Journal of Modern Physics, 2012, 3, 1891-1894
http://dx.doi.org/10.4236/jmp.2012.312238 Published Online December 2012 (http://www.SciRP.org/journal/jmp)
Ab-Initio Structural Study of SrMoO3 Perovskite
Avinash Daga, Smita Sharma
Government Dungar College, Bikaner, India
Received August 10, 2012; revised September 27, 2012; accepted October 10, 2012
ABSTRACT
The equilibrium crystal structure parameter and bulk modulus of the SrMoO3 perovskite has been calculated with
ab-initio method based on density functional theory (DFT) using both local density approximation (LDA) and general-
ized gradient approximation (GGA). The corresponding total free energy along with its various components for SrMoO3
was obtained. The lattice parameter and bulk modulus calculated for SrMoO3 within LDA are 3.99 Å and 143.025 GPa
respectively whereas within GGA are 4.04 Å and 146.14 GPa respectively, both agree well with the available experi-
mental data. The total energy calculated within LDA and GGA is almost the same however lower results are obtained
for GGA. All calculations have been carried out using ABINIT computer code.
Keywords: Perovskite; DFT; LDA; GGA; ABINIT
1. Introduction
Crystal and electronic structures of solid materials are
crucial to understand and improve properties. Many
technological applications, including catalysis, micro-
electronics, substrates for growth of high Tc supercon-
ductors, etc., are based on thin films of ABO3 perovskite.
Until recently, 4d transition metal oxides (TMO) have
attracted less attention because they had the crystalline
defects and having more extended d-orbitals compared to
3d TMO. Yet, numerous studies have shown that this is
no longer the case for some promising TMO such as
molybdates. These oxides are observed to exhibit un-
conventional superconductivity [1] and research is going
on to understand the mechanism [2] of this new quantum
order due to strong electron-electron interaction. Pseudo
gap formation [3], metal-insulator transitions [4,5] and
high-voltage applications are the other significant prop-
erties which draw a considerable attention to 4d TMO.
Some related data were reported by daga et al. [6].
The density functional theory (DFT) is a good ap-
proach for the description of ground state properties of
metals, semiconductors, and insulators. The success of
this technique is that it has allowed us to better under-
stand materials and processes. It has deepened the inter-
pretation of experimental findings. We have used AB-
INIT computer code in order to perform first-principles
DFT calculations. This code is open source ab initio elec-
tronic structure calculation software and has been under
continuous development.
In the present study we calculated lattice constant,
bulk modulus and total energy along with its components
for SrMoO3 perovskite. The chosen perovskite has sim-
ple, cubic Pm3m symmetry.
2. Calculation Method
There are some approximations existing which permit the
calculation of certain physical quantities quite accurately.
In physics the most widely used and the simplest ap-
proximation is the local-density approximation (LDA). It
is based upon exact exchange energy for a uniform elec-
tron gas. The unknown part is exchange-correlation part
of the total-energy functional and it must be approxi-
mated. The functional depends only on the density at the
coordinate. Generalized gradient approximations (GGA)
are still local but also take into account the gradient of
the density at the same coordinate.
In this work, LDA and GGA density functionals are
considered for computation of lattice parameter, bulk
modulus and the total energy. The calculations are carried
out using numerical implementation of the formulation of
DFT; the ABINIT code, based on the DFT using plane
waves and pseudopotentials. Plane waves are used as a
basis set for the electronic wave functions. Many input
variables are needed to run the ABINIT code for the cal-
culations. The main input variables have been listed in
Table 1. “Spgroup” defines space group number of the
perovskite in the input file. “acell” parameter gives the
length scales by which dimensionless primitive transla-
tions are to be multiplied and is specified in Bohr atomic
units. We include input variables “ntypat” and “znucl”,
where “ntypat” gives the number of types of atoms and
“znucl” gives nuclear charge Z of the elements in order
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opyright © 2012 SciRes. JMP

A. DAGA, S. SHARMA 1892
Table 1. Main input variables used for calculation for
SrMoO3.
