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A global ab initio -based potential energy surface for of H 5 + , vibrational zero-point, and reaction dynamics of H

A global ab initio -based potential energy surface for of H 5 + , vibrational zero-point, and reaction dynamics of H 3 + + HD. JMB, Bas Braams, Zhen Xie, Emory University, . National Science Foundation, Office of Naval Research. Issues in Astrophysics. Deuterium fraction Spectroscopy

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A global ab initio -based potential energy surface for of H 5 + , vibrational zero-point, and reaction dynamics of H

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  1. A global ab initio-based potential energy surface for of H5+, vibrational zero-point, and reaction dynamics of H3+ + HD JMB, Bas Braams, Zhen Xie, Emory University, NationalScience Foundation, Office of Naval Research

  2. Issues in Astrophysics • Deuterium fraction • Spectroscopy • Thermochemistry • Reaction rates D. Gerlich, E. Herbst, and E. Roueff, Planet Space Sci. 50, 1275 (2002) D. Gerlich, S. Schlemmer, , Planet. Space Science 50, 1287(2002)

  3. Challenges for Theoretical Chemistry • Potential energy surfaces • Spectroