Density functional theory calculations are often used to interpret experimental shifts in core level binding energies. Calculations based on gradient-corrected (GC) exchange-correlation functionals are known to reproduce measured core level shifts (CLS) of isolated molecules and metal surfaces with reasonable accuracy. In the present study, we discuss a series of examples where the shifts calculated within a GC-functional significantly deviate from the experimental values, namely the CLS of C 1s in ethyl trifluoroacetate, Pd 3d in PdO and the O 1s shift for CO adsorbed on PdO(101). The deviations are traced to effects of the electronic self-interaction error with GC-functionals and substantially better agreements between calculated and measured CLS are obtained when a fraction of exact exchange is used in the exchange-correlation functional.
REFERENCES
1.
E.
Lundgren
, G.
Kresse
, C.
Klein
, M.
Borg
, J. N.
Andersen
, M.
De Santis
, Y.
Gauthier
, C.
Konvicka
, M.
Schmid
, and P.
Varga
, Phys. Rev. Lett.
88
, 246103
(2002
).2.
M.
Todorova
, E.
Lundgren
, V.
Blum
, A.
Mikkelsen
, S.
Gray
, J.
Gustafson
, M.
Borg
, J.
Rogal
, K.
Reuter
, J. N.
Andersen
, and M.
Scheffler
, Surf. Sci.
541
, 101
(2003
).3.
J. N.
Andersen
and C.-O.
Almbladh
, J. Phys.: Condens. Matter
13
, 11267
(2001
).4.
M.
Birgersson
, C.-O.
Almbladh
, M.
Borg
, and J. N.
Andersen
, Phys. Rev. B
67
, 045402
(2003
).5.
O.
Takahashi
and L. G. M.
Pettersson
, J. Chem. Phys.
121
, 10339
(2004
).6.
A.
Alkauskas
, P.
Broqvist
, and A.
Pasquarello
, Phys. Status Solidi B
248
, 775
–789
(2011
).7.
A.
Alkauskas
and A.
Pasquarello
, Phys. Rev. B
84
, 125206
(2011
).8.
N.
Mårtensson
and A.
Nilsson
, J. Electron Spectrosc. Relat. Phenom.
75
, 209
(1995
).9.
E.
Pehlke
and M.
Scheffler
, Phys. Rev. Lett.
71
, 2338
(1993
).10.
J. N.
Andersen
, D.
Hennig
, E.
Lundgren
, M.
Methfessel
, R.
Nyholm
, and M.
Scheffler
, Phys. Rev. B
50
, 17525
(1994
).11.
A.
Pasquarello
, M. S.
Hybertsen
, G.-M.
Rignanese
, and R.
Car
, in Fundamental Aspects of Ultrathin Dielectrics on Si-based Devices
, NATO Science Series
Vol. 47
, edited by E.
Garfunkel
, E.
Gusev
, and A.
Vul
(Springer
, Netherlands
, 1998
), pp. 89
–102
.12.
S.
Lizzit
, A.
Baraldi
, A.
Groso
, K.
Reuter
, M. V.
Ganduglia-Pirovano
, C.
Stampfl
, M.
Scheffler
, M.
Stichler
, C.
Keller
, W.
Wurth
, and D.
Menzel
, Phys. Rev. B
63
, 205419
(2001
).13.
L.
Köhler
and G.
Kresse
, Phys. Rev. B
70
, 165405
(2004
).14.
J. G.
Wang
, W. X.
Li
, M.
Borg
, J.
Gustafson
, A.
Mikkelsen
, T. M.
Pedersen
, E.
Lundgren
, J.
Weissenrieder
, J.
Klikovits
, M.
Schmid
, B.
Hammer
, and J. N.
Andersen
, Phys. Rev. Lett.
95
, 256102
(2005
).15.
W.
Olovsson
, C.
Göransson
, T.
Marten
, and I. A.
Abrikosov
, Phys. Status Solidi B
243
, 2447
–2464
(2006
).16.
J.
Jaramillo
, G. E.
Scuseria
, and M.
Ernzerhof
, J. Chem. Phys.
118
, 1068
(2003
).17.
S. L.
Dudarev
, G. A.
Botton
, S. Y.
Savrasov
, C. J.
Humphreys
, and A. P.
Sutton
, Phys. Rev. B
57
, 1505
(1998
).18.
J. F.
Binder
, P.
Broqvist
, H.-P.
Komsa
, and A.
Pasquarello
, Phys. Rev. B
85
, 245305
(2012
).19.
L. O.
Paz-Borbón
, A.
Hellman
, and H.
Grönbeck
, J. Phys. Chem. C
116
, 3545
(2012
).20.
G.
Kresse
and J.
Furthmüller
, Comput. Mater. Sci.
6
, 15
(1996
).21.
G.
Kresse
and J.
Furthmüller
, Phys. Rev. B
54
, 11169
(1996
).22.
G.
Kresse
and J.
Hafner
, Phys. Rev. B
49
, 14251
(1994
).23.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
).24.
J. P.
Perdew
, M.
Ernzerhof
, and K.
Burke
, J. Chem. Phys.
105
, 9982
(1996
).25.
C.
Adamo
and V.
Barone
, J. Chem. Phys.
110
, 6158
(1999
).26.
P. E.
Blöchl
, Phys. Rev. B
50
, 17953
(1994
).27.
G.
Kresse
and D.
Joubert
, Phys. Rev. B
59
, 1758
(1999
).28.
H. J.
Monkhorst
and J. D.
Pack
, Phys. Rev. B
13
, 5188
(1976
).29.
J. D.
Pack
and H. J.