Input Variables LDA GGA
spgroup 221 221
acell (Bohr) 7.55 7.652
ntypat 3 3
znucl 38 42 8 38 42 8
natom 5 5
typat 1 2 3 3 3 1 2 3 3 3
xred 0.5 0.5 0.5 0.5 0.5 0.5
0.0 0.0 0.0 0.0 0.0 0.0
0.5 0.0 0.0 0.5 0.0 0.0
0.0 0.5 0.0 0.0 0.5 0.0
0.0 0.0 0.5 0.0 0.0 0.5
ixc 1 11
ecut (Hartree) 45 69.57
ntime 10 50
nstep 10 60
toldfe (Hartree) 1.0d-6 1.0d-6
to define the atom types.
Atoms in the unit cell can be described by using vari-
ables “natom” which gives the total number of atoms in
the unit cell; “typat” which is an array that gives an inte-
ger label to every atom in the unit cell to denote its type;
“xred” which gives the atomic locations within unit cell
in coordinates relative to real space primitive translations.
The array “typat” must agree with “xred” and “natom”.
Exchange correlation functional can be included in our
calculation by using “ixc” which has a different integer
value for LDA and GGA. The plane wave basis set can
be defined by “ecut” which is used for kinetic energy
cutoff which controls number of plane waves at given
k-points. We get a good convergence for the bulk total
energy calculation with the choice of cut-off energies at
45 Ha for LDA calculations and 69.57 Ha for GGA for
SrMoO3 4 × 4 × 4 Monkhorst-Pack mesh grid.
The number of self-consistent field cycles (SCF) are
defined by variables “nstep” which gives the maximum
number of SCF iterations and “toldfe” which sets a tol-
erance for absolute differences of total energy that reached
twice successively, will cause one SCF cycle to stop.
Apart from these variables input files also include vari-
ables for optimization of the lattice parameters and vari-
ables defining k-points grids.
3. Results & Discussions
This work analyses the overall performance of the local
density approximation and generalized gradient approxi-
mation in describing the structural properties of SrMoO3
perovskite. The overall accuracy of the calculated values
depends on both the accuracy of the potentials associated
with the exchange correlation and non additive kinetic
functionals as well as on these functionals themselves.
The computed values of total free energy and the differ-
ent components of the total energy for this perovskite
have been assembled in Table 2. The different compo-
nents of total energy are kinetic energy, Hartree energy,
exchange and correlation (XC) energy, Local pseudopo-
tential energy, Non-local pseudopotential energy, local
pseudopotential “core correction” (PspCore) energy and
Ewald energy. On average, LDA total free energy and its
components are similar to the GGA ones. But viewing
precisely both the LDA total energy and its components
are all smaller in absolute magnitude than the corre-
sponding calculated values in GGA.
In Table 3, it is observed that, near the nucleus, the
LDA density is too small while GGA gives an increased
charge density due to the lower value at short distances.
This increase in the GGA density results in an increase in
the magnitude of all the components of the total energy.
Consequently, the GGA yields improvements not only in
Exc but also in other components of the total energy be-
cause of the exchange-correlation at the nucleus.
Lattice constant of the perovskite is calculated using a
series of total energy calculations. Energy versus lattice
constant curve is obtained from this calculation. The cor-
responding “acell” parameter for which minima of en-
ergy occurs is the lattice parameter for the perovskite.
The curves obtained using LDA and GGA are shown in
the Figures 1 and 2 respectively. The value of lattice
parameter within LDA is 3.9897 Å and within GGA is
4.0423 Å. Both the values calculated are in good agree-
ment with the experimental value 3.98 Å [6].
Figure 1. Total energy versus acell using LDA.
Figure 2. Total energy versus acell using GGA.

A. DAGA, S. SHARMA 1893
Table 2. Eight components of total free energy of SrMoO3.
