Rajasekarakumar VadapooHW:#2

Electronic structure theory.

Calculate the electronic structure of a single O atom

AIM:

Calculate the energy and magnetization of oxygen atom using VASP in the following different ways:

• Non-magnetic calculation• Magnetic calculation• Magnetic calculation without symmetry

INPUT files:

The 4 necessesary input files INCAR, KPOINTS, POSCAR,POTCAR along with the .pbs file to run VASP have been made.

The POTCAR file has the pseudo potential file of the oxygen atom. In our calcualtion we have used PAW-PBE pseudopotential. The automatic generated mesh of Gamma centered 2x2x2 kpts have been used, since there was a minimum of 4 kpts required for this calculation. The interaction of the atoms were calculated using the variation of unit cell size as shown in fig.1 and the unit cell of lattice parameter of 9 A0 have been selected for the calulations by setting the interaction between the oxygen atom to minimum in this way. The POSCAR made with oxygen atom at the middle of the cell with cubic lattice with a = 9A0 . The INCAR file has ISMEAR -5 for all the 4 calculations made. For magnetic calculation the flag ISPIN 2 used. For the magnetic without symmetry with the above two flags isym 0 was also used. The fourth calculation have been done to understand the utility of isym flag by changing the atomic position of the oxygen from 0.5 0.5 0.5 to 0.25 0.25 0.25 in the unit cell with isym default (on). RESULTS:

Fig. 1. The interaction energy of O-O with respect to the unit cell size.

1 2 3 4 5 6 7 8 9 10 11

-5

-4

-3

-2

-1

0

En

erg

y (e

V)

unit cell size (A0)

Non magnetic Magnetic with symmetry

Magnetic without symmetry( tag ISYM 0)

Magnetic without symmetry(change atom position in POSCAR)

Energy (eV) -0.005462 -1.517320 -1.889604 -1.517319Magnetic moment in Bohr Magnetron (μB)

--- 2.0001 1.9990 2.0001

Table.1. Energy and magnetic moments of oxygen atom at non magnetic, magnetic with symmetry, magnetic without symmetry and magnetic with shift of atom in the unit cell.

DISCUSSION:

The results shows that the magnetic without symmetry is the most stable one and the magnetic with symmetry is more stable than the non magnetic. The other one which we used the non center atom in the unit cell with the tag ISYM on, which is default in VASP gives almost similar energy as magnetic with symmetry but little less in the -5 th order.

The magnetic moment is larger for magnetic with symmetry (2.001) than magnetic without symmetry (1.999). In the case of change in position of atom from the center in the unit cell has the same magnetic moment as magnetic with symmetry, which has almost same energies leads to the conclusion that the change in position of oxygen atom within the unit cell didn't break the symmetry in our case. It might be due to shift in the position of a single atom in the unit cell would construct the symmetry when we make infinite crystal.

CONCLUSION:

In case of oxygen atom the magnetic without symmetry is the stable one than the other cases taken in our calculations.