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Study of Ozone in Tribhuvan University, Kathmandu, Nepal
Prof. S. GurungCentral Department of Physics,
Tribhuvan University, Kathmandu, Nepal
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Country of the Mt Everest
3View of the Mt Everest
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5
6Central Department of Physics, Kathmandu
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8
9
10Dr. Ken Lamb Calibrating Brewer
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12Dr. Arne Dahlback at CDP, Kathmandu
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14
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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
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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
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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 D
U
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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
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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
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• 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…)
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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)]:
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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 i
m
Ze ie
rE ii
r
r
Retaining 1st, 3rd and 4th terms one gets “HF equation”.
0
H E
OR,
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• 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 i
m
j je d i E i
rr R r r
rr r
Exchange
Coulomb
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• 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…)
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• 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…)
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• 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…)
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• 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…)
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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
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• 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…)
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• 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…)
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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**
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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**
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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)
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• 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
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• 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)]
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Binding is due to correlation effects,
Similar results observed in solid halogens, H2O2,and
B2H
[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
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• 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 equilateral triangle having sides ~3.80 Ǻ
Central atoms are in a straight lineDistance between central consecutive atoms ~ 3.5 Ǻ
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• 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 Ǻ
Central 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
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• 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
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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
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Acknowledgment
We acknowledge Prof. T.P. Das (State University of New York, Albany, NY, USA)
for the support to carry out this research