Energy Components (Hartree) LDA GGA
Kinetic energy 4.320E+01 4.558E+01
Hartree energy 1.913E+01 2.022E+01
XC energy –1.278E+01 –1.310E+01
Loc.psp. energy –6.732E+01 –7.123E+01
NL psp. energy –2.060E+00 –2.352E+00
PspCore energy 5.007E+00 4.813E+00
Ewald energy –4.162E+01 –4.108E+01
Etotal (ev) –1.536E+03 –1.555E+03
Figure 3. B.E. versus atomic Vol. using LDA.
Figure 4. B.E. versus atomic Vol. using GGA.
Table 3. Maximum & minimum values of charge density along with their reduced coordinates for SrMoO3.
SrMO3 Max. I
[el/Bohr^3] Red. Coord Max. II [el/Bohr^3] Red. Coord Min. I [el/Bohr^3] Red. Coord Min. II [el/Bohr^3] Red. Coord
SrMoO3 9.9498E−01 0.5185 9.9498E−01 0.4815 1.2087E−06 0.5000 4.1731E−06 0.000
(LDA) 0.9444 0.9444 0.5000 0.000
0.9815 0.9815 0.5000 0.000
SrMoO3 1.08 0.5000 1.08 0.9556 3.9706E−07 0.5000 4.7765E−07 0.000
(GGA) 0.9556 0.5000 0.5000 0.000
0.9667 0.9667 0.5000 0.000
Bulk modulus for SrMoO3 perovskite can be obtained
by binding energy per atom versus atomic volume curves.
A quadratic polynomial fitting of the curves is then ob-
tained. From this polynomial, “c2” which is the coeffi-
cient of x2 in the quadratic equation is obtained. By using
the atomic volume and the calculated value of c2, we
obtained the bulk modulus for the perovskite. Binding
energy per atom versus atomic volume curves forSrMoO3
perovskite using LDA & GGA are shown in the Figures
3 and 4.
The computed value of Bulk modulus within LDA is
143.025 GPa and within GGA is 146.1381 GPa which is
in accordance with the reported value calculated by oth-
ers [7]. The maximum and minimum values of the charge
density for this perovskite along with their reduced coor-
dinates have been assembled in Table 3. The values are
slightly greater in case of GGA.
4. Conclusion
The structural properties of transition metal oxide,
SrMoO3, with cubic perovskite structure are studied us-
ing an ab-initio pseudopotential method using ABINIT
code using LDA & GGA. A detailed description of its
total free energy and its different components are given.
Maximum and minimum value of charge density has also
been provided which is helpful in knowledge of charge
accumulation in the unit cell of the considered perovskite.
It is found that both GGA and LDA functionals lead to a
reasonable description of the key parameters of the total
energy of SrMoO3 perovskite. The calculated energies
depend on both the accuracy of the potentials associated
with the exchange correlation and non additive kinetic
functionals as well as on these functionals themselves.
Both the total energy and its components have larger
values in GGA than in LDA, which is associated with the
calculated values of charge density that show the LDA
density is too small while GGA has an increased charge
density. This increase in the GGA density results in an
increase in the magnitude of all the components of the
total energy. Consequently, the GGA yields improve-
ments not only in Exc but also in other components of

A. DAGA, S. SHARMA 1894
the total energy.
On the other hand, quantities related to the single-par-
ticle eigenvalues are not improved in GGA relative to
LDA. On average, LDA lattice parameters and bulk
modulus agree better than the GGA ones. The LDA lat-
tice parameter is almost exactly similar to the experi-
mental data, whereas the GGA lattice parameter is some-
what overestimated. Similarly LDA bulk modulus is closer
to the reported values of bulk modulus for SrMoO3
perovskite as compared to GGA bulk modulus. This in-
dicates that the errors in the non additive kinetic energy
and exchange-correlation energy functionals and poten-
tials compensate better at the LDA than GGA level. Such
compensation can be explained in the LDA case by the
fact that the exchange and kinetic functionals use the
same approximation to one-particle density matrix. Un-
fortunately, a similar construction of a pair of functionals
based on the same approximation to one-particle density
matrix is not unique for gradient-dependent functional.
Lattice parameters and bulk modulus are found to com-
pare well with the available data in the literature also
show the relevance of this approach for the SrMoO3
perovskite.
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