Study of Ozone in Tribhuvan University, Kathmandu, Nepal Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal 1
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Central Department of Physics, Kathmandu 6
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Dr. Ken Lamb Calibrating Brewer 10
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Dr. Arne Dahlback at CDP, Kathmandu 12
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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 16
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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 18
Comparison between Brewer and OMI data 2002 350 Ozone in DU 300 250 200 Brewer 150 OMI 100 50 0 1 2 3 4 5 6 7 8 9 10 11 12 Months 19
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First-Principles study of Ozone Group Memebers Prof. D.R. Mishra (Group Leader) Prof. M.M. Aryal Prof. S. Gurung Dr. N.P. Adhikari Mr. N. Subedi 21
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 22
ab initio : an overview (contd ) 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 23
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)]: OR, 2 ћ ћ Z i e i) i 2 m e 2 e i j 2 2 k () () i ( k 2mk k k i rik 0 1 2 ZkZl ( i) e ( i) E ( i) r r ij H E k l kl Retaining 1 st, 3 rd and 4 th terms one gets HF equation. 24
ab initio : an overview (contd ) Hartree-Fock SCF Method: Independent particle approximation * Z N 2 j 2 j j j ri R j 1 s ri rj 2 ћ ( ) ( ) () () () i i e i e drj i 2 m ( j) ( j) N * 2 e drj i E i 1 s ri rj j () () j Coulomb Exchange 25
ab initio : an overview (contd ) 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. 26
ab initio : an overview (contd ) Perturbation method (MP): The difference between the Fock operator and exact Hamiltonian can be considered as a perturbation Lowest level of perturbation is 2 nd order Speed of the same order of magnitude as HF Limitation: Not variational, the correlation energy could be overcorrected 27
ab initio : an overview (contd ) 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 28
ab initio : an overview (contd ) 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 29
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 Exchange-Correlation Functional 2 ћ Z ( ) 2 j r j H e dr i j V 2 m j ri R j ri rj xc [ ( r)] In principle, it s exact but in practice one must rely on approximations of exchange correlation functional 30
ab initio : an overview (contd ) 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 31
ab initio : an overview (contd ) 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. 32
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), Basis set 6-311G** Basis set 6-311G** -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 33
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** 34
Results and discussion Oxygen molecule Basis set 6-311G** Parameters Levels of Calculation Estimated values Experimental values a Bond length (Ǻ) HF 1.157 (4%) 1.21 HF+MP2 1.224 (1%) QCISD 1.190 (2%) DFT 1.193 (1%) Binding Energy (ev) HF 1.35 (74%) 5.21 HF+MP2 5.10 (2%) QCISD 3.81 (27%) DFT 5.17 (<1%) a Experimental data are from Levine(2003) Mainali(2004) 35
Results and discussion 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** 36
Results and discussion Ozone molecule: Ground state Isomeric excited state Bond length =1.26 Ǻ Bond angle = 129.86 0 Total energy = -224.8774 a.u. Bond length =1.39 Ǻ Bond angle = 60 0 Total energy = -224.8415 a.u. At QCISD/6-311G** level of approximation 37
Results and discussion Ozone molecule: Ground state Isomeric excited state 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 Binding Energy = 99.40 kcal/mol (HF+MP2) = 30.44 kcal/mol (QCISD) = 98.28 kcal/mol (DFT) No binding in the HF approximation 6-311G** basis set Experimental value142.2 kcal/mol [Foresman & Frisch (1996)] 38
Results and discussion Binding is due to correlation effects, Similar results observed in solid halogens, H 2 O 2, and B 2 H [Aryal et al. (2004), Lamsal(2004), Khanal(2005) ] 39
Results and discussion Dissociation energy: ΔE1=E(O)+E(O 2 )-E(O 3 ) HF+MP2/6-31G** O 3 -> O 2 +O ΔE1= 104.31 KJ/mol (~1%) [105 KJ/mol, Baird (1995)] ΔE2= 3E(O 2 )-2E(O 3 ) 2O 3 -> 3O 2 +O [HF+MP2/6-31G**] ΔE2 = -288.74 kcal/mol 40
Results and discussion Ozone cluster : dimer of ozone (equilibrium configuration) Distance between central atoms =3.85 Ǻ 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 41
Results and discussion Ozone cluster : trimer of ozone (equilibrium configuration) Central atoms form an equilateral triangle having sides ~3.80 Ǻ Central atoms are in a straight line Distance between central consecutive atoms ~ 3.5 Ǻ 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)] B.E. (DFT) = 0.113 ev 42
Results and discussion Ozone cluster : quadramer of ozone (equilibrium configuration) 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) = 0.151 ev B.E. (HF) = 0.103 ev B.E. (DFT) = 0.073 ev B.E. (HF) = 0.062 ev 43
Conclusions 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. 44
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 45
Acknowledgment We acknowledge Prof. T.P. Das (State University of New York, Albany, NY, USA) for the support to carry out this research 46