Usman presentation.ppt on density functional theory

Theoretical aspects of density functional theory

2. Theoretical Investigations of Structural
and Electronic Properties of Bi2MoO6
Usman Yasir
M.Phil Physics (2019-2021 Fall)

Supervisor:
Dr. Ijaz Mujtaba Ghauri
School of Physics
Minhaj University Lahore

3. Outline
Introduction
Purpose of Research work
Theoretical Background
About the Software
Results and Discussion
Conclusion

4. Introduction
Bismuth molybdates are the compounds having chemical formula Bi
2O
3·nMoO
3, where
n determines the nature of phase of the structure, e.g. n = 1 corresponds to γ -phase (γ-
Bi
2
MoO
6
), while n=2 and 3 correspond to β-phase (β-Bi
2
Mo
2
O
9
) and α-phase (α-
Bi
2Mo
3O
12) of bismuth molybdate.
The α and β phases have monoclinic structure, while γ-phase is orthorhombic.
The γ –phase (BMO) is unique one having a layered structure in which [Bi
2O
2]
2+
layers
sandwich the distorted MoO6 octahedrons.
Since, the structure of a compound has direct influence on its applications, so BMO
has been widely used in many fields including as a photo catalyst and as an electrode
material for supercapacitors & energy storage devices.

5.  To provide different
theoretical properties using Density
Functional Theory (DFT) including
structural, and electronic
properties.
 These properties of
materials are then used to fabricate
different devices like energy
storage devices, gas sensor devices,
and supercapacitors.
 Further, this theoretical
work will be helpful for the
experimentalists to develop
potential photo catalyst materials to
cope with environmental and
energy issues.
Purpose of Current Thesis Work

6. Schrödinger Equation
02
Hamiltonian of Many Body Problem
Kinetic
energy of
electrons
Electron
nuclei
interaction
Electron-
electron
interaction
Nucleus-
nucleus
interaction
Kinetic
energy of
Nucleus
Problem:
Schrodinger equation is too complex to solve
Solution:
Approximations

7. Born-Oppenheimer Approximation
The motion of the nuclei is comparably much slower than the motion of
the electrons in a system so that they can be considered to be
stationary
The reduced Hamiltonian is
Problem:
Schrodinger equation is still too complex to solve

8. Hartree Approximation
Draw Back in Hartree Approximation
The main criterion for a many fermions wave function i.e. anti-symmetry
principle. which states that “wave function must change sign if two
electrons are interchanged” i.e.
The functional form of system of many electron wave functions can be
computed in a product of single electron wave function
But in Hartree Approximation
The most convenient way to overcome this drawback is to
write the Ψ of a many electron system in terms of a Slater
determinant of single electron wave functions
Solution:

9. Slater Determinant
1.Fulfills the Pauli Exclusion Principle.
2.Exchanging any two rows or columns of a Slater
determinant changes the sign of Ψ, which leads to the anti-
symmetry principle.
3.Ψ will vanish for any two identical rows in a determinant.
No two identical electrons occupy the same spin orbitals
simultaneously

10. Kohn-Sham Equations
Vext (r) is the Coulomb interaction between an electron and the atomic nuclei,
VH (r) is the Hartree Coulomb interaction between electrons
VXC (r) is exchange correlation potential
Ground state electron density n (r) can be expressed by a set of equations which only
involves a system of N non-interacting electrons
Energy Functional
Kohn-Sham potential
Density of interacting system

11. Exchange-Correlation Functional
The LDA approximation is exact for a homogeneous electron gas.
In GGA, exchange and correlation energies include
electron density and gradient of electron density
Problem:
But the real electron densities are not typically homogeneous over the
entire system
Solution:

12. 03
Flow Chart of SCF cycle in Wein 2k

13. Structural Properties of BMO
Energy
Murnaghan’s
equation Volume

14. No Properties
Bi
2
MoO
6
This Work Other work
1
a
o
(Å) a=5.59;
b=16.40;
c=5.622;
a= 5.506;
b= 16.226;
c= 5.487;
2 V
0
(Å)
3 515.40 490.211
Table Of Structural Properties

15. Structure File

16. Electronic Properties of BMO
Band Structure

17. Total DOS

18. PDOS contribution of Bi-p states

19. PDOS contribution of Bi-s states

20. PDOS contribution of Mo-p states

21. PDOS contribution of Mo-s states

22. PDOS contribution of O-p states

23. PDOS contribution of O-s states

24. The structural and electronic properties of orthorhombic BMO have been
studied within the frame work of DFT based on the Generalized Gradient
Approximation.
The structural properties of BMO at ambient pressure such as lattice
constant, and cell volume are in good agreement with the previous
experimental and theoretical studies ensuring the validity of the results.
From our calculations it has been found that BMO is an anti
ferromagnetic material which is consistent with the experimental results.
The results showed that the BMO is direct band-gap semiconductor in
nature having potential applications to be used in optoelectronic devices
such as optical non-magnetic sensors.
Conclusion

25. Thank You