1 Study of Ozone in Tribhuvan University, Kathmandu, Nepal Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal

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3 View of the Mt Everest

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6 Central Department of Physics, Kathmandu

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10 Dr. Ken Lamb Calibrating Brewer

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12 Dr. Arne Dahlback at CDP, Kathmandu

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16 Data/ Years ProductionConsumptionOMI Average O3 in DU Sunspot

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18 Comparison Between Brewer and OMI data 2002 MonthsBrewer DUOMI DU January February March April May June July August September October November December

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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)]: Retaining 1 st, 3 rd and 4 th terms one gets “HF equation”. 0 OR,

25 Hartree-Fock SCF Method: Independent particle approximation ab initio : an overview (contd…) 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 2 nd 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 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 a.u., Maximum displacement – a.u. Maximum force – 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.); (HF), (HF+MP2), (QCISD), (DFT), (Experimental) [Thijsen(2001)] Results of present work agree within 1% to the experimental value Correlation energy = eV in the QCISD approximation 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 ParametersLevels of Calculation Estimated values Experimental values a Bond length (Ǻ) HF (4%)1.21 HF+MP (1%) QCISD (2%) DFT (1%) Binding Energy (eV) HF 1.35 (74%)5.21 HF+MP (2%) QCISD 3.81 (27%) DFT 5.17 (<1%) Oxygen molecule Basis 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 Ǻ Bond angle = Total energy = a.u. Bond length =1.39 Ǻ Bond angle = 60 0 Total energy = a.u. At QCISD/6-311G** level of approximation Ground state Isomeric excited state Results and discussion

38 Ozone molecule: Results and discussion Ground state Isomeric excited state Binding Energy = kcal/mol (HF+MP2) = kcal/mol (QCISD) = kcal/mol (DFT) No binding in the HF approximation Binding Energy = kcal/mol (HF+MP2) [~1%] = kcal/mol (QCISD) = 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, H 2 O 2, and B 2 H [Aryal et al. (2004), Lamsal(2004), Khanal(2005) ] Results and discussion

40 Dissociation energy: ΔE1=E(O)+E(O 2 )-E(O 3 ) HF+MP2/6-31G** O 3 -> O 2 +O ΔE1= 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 = kcal/mol Results and discussion

41 Ozone cluster : dimer of ozone (equilibrium configuration) Binding Energy =2E(O3) - E(O3-O3) B.E. (DFT) = eV (4%), [ eV, Murai et. al, (2003)] B.E. (HF) = eV Results and discussion Distance between central atoms =3.85 Ǻ

42 Ozone cluster : trimer of ozone (equilibrium configuration) B.E. (DFT) = eV Results and discussion Binding Energy =3E(O3) - E(O3-O3-O3) B.E. (DFT) = eV (~10%) B.E. (HF) = 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 line Distance between central consecutive atoms ~ 3.5 Ǻ

43 Ozone cluster : quadramer of ozone (equilibrium configuration) B.E. (DFT) = eV B.E. (HF) = 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) = eV B.E. (HF) = eV

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