Rajasekarakumar Vadapoo

S.No: 401-03-9023

Electronic Structure Theory HW# : 3

Oxygen Molecule- Using VASP

AIM:

To calculate the equilibrium distance between the oxygen atoms in the oxygen molecule by the following ways:

1) Manual change of the inter -atomic distance 2) Using the atomic structure relaxation.

INTRODUCATION:

In this calculation we use oxygen molecule to find out the magnetic moment and minimum energy in different environments. We used VASP-code for this calculation.

1) To find out the interatomic distance manually, we used three different parameters: a. symmetry on with spin off b. Symmetry off with spin off c. Symmetry off with spin on

2) To use the atomic structure relaxation, we have used six different parameters: a. Both atoms have 3 degrees of freedom and relaxed with spin on b. Both atoms have 3 degrees of freedom and relaxed with spin off and then a

static run with spin on c. Single atom fixed with another has 3 degrees of freedom d. Single atom fixed with another has 2 degrees of freedom e. Single atom fixed with another has degree of freedom only in c-direction f. Single atom fixed with another has degree of freedom only in a-direction

CALCULATIONS:

INPUT files:

Since we want to calculate the details for oxygen molecule, we have made a unit cell with sufficient vacuum around it, so that the interaction between each molecule would be negligible. We have used a unit cell with a single oxygen atom with a = b = 13 A0 and c = 14

Figure 1. Unit cell contains oxygen atom

A0 as shown in fig.1. and the corresponding POSCAR files are as shown below.

1) POSCAR: O

1.000000

13.000000 0.000000 0.000000

0.000000 13.000000 0.000000

0.000000 0.000000 14.000000

2

Direct

0.500000 0.500000 0.447143

0.500000 0.500000 0.552857

For atomic structure calculation to have no translation of the centre of mass we have used the following POSCAR with different atomic directions fixes as the cases comes.

O

1.000000

13.000000 0.000000 0.000000

0.000000 13.000000 0.000000

0.000000 0.000000 14.000000

2

Selective dynamics

Cartesian

0.500000 0.500000 0.447143 F F F

0.500000 0.500000 0.552857 T T T

~

2) KPOINTS:

We have used only one K-pt ( Gamma Pt.), since the unit cell is really big in the real space which makes the reciprocal state very small. The k-pt file used in the calculation as follows:

automatic k mesh

0

g

1 1 1

0.0 0.0 0.0

3) POTCAR:

POTCAR files would be the same since we have only oxygen for all the calculations.

4) INPUT:

We have used two different input files.

a) For manual change of atomic distance we used the following input file System = oxygen ISYM = 0 ISMEAR =0 LPLANE=.FALSE. NPAR=4 number of nodes to use LSCALU=.FALSE. do you have SCALAPACK NSIM=1 nodes grouping for efficiency

• We have used the flag ISYM= 0 for the symmetric off calculations and left to the default value for the symmetric on calculations. For the spin calculation addition of the above details we have included another flag ISPIN= 2

b) For Automatic atomic structure calculations we have used the following input file: System = oxygen ISMEAR =0 ISYM = 0 LPLANE=.FALSE. NPAR=4 number of nodes to use LSCALU=.FALSE. do you have SCALAPACK NSIM=1 nodes grouping for efficiency NSW = 400 number of steps for IOM

IBRION = 2 ionic relax: 0-MD 1-quasi-New 2-CG ISIF = 2 stress and relaxation IWAVPR = 11 prediction: 0-non 1-charg 2-wave 3-comb ISYM = 0 0-nonsym 1-usesym 2-fastsym ISPIN= 2

• We have used the default value for ISPIN for the calculations without spin

RESULTS AND DISCUSSION:

1) Manual change of interatomic distance:

We have done the calculation to find out the equilibrium distance for the oxygen molecule manually in 3 different ways and the results are as shown in figure.2. The corresponding details are shown in table.1.

Type Symmetry on -spin

Off

Symmetry off- spin off Symmetry off –spin on

Emin -8.82469 -8.82475 -9.8636

Inter atomic distance for min Energy

1.26 1.26 1.12

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

-10

0

10

20

30

40

Ene

rgy

(eV

)

Inter atomic distance (A0 )

symmetryon-spin off symmetryoff-spin off symmetry off-spinon

Figure.2. Energy Vs Inter atomic distance

Table.1. Minimam Energy position for manually

changed interatomic distances.

From fig.2, we infer that there is no difference between the symmetry on-spin off & symmetry off-spin off calculations both gave the minimum energy at around -8.824 eV @ interatomic distance of 1.26 A0. Among the three related calculations the one with symmetry off-

spin on calculations gave a low energy than all which is -9.8636 @1.12 interatomic distance. And this is the most stable one.

Fig.3. shows the magnetization of the symmetry off – spin on case for different atomic distance. All other cases spin is off, so the magnetization is zero. Fig.3 shows some anomaly of magnetization at two different inter atomic distances and for all other it gave the value of 2 Bohr magnetron.

2) Atomic structure relaxation:

The atomic structure relaxation with fixing the degrees of freedom of atoms is shown in table.2. Among all the cases of calculations carried out the one which allowed to have 3 degrees of freedom for both the atoms in the oxygen molecule is the most stable one with the Emin @ -9.863440 eV and all other cases are less stable but the one with single atom fixed and the other

Properties

Both atoms have 3 degrees of freedom with spin on

Both atoms have 3 degrees of freedom relaxed without spin then static run with spin on

Single atom fixed with another has 3 degres of freedom

Single atom fixed with another has 2 degrees of freedom

Single atom fixed and the other has freedom of motion only in c-direction

Single atom fixed and the other has freedom of motion only in a-direction

Emin (eV)

-9.863440

-9.862970 -9.859520 -9.859520 -9.859520 3865.811354

Magnetization

2 2 2 2 2 3.9994

Table. 2. Atomic structure relaxation with fixing the degrees of freedom of atoms

Figure.3. magnetization Vs Inter atomic

distance

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

-4

-3

-2

-1

0

1

2

3

4

mag

netiz

atio

n (B

ohr

mag

neto

n)

atomic distance (Ao)

symmetry off-spin on

has the degree of freedom only in a- direction shown highly unstable with the energy of 3865.811354 eV. In the case of magnetization all the cases have the value of 2 Bohr magneton except the highly unstable one has a value of 3.9994 Bohr magneton.

CONCLUSION:

We have successfully carried out the ab-initio calculations of oxygen molecule with VASP-code to find the Energy minimal position mainly by two different ways manually and by atomic structure relaxation. The results show that for the oxygen molecule the calculations with spin and without spin gives different energy minimal positions. The one with spin gives the most stable one. The manually calculated with spin on and symmetry off has the almost same energy (-9.863 eV) with the one in the atomic structure calculation carried out on the case where both the atoms have complete degrees of freedom which are the most stable ones. In the case of magnetic properties all the calculations done by atomic structure calculations have the magnetization of 2 Bohr magneton except the most unstable one having the value of 3.9994 Bohr magneton.