1

Study of Ozone in Tribhuvan University, Kathmandu, Nepal

Prof. S. GurungCentral Department of Physics,

Tribhuvan University, Kathmandu, Nepal

2Country of the Mt Everest

3View of the Mt Everest

4

5

6Central Department of Physics, Kathmandu

7

8

9

10Dr. Ken Lamb Calibrating Brewer

11

12Dr. Arne Dahlback

at CDP, Kathmandu

13

14

15

16

Data/ Years

Production Consumption OMI Average O3 in DU

Sunspot

1992 11348 15657 269 94

1993 12661 13063 257 54

1994 21946 20760 266 29

1995 37755 34192 - 17

1996 40574 33745 247 8

1997 45517 35968 262 21

1998 28020 22409 266 64

1999 22732 19392 258 93

2000 270 119

2001 269 111

2002 263 104

2003 265 64

2004 263 40

2005 271 32

17

18

Comparison Between Brewer and OMI data 2002

Months Brewer DU OMI DU

January 252.4 242

February 265 251

March 284.3 277

April 282.9 272

May 290.7 278

June 281.9 281

July 283.5 270

August 276.2 267

September 273.3 261

October 274.5 260

November 260.9 250

December 255.5 243

19

Comparison between Brewer and OMI data 2002

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8 9 10 11 12

Months

Brewer

OMI

Ozo

ne in

DU

20

21

Group Memebers

•

Prof. D.R. Mishra

(Group Leader)•

Prof. M.M. Aryal

•

Prof. S. Gurung•

Dr. N.P. Adhikari

•

Mr. N. Subedi

First-Principles study of Ozone

22

First-Principles study of Ozone

•

ab initio –

does not use empirical information (except for fundamental constants), may not be exact!

•

In spite of necessary approximations, its successes and failures are more or less predictable

23

•

Approximations (solving Schroedinger

Equation (SE)):

•

Time independence : Stationary states

•

Neglect of relativistic effects

•

Born-Oppenheimer approximation

•

Orbital approximation: Electrons are confined to certain regions of space

ab initio : an overview

(contd…)

24

ab initio : an overview

(contd…)

•

Hartree-Fock SCF Method:•

SE for an electron i in the field of other electrons and nuclei k is [Blinder(1965)]:

22

22

2ћ ( ) (

1

ћ ( )2

)2 |

()

|

( () )

i kk

k

kk

i j i

ie ik

j

k l

k l kl

im

Z

Zi e im

Ze ier

E iir

r

Retaining 1st, 3rd

and 4th

terms one gets “HF equation”.

0

H E

OR,

25

•

Hartree-Fock SCF Method:

Independent particle approximation

ab initio : an overview

(contd…)

*22 2

1

*2

1

( ) ( )ћ ( ) ( ) ( )2 | | | |

( ) ( ) ( ) ( )| |

i

j

j

Nj

jj si j i j

N

js i j

Z j ji e i e d im

j je d i E i

rr R r r

rr r

Exchange

Coulomb

26

•

HF SCF Method:

•

Advantages:

Variational, computationally efficient

•

Limitations:

Neglect of correlation energy

•

Correlations are important even though it is ~1% of the total energy of a molecule (Cramer (2004))

•

Correlations are taken into account by CI, MP, DFT etc.

ab initio : an overview(contd…)

27

•

Perturbation method (MP):

The difference between the Fock

operator and exact Hamiltonian

can be considered as a perturbation

•

Lowest level of perturbation is 2nd

order

•

Speed

–

of the same order of magnitude as HF

•

Limitation:

Not variational, the correlation energy could be overcorrected

ab initio : an overview

(contd…)

28

•

Configuration Interaction (CI):

Uses wave function which is a linear combination of the HF determinant and determinants from excitations of electrons

•

Variational

and full CI is exact

•

Computationally expensive and works only for small systems

ab initio : an overview

(contd…)

29

•

Density functional theory (DFT):

The dynamical correlation effects due to electrons moving out of each other’s way as a result of the coulomb repulsion between them are accounted for

•

Energy is computed with density of electrons

ab initio : an overview

(contd…)

30

ab initio : an overview

(contd…)

•

DFT: Many-body system Hamiltonian can be constructed only from the density of electrons (ρ) and their positions and atomic number of the nuclei

22 ( )ћ [ ( )]

2 | | | |i

j jj xc

j i j i

ZH e d V

m

j

rr r

r R r r

In principle, it’s exact but in practice one must rely on approximations of exchange correlation functional

Exchange-Correlation Functional

31

•

LDA

–

Local density approximation

•

LSDA

–

Local spin density approximation

•

GGA

–Genaralized

gradient approximation

•

Hybrid

–

MPW1PW91, B3LYP (better than others ? depends upon system)

•

Present work

– MPW1PW91

ab initio : an overview

(contd…)

32

•

Basis set : Compromise between accuracy and computational cost

•

Gaussian 98 set of programs

•

Basis set convergence, 6-311G**(* refers to the inclusion of polarization functions)

•

Convergence : Energy -10-8

a.u., •

Maximum displacement –

0.0018 a.u.