Monkhorst
, Phys. Rev. B
16
, 1748
(1977
).30.
A. R.
Williams
and N. D.
Lang
, Phys. Rev. Lett.
40
, 954
(1978
).31.
D.
Spanjaard
, C.
Guillot
, M.-C.
Desjonquères
, G.
Tréglia
, and J.
Lecante
, Surf. Sci. Rep.
5
, 1
(1985
).32.
C.
Nordling
, S.
Hagström
, and K.
Siegbahn
, Z. Phys.
178
, 433
(1964
).33.
P. S.
Bagus
, E. S.
Ilton
, and C. J.
Nelin
, Surf. Sci. Rep.
68
, 273
(2013
).34.
R.
Nyholm
, J. N.
Andersen
, U.
Johansson
, B. N.
Jensen
, and I.
Lindau
, Nucl. Instrum. Methods Phys. Res. A
467–468
, 520
(2001
).35.
N. M.
Martin
, M.
Van den Bossche
, H.
Grönbeck
, C.
Hakanoglu
, F.
Zhang
, T.
Li
, J.
Gustafson
, J. F.
Weaver
, and E.
Lundgren
, J. Phys. Chem. C
118
, 1118
(2014
).36.
J.
Knudsen
, N. M.
Martin
, E.
Grånäs
, S.
Blomberg
, J.
Gustafson
, J. N.
Andersen
, E.
Lundgren
, S.
Klacar
, A.
Hellman
, and H.
Grönbeck
, Phys. Rev. B
84
, 115430
(2011
).37.
S.
Klacar
, N. M.
Martin
, J.
Gustafson
, S.
Blomberg
, Z.
Liu
, S.
Axnanda
, R.
Chang
, E.
Lundgren
, and H.
Grönbeck
, Surf. Sci.
617
, 167
(2013
).38.
N. M.
Martin
, M.
Van den Bossche
, H.
Grönbeck
, C.
Hakanoglu
, J.
Gustafson
, S.
Blomberg
, M. A.
Arman
, A.
Antony
, R.
Rai
, A.
Asthagiri
, J. F.
Weaver
, and E.
Lundgren
, J. Phys. Chem. C
117
, 13510
(2013
).39.
K.
Siegbahn
and C.
Nordling
, ESCA, Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy
(Almqvist & Wiksell
, 1967
).40.
41.
M. E.
Defonsi Lestard
, M. E.
Tuttolomondo
, D. A.
Wann
, H. E.
Robertson
, D. W. H.
Rankin
, and A. B.
Altabef
, J. Raman Spectrosc.
41
, 1357
–1368
(2010
).42.
O.
Travnikova
, K. J.
Børve
, M.
Patanen
, J.
Söderström
, C.
Miron
, L. J.
Sæthre
, N.
Mårtensson
, and S.
Svensson
, J. Electron Spectrosc. Relat. Phenom.
185
, 191
(2012
).43.
R. F. W.
Bader
, Encyclopedia of Computational Chemistry
(John Wiley and Sons, Ltd.
, 2002
).44.
R.
Westerström
, M. E.
Messing
, S.
Blomberg
, A.
Hellman
, H.
Grönbeck
, J.
Gustafson
, N. M.
Martin
, O.
Balmes
, R.
van Rijn
, J. N.
Andersen
, K.
Deppert
, H.
Bluhm
, Z.
Liu
, M. E.
Grass
, M.
Hävecker
, and E.
Lundgren
, Phys. Rev. B
83
, 115440
(2011
).45.
N.
Seriani
, J.
Harl
, F.
Mittendorfer
, and G.
Kresse
, J. Chem. Phys.
131
, 054701
(2009
).46.
J.
Paier
, M.
Marsman
, K.
Hummer
, G.
Kresse
, I. C.
Gerber
, and J. G.
Ángyán
, J. Chem. Phys.
124
, 154709
(2006
).47.
P. O.
Nilsson
, J. Phys. C
12
, 1423
(1979
).48.
H.
Okamoto
and T.
Asô
, Jpn. J. Appl. Phys.
6
, 779
(1967
).49.
H.
Grönbeck
and M.
Odelius
, Phys. Rev. B
82
, 085416
(2010
).50.
In VASP, the core-excited PAW potential can be automatically generated from the provided PAW potential by removing the desired core electron. The other core electrons are in this approach kept frozen, which is justified as screening of the core hole by the other core electrons has little influence on the core-level shift.4,18
51.
Also the second moments of the valence charge density distribution close to the carbon nuclei were computed, in order to compare the degree of charge localization for the different functionals. The values of the second moments calculated with PBE (PBE0) are 0.513 (0.515), 0.525 (0.527), 0.544 (0.546), and 0.569 Å2 (0.571 Å2) for carbon atoms 1 till 4, respectively. The second moments are very similar in both functionals, which indicates that charge transfer, rather than charge localization, is the main result upon inclusion of the exact exchange.
52.
The experimental CLS of 1.6 eV is obtained with an admixture of 16% of Fock exchange.
53.
The binding energies within PBE0 are 1.38 eV and 0.60 eV for the atop and bridge positions, respectively.
54.
When the lateral dimension of the PdO(101) surface cell is increased to (4×2) and (6×3), the O 1s shift for CO adsorbed atop a threefold coordinated Pd atom, is increased to 3.19 eV and 3.23 eV. Thus, this particular CLS has a dependence on the concentration of core excited molecules. Note that the dependence on surface cell dimension does not affect the comparison between PBE and PBE0.
© 2014 Author(s).
2014
Author(s)
You do not currently have access to this content.
