willand
,
M.
Gramzow
,
S. A.
Ghasemi
,
L.
Genovese
,
T.
Deutsch
,
K.
Reuter
, and
S.
Goedecker
,
Phys. Rev. B
81
,
201405
(
2010
).
33.
S.
De
,
A.
Willand
,
M.
Amsler
,
P.
Pochet
,
L.
Genovese
, and
S.
Goedecker
,
Phys. Rev. Lett.
106
,
225502
(
2011
).
34.
M.
Amsler
,
J. A.
Flores-Livas
,
L.
Lehtovaara
,
F.
Balima
,
S. A.
Ghasemi
,
D.
Machon
,
S.
Pailhès
,
A.
Willand
,
D.
Caliste
,
S.
Botti
,
A. S.
Miguel
,
S.
Goedecker
, and
M. A. L.
Marques
,
Phys. Rev. Lett.
108
,
065501
(
2012
).
35.
J. A.
Flores-Livas
,
M.
Amsler
,
T. J.
Lenosky
,
L.
Lehtovaara
,
S.
Botti
,
M. A. L.
Marques
, and
S.
Goedecker
,
Phys. Rev. Lett.
108
,
117004
(
2012
).
36.
M.
Amsler
,
J. A.
Flores-Livas
,
T. D.
Huan
,
S.
Botti
,
M. A. L.
Marques
, and
S.
Goedecker
,
Phys. Rev. Lett.
108
,
205505
(
2012
).
37.
T. D.
Huan
,
M.
Amsler
,
V. N.
Tuoc
,
A.
Willand
, and
S.
Goedecker
,
Phys. Rev. B
86
,
224110
(
2012
).
38.
T. D.
Huan
,
M.
Amsler
,
M. A. L.
Marques
,
S.
Botti
,
A.
Willand
, and
S.
Goedecker
,
Phys. Rev. Lett.
110
,
135502
(
2013
).
39.
A.
Togo
,
F.
Oba
, and
I.
Tanaka
,
Phys. Rev. B
78
,
134106
(
2008
).
40.
K.
Parlinski
,
Z. Q.
Li
, and
Y.
Kawazoe
,
Phys. Rev. Lett.
78
,
4063
(
1997
).
41.
L. G.
Hector
 Jr.
,
J. F.
Herbst
,
W.
Wolf
,
P.
Saxe
, and
G.
Kresse
,
Phys. Rev. B
76
,
014121
(
2007
).
42.
J. F.
Herbst
,
L. G.
Hector
 Jr.
, and
W.
Wolf
,
Phys. Rev. B
82
,
024110
(
2010
).
43.
A.
Bil
,
B.
Kolb
,
R.
Atkinson
,
D. G.
Pettifor
,
T.
Thonhauser
, and
A. N.
Kolmogorov
,
Phys. Rev. B
83
,
224103
(
2011
).
44.
V.
Ozolins
,
E. H.
Majzoub
, and
C.
Wolverton
,
Phys. Rev. Lett.
100
,
135501
(
2008
).
45.
J.
Voss
,
J. S.
Hummelshøj
,
Z.
Łodziana
, and
T.
Veege
,
J. Phys. Condens. Matter
21
,
012203
(
2009
).
46.
B.
Dai
,
D. S.
Sholl
, and
J. K.
Johnson
,
J. Phys. Chem. C
112
,
4391
(
2008
).
47.
Y.
Filinchuk
,
R.
Černý
, and
H.
Hagemann
,
Chem. Mater.
21
,
925
(
2009
).
48.
M.
Dion
,
H.
Rydberg
,
E.
Schroder
,
D. C.
Langreth
, and
B. I.
Lundqvist
,
Phys. Rev. Lett.
92
,
246401
(
2004
).
49.
T.
Thonhauser
,
V. R.
Cooper
,
S.
Li
,
A.
Puzder
,
P.
Hyldgaard
, and
D. C.
Langreth
,
Phys. Rev. B
76
,
125112
(
2007
).
50.
G.
Roman-Perez
and
J. M.
Soler
,
Phys. Rev. Lett.
103
,
096102
(
2009
).
51.
T. D.
Huan
,
M.
Amsler
,
R.
Sabatini
,
V. N.
Tuoc
,
L. B.
Nam
,
L. M.
Woods
,
N.
Marzari
, and
S.
Goedecker
,
Phys. Rev. B
88
,
024108
(
2013
).
52.
K.
Lee
,
É. D.
Murray
,
L.
Kong
,
B. I.
Lundqvist
, and
D. C.
Langreth
,
Phys. Rev. B
82
,
081101
R
(
2010
).
53.
See the supplementary material at http://dx.doi.org/10.1063/1.4869194 for additional information reported in this work.
54.
J. P.
Perdew
,
A.
Ruzsinszky
,
G. I.
Csonka
,
O. A.
Vydrov
,
G. E.
Scuseria
,
L. A.
Constantin
,
X.
Zhou
, and
K.
Burke
,
Phys. Rev. Lett.
100
,
136406
(
2008
).
55.
S.
Grimme
,
J. Comput. Chem.
27
,
1787
(
2006
).
56.
A.
Tkatchenko
and
M.
Scheffler
,
Phys. Rev. Lett.
102
,
073005
(
2009
).
57.
T.
Bučko
,
S.
Lebègue
,
J.
Hafner
, and
J. G.
Ángyán
,
Phys. Rev. B
87
,
064110
(
2013
).
58.
T.
Bučko
, private communication (
2013
).
59.
In a plane-wave DFT code like vasp, the XC energies are computed on a discrete grid in the real space, thereby breaking the translational invariance and leading to an error of ∼0.3 THz (10 cm−1) in the phonon frequency. This error is generally larger with GGA than with LDA because GGA functionals vary more strongly in the real space. In this work, phonon spectrum with LDA has no imaginary mode, clearly indicating that the very small imaginary frequencies shown for the C2221 structure in Fig. 1 are originated from the translational symmetry breaking. Discussions (by Stefano de Gironcoli, June 2008) on this problem can be found elsewhere, e.g., in User's Guide for the PHonon package (QUANTUM ESPRESSO, VERSION 5.0.2).
60.
W. G.
Schmidt
,
F.
Bechstedt
, and
G. P.
Srivastava
,
Phys. Rev. B
52
,
2001
(
1995
).
61.
T.
Yildirim
,
O.
Gülseren
,
J. W.
Lynn
,
C. M.
Brown
,
T. J.
Udovic
,
Q.
Huang
,
N.
Rogado
,
K. A.
Regan
,
M. A.
Hayward
,
J. S.
Slusky
,
T.
He
,
M. K.
Haas
,
P.
Khalifah
,
K.
Inumaru
, and
R. J.
Cava
,
Phys. Rev. Lett.
87
,
037001
(
2001
).
62.
J.
Rodríguez-Carvajal
,
Physica B
192
,
55
(
1993
).
63.
W.
Ostwald
,
Z. Phys. Chem.
22
,
289
(
1897
).
66.
K.
Momma
and
F.
Izumi
,
J. Appl. Crystallogr.
41
,
653
(
2008
).

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