Effects of strain, d-band filling and oxidation state on the bulk
electronic structure of cubic 3d perovskites
Sneha A. Akhade and John R. Kitchin*
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania
15213, USA
*Corresponding author, Email: jkitchin@andrew.cmu.edu
Supporting Information Available:
1. Comparison of DFT calculated lattice constants to experimental values.
2. Example of bulk electronic structure convergence with computational parameters.
3. Strain dependence of fractional band filling of bulk LaBO3 and SrBO3 systems
(where B = Sc, Ti, V, Cr, Mn, Fe, Co, Ni and Cu).
4. Effect of strain on the atom-projected density of states of the bulk LaBO3 and
SrBO3 systems calculated as ±5%, ±2.5% and 0% of the DFT equilibrium volume.
5. Defining the d-band based on the effect of high tensile strain on the atomprojected density of states of the bulk LaBO3 and SrBO3 structures.
6. Derivation of the rectangular band model used in this work.
Example of bulk electronic structure convergence with computational
parameters.
We performed a convergence study of the atom-projected density of states for k-point meshes in
the range of 222 to 888 for bulk LaMnO3. The results are shown below. The integral properties,
e.g. the d-band center, filling and d-band width, of the 666 and 888 are practically
indistinguishable from each other.
8×8×8
6×6×6
4×4×4
2×2×2
Figure S1 Atom-projected density of states (DOS) for the Mn d-orbital (blue line) and the O s, p-orbital
(green line) projections at different strains in the bulk LaMnO3 system using a plane-wave cutoff energy of 350 eV.
The convergence calculations were tested relative to the Monkhorst-Pack k-point mesh. The shaded grey area
indicates the occupied d-states up to the Fermi level (Ef).
Table 1. Convergence results of atom-projected density of states of bulk LaMnO3
relative to k-point sampling at the equilibrium volume.
2×2×2
4×4×4
6×6×6
8×8×8
Total # d-states
8.9
8.92
8.93
8.93
# occupied d-states
3.76
3.99
4.05
4.08
Fractional d-band filling
0.42
0.45
0.45
0.46
d-band center (eV)
0.01
-0.24
-0.26
-0.25
d-band width (eV)
2.67
2.7
2.73
2.73
Comparison of DFT calculated lattice constants to experimental
values
The DFT calculated lattice constants for the LaBO3 and SrBO3 bulk systems
employing a Monkhorst-Pack k-point grid of 6×6×6 and a plane-wave cutoff of 400
eV were in reasonable agreement with corresponding experimental values perovskites
with an absolute mean error calculated as 0.08 Å. This is depicted in Error! Reference
source not found. (
Table S 1).
4.10
DFT values
4.05
Parity line
DFT Values (Å)
4.00
LaRhO3
LaTiO3
3.95
LaScO3
SrTiO3
LaCrO3
LaNiO3
SrVO3
3.85
SrCrO3
3.80
SrCuO3
LaGaO3
3.90
LaAlO3
3.75
3.75
SrFeO3
SrCoO3
SrMnO3
3.80
3.85
LaVO3
LaMnO3
LaCoO3 LaFeO3
3.90
3.95
4.00
4.05
Experimental values (Å)
Figure S 1. Comparison of DFT lattice constants to experimental values.
Table S 1. Comparison between DFT lattice constants and Experimental values.
Perovskite
DFT values (Å)
LaAlO3
LaScO3
LaTiO3
LaVO3
LaCrO3
LaMnO3
LaFeO3
LaCoO3
LaNiO3
LaCuO3
SrTiO3
SrVO3
SrCrO3
SrMnO3
3.78
4.05
3.92
3.91
3.87
3.95
3.92
3.90
3.88
3.82
3.94
3.84
3.82
3.81
Experimental Values
(Å)
3.80
3.94
3.95
3.88
3.85
3.83
3.83
3.83
3.84
3.01
3.91
3.84
3.82
3.81
Absolute Error
(Å)
0.02
0.11
0.03
0.03
0.02
0.11
0.09
0.07
0.04
0.81
0.03
0.00
0.00
0.01
4.10
3.83
3.82
3.84
3.92
SrFeO3
SrCoO3
SrNiO3
SrCuO3
3.85
3.84
n/a
3.93
Average Error (Å) =
0.02
0.02
n/a
0.00
0.08
Strain dependent d-band filling
The d-band filling was calculated to be roughly constant for the bulk LaBO3 and SrBO3