Maximum force –

0.0045 a.u.

ab initio : an overview

(contd…)

33

Results and discussion

•

Oxygen atom :Triplet state is more stable than the singlet state

Energy difference = 3.46 eV (HF)=2.63 eV (QCISD)= 3.00 eV (DFT)

Ground state energy (in a.u.);

-74.805 (HF) , -74.918 (HF+MP2), -74.931 (QCISD),-75.085 (DFT),

-75.113 (Experimental) [Thijsen(2001)]

Results of present work agree within 1% to the experimental value

Correlation energy = -3.429 eV in the QCISD approximation

Basis set 6-311G**

Basis set 6-311G**

34

Results and discussion

•

Oxygen molecule :

Triplet state is more stable than the singlet state

Energy difference = 2.31 eV (HF) = 1.62 eV (QCISD)= 1.78 eV (DFT)

Basis set 6-311G**

35

Results and discussion

Parameters Levels of Calculation

Estimated values

Experimental valuesa

Bond length (Ǻ)

HF 1.157 (4%) 1.21HF+MP2 1.224 (1%)QCISD 1.190 (2%)DFT 1.193 (1%)

Binding Energy (eV)

HF 1.35 (74%) 5.21HF+MP2 5.10 (2%)QCISD 3.81 (27%)DFT 5.17 (<1%)

Oxygen moleculeBasis set 6-311G**

a

Experimental data are from Levine(2003) Mainali(2004)

36

•

Ozone molecule:

•

Singlet state is more stable than the triplet state

Energy difference

=2.01 eV (HF+MP2)=1.11 eV (QCISD)=0.92 eV (DFT)= 0.36 eV (HF)

Basis set 6-311G**

Results and discussion

37

•

Ozone molecule:

Bond length =1.26 ǺBond angle = 129.860

Total energy = -224.8774 a.u.

Bond length =1.39 ǺBond angle = 600

Total energy = -224.8415 a.u.

At QCISD/6-311G** level of approximation

Ground stateIsomeric excited state

Results and discussion

38

•

Ozone molecule:

Results and discussion

Ground state Isomeric excited state

Binding Energy= 99.40 kcal/mol (HF+MP2)= 30.44 kcal/mol (QCISD)= 98.28 kcal/mol (DFT)

No binding in the HF approximation

Binding Energy= 140.41 kcal/mol (HF+MP2) [~1%]= 53.31 kcal/mol (QCISD)= 128.26 kcal/mol (DFT)

No binding in the HF approximation

6-311G** basis set

Experimental value142.2 kcal/mol [Foresman

& Frisch (1996)]

39

Binding is due to correlation effects,

Similar results observed in solid halogens, H2

O2,

and B2

H[Aryal et al. (2004), Lamsal(2004), Khanal(2005) ]

Results and discussion

40

•

Dissociation energy:•

ΔE1=E(O)+E(O2

)-E(O3

) HF+MP2/6-31G**

O3

-> O2

+O

•

ΔE1= 104.31 KJ/mol (~1%) [105 KJ/mol, Baird (1995)]

•

ΔE2= 3E(O2

)-2E(O3

)

•

2O3

-> 3O2

+O•

[HF+MP2/6-31G**]

•

ΔE2 = -288.74 kcal/mol

Results and discussion

41

•

Ozone cluster : dimer of ozone (equilibrium configuration)

Binding Energy =2E(O3) -

E(O3-O3)

B.E. (DFT) = 0.0396 eV (4%), [0.0415 eV, Murai

et. al, (2003)]B.E. (HF) = 0.0321 eV

Results and discussion

Distance between central atoms =3.85 Ǻ

42

•

Ozone cluster : trimer

of ozone (equilibrium configuration)

B.E. (DFT) = 0.113 eV

Results and discussion

Binding Energy =3E(O3) -

E(O3-O3-O3)

B.E. (DFT) = 0.115 eV (~10%) B.E. (HF) = 0.106 eV (<3%)[0.104 eV, Murai

et al (2003)]

Central atoms form an equilateraltriangle having sides ~3.80 Ǻ

Central atoms are in a straight lineDistance between central consecutiveatoms ~ 3.5 Ǻ

43

•

Ozone cluster : quadramer

of ozone (equilibrium configuration)

B.E. (DFT) = 0.151 eVB.E. (HF) = 0.103 eV

Results and discussion

Central atoms form almost a parallelogram, with sides ~3.85 Ǻ

and ~4.2 ǺCentral atoms are in a straight line with distance between two consecutive atoms ~ 3.25 Ǻ

Binding Energy =4E(O3) -

E(O3-O3-O3-O3)

B.E. (DFT) = 0.073 eVB.E. (HF) = 0.062 eV

44

•

The present work shows that ozone cluster with four molecules of ozone is stable with binding energy of 0.151 eV

and the equilibrium geometry as shown below.

•

Previous studies (Murai

et al (2003)) were unable to obtain the equilibrium configuration of ozone clusters with n=4 or more.

•

We are studying the stability of ozone clusters with higher number (n≥5) of ozone molecules and interaction of ozone with halogens.

Conclusions

45

References

•

Aryal

MM, Mishra

DR, Byahut

SP, Paudyal

DD, Scheicher

RH, Jeong

J, Gaire

C and Das TP, “First principles investigation of binding and nuclear quadrupole interactions of Halogens molecules in solid halogens”, Paper presented at the March meeting of APS, Montreal, Canada, 2004

•

Blinder SM, Am. J. Phys., 33,431(1965)•

Cramer CJ, Essentials of Computational Chemistry, John wiley

& sons, Ltd., New York, 2002

•

Khanal

K, M.Sc. Dissertation(2005), Tribhuvan University, Kathmandu, Nepal

•

Lamsal

C, M.Sc. Dissertation(2004), Tribhuvan University, Kathmandu, Nepal

•

Levine IN, Quantum chemistry, Pearson education, Singapore, 2003•

Mainali

L, M.Sc. Dissertation (2004), Tribhuvan University, Kathmandu, Nepal

•

Murai

et. al, Ozone Science & Engineering, 25, 211(2003)•

Thijsen

JM, Computational Physics, Cambridge University, Press, Cambridge, 2001

46

Acknowledgment

We acknowledge Prof. T.P. Das (State University of New York, Albany, NY, USA)

for the support to carry out this research