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Study of Ozone in Tribhuvan University, Kathmandu, Nepal

Study of Ozone in Tribhuvan University, Kathmandu, Nepal. Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal. Country of the Mt Everest. View of the Mt Everest. Central Department of Physics, Kathmandu. Dr. Ken Lamb Calibrating Brewer.

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Study of Ozone in Tribhuvan University, Kathmandu, Nepal

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

  2. Country of the Mt Everest

  3. View of the Mt Everest

  4. Central Department of Physics, Kathmandu

  5. Dr. Ken Lamb Calibrating Brewer

  6. Dr. Arne Dahlback at CDP, Kathmandu

  7. Comparison Between Brewer and OMI data 2002

  8. 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

  9. 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

  10. 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

  11. 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, 0 Retaining 1st, 3rd and 4th terms one gets “HF equation”.

  12. ab initio : an overview(contd…) • Hartree-Fock SCF Method: Independent particle approximation Coulomb Exchange

  13. 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.

  14. 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 2nd order • Speed – of the same order of magnitude as HF • Limitation: Not variational, the correlation energy could be overcorrected

  15. 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

  16. 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

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

  18. 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

  19. 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.

  20. 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**

  21. 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**

  22. Results and discussion Oxygen molecule Basis set 6-311G** aExperimental data are from Levine(2003) Mainali(2004)

  23. 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**

  24. Results and discussion • Ozone molecule: Isomeric excited state Ground state Bond length =1.39 Ǻ Bond angle = 600 Total energy = -224.8415 a.u. Bond length =1.26 Ǻ Bond angle = 129.860 Total energy = -224.8774 a.u. At QCISD/6-311G** level of approximation

  25. Results and discussion • Ozone molecule: Isomeric excited state Ground 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)]

  26. Results and discussion Binding is due to correlation effects, Similar results observed in solid halogens, H2O2,andB2H [Aryal et al. (2004), Lamsal(2004), Khanal(2005) ]

  27. Results and discussion • 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

  28. 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

  29. Results and discussion • Ozone cluster : trimer of ozone (equilibrium configuration) Central atoms are in a straight line Distance between central consecutive atoms ~ 3.5 Ǻ Central atoms form an equilateral triangle having sides ~3.80 Ǻ Binding Energy =3E(O3) - E(O3-O3-O3) B.E. (DFT) = 0.113 eV B.E. (DFT) = 0.115 eV (~10%) B.E. (HF) = 0.106 eV (<3%) [0.104 eV, Murai et al (2003)]

  30. Results and discussion • Ozone cluster : quadramer of ozone (equilibrium configuration) Central atoms are in a straight line with distance between two consecutive atoms ~ 3.25 Ǻ Central atoms form almost a parallelogram, with sides ~3.85 Ǻ and ~4.2 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

  31. 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.

  32. 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

  33. Acknowledgment We acknowledge Prof. T.P. Das (State University of New York, Albany, NY, USA) for the support to carry out this research

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