perovskites for all strains as shown in Figure S 2.
(b)
1.2
LaScO3
LaCrO3
LaCoO3
1.0
LaTiO3
LaMnO3
LaNiO3
LaVO3
LaFeO3
LaCuO3
fractional d-band filling ratio (fd)
fractional d-band filling ratio (fd)
(a)
0.8
0.6
0.4
0.2
0.0
-5
-2.5
0
Strain ε (%)
2.5
5
1.2
SrTiO3
SrMnO3
SrNiO3
1.0
SrVO3
SrFeO3
SrCuO3
SrCrO3
SrCoO3
0.8
0.6
0.4
0.2
0.0
-5
-2.5
0
Strain ε (%)
2.5
5
Figure S 2. Strain dependence on the d-band filling of bulk LaBO3 and SrBO3 perovskites at ±5, ±2.5
and 0% of the DFT equilibrium volume.
Effect of strain on the atom-projected density of states results for bulk
LaBO3 and SrBO3 perovskites
The effect of strain on the bulk electronic structure for various LaBO3 and SrBO3 (where B =
Sc, Ti, V, Cr, Mn, Co, Ni and Cu) perovskites was computed using the atom-projected
density of states of the bulk 3d transition metal perovskites. The states were obtained using an
infinite cutoff radius and employed a Monkhorst-Pack grid of 6×6×6 and a plane-wave cutoff
of 400 eV. The d-band properties such as the d-band width (Wd) were evaluated using the
results illustrated in Figure S 3.
LaScO3
ɛ = +5%
ɛ = +2.5%
ɛ = 0%
ɛ = −2.5%
ɛ = −5%
LaTiO3
SrTiO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(d) LaVO3
(e) SrVO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(f) LaCrO3
(g) SrCrO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(h) LaMnO3
(i) SrMnO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(j) LaFeO3
(k) SrFeO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(l) LaCoO3
(m) SrCoO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(n) LaNiO3
(o) SrNiO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
(p) LaCuO3
(q) SrCuO3
ɛ = +5%
ɛ = +5%
ɛ = +2.5%
ɛ = +2.5%
ɛ = 0%
ɛ = 0%
ɛ = −2.5%
ɛ = −2.5%
ɛ = −5%
ɛ = −5%
Figure S 3. Atom-projected density of states (DOS) for the B d-orbital (blue line) and
the O s, p-orbital (green dots) projections at different strains in the bulk LaBO3 and
SrBO3 system using a 400 eV cutoff and a 6×6×6 Monkhorst-Pack k-point mesh. The
shaded grey area indicates the occupied d-states up to the Fermi level (Ef).
d-band evolution at high tensile strain on the atom-projected density
of states of the bulk LaBO3 and SrBO3 structures
The atom-projected density of states were computed at high tensile strain to study the effect
of strain on the shift and width of the d-band. At high tensile strain, a reduced overlap
between the d- and s,p-orbitals led to narrowing of the bands and consequently a high
concentration at the Fermi level. In addition, the d-orbital projection of the B atom was
computed alone to assess the effect of s,p-interaction and hybridization. Based on the analysis
the appropriate d-band was selected. The results of the atom-projected density of states
computed at high tensile strain are shown in Figure S 4 for the LaBO3 and Figure S 5 for the
SrBO3 perovskites.
LaScO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 5%
ɛ = 0%
LaTiO3
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 10%
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaVO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaCrO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 10%
ɛ = 5%
ɛ = 0%
LaMnO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaFeO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaCoO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaNiO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
LaCuO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 10%
ɛ = 5%
ɛ = 0%
Figure S 4. (1)Atom-projected density of states for the B d-orbital (blue line) and the O s, porbital (green dots) projections of LaBO3 bulk perovskites on the left. The red lines at varying
strain indicate the evolution of the d-band. (2) Atom-projected density of states for the
corresponding B d-orbital (blue) alone on the right. The above DOS calculations were calculated
at different tensile strains using 400 eV cutoff and a k-point grid of 6×6×6. The shaded grey area
indicates the occupied d-states up to the Fermi level (Ef).
SrTiO3
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
SrVO3
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
SrCrO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
SrMnO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 10%
ɛ = 5%
ɛ = 0%
SrFeO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 5%
ɛ = 0%
SrCoO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 30%
ɛ = 40%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 10%
ɛ = 5%
ɛ = 5%
ɛ = 0%
ɛ = 0%
SrNiO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 10%
ɛ = 5%
ɛ = 0%
SrCuO3
ɛ = 50%
ɛ = 50%
ɛ = 40%
ɛ = 40%
ɛ = 30%
ɛ = 30%
ɛ = 20%
ɛ = 20%
ɛ = 10%
ɛ = 5%
ɛ = 0%
ɛ = 10%
ɛ = 5%
ɛ = 0%
Figure S 5. (1)Atom-projected density of states for the B d-orbital (blue) and the O s, p-orbital
(green) projections of SrBO3 bulk perovskites on the left. The red lines at varying strain indicate
the evolution of the d-band. (2) Atom-projected density of states for the corresponding B dorbital (blue) alone on the right. The above DOS calculations were calculated at different tensile
strains using 400 eV cutoff and a k-point grid of 6×6×6. The shaded grey area indicates the
occupied d-states up to the Fermi level (Ef).
(a)
(b)
2.5
2.5
LaScO3
LaTiO3
LaVO3
LaCrO3
LaMnO3
LaFeO3
LaCoO3
LaNiO3
LaCuO3
1.5
1.0
0.5
0.0
0.0
2.0
d-band width (Wd)
d-band width (Wd)
2.0
1.5
SrTiO3
SrVO3
SrCrO3
SrMnO3
SrFeO3
SrCoO3
SrNiO3
SrCuO3
1.0
0.5
0.0
0.5
1.0
1.5
s,p-band width (Wp)
0.0
2.0
(c)
0.5
1.0
1.5
s,p-band width (Wp)
2.0
(d)
8
5
d-band center (Ed)
6
4
2
0
-2
SrTiO3
SrVO3
SrCrO3
SrMnO3
SrFeO3
SrCoO3
SrNiO3
SrCuO3
4
d-band center (Ed)
LaScO3
LaTiO3
LaVO3
LaCrO3
LaMnO3
LaFeO3
LaCoO3
LaNiO3
LaCuO3
3
2
1
0
-4
-8
-6
-4
s,p-band center (Ep)
-2
-1
-7
-5
-3
s,p-band center (Ep)
Figure S 6. Correlation between the d-band width and s, p-band width for (a) bulk LaBO3 and (b) bulk
SrBO3 structures at varying strain. Correlation between the d-band center and s, p-band center for
(c) bulk LaBO3 and (d) bulk SrBO3 structures at varying strain.
Rectangular band model derivation
In this work, we define the following quantities for the moments of the d-band:

Ed 

d
EdE


  dE
d


Wd 


d
( E  Ed ) 2 dE

  dE
d

We assume a rectangular band of height h that contains ten states, with a fractional filling
fd=Nelectrons/10 as shown below.
With some algebra one can show that:
Ed  0.5
(W12  W2 2 )
(W1  W2 )
and
the d-band width is simply defined by the band edges:
Wd  3/6(W1 -W2 ) .
The band edges are determined by the equations:
10  h(W1  W2 )
hW2
10
Assuming the constraint that the total number of states in the band and the band-filling does
fd 
not change with changes in band-width, this leads to the fact that the d-band center and width
are correlated by the following equation:
Wd  Ed
3
1
.
6 0.5  f d
Thus, for fd>0.5, the slope of the correlation should be negative, and for fd<0.5, the slope should be
positive. At fd=0.5, the d-band center is equal to zero, leading to 0/0. The width is then simply
defined to make fd=0.5 with the total number of states = 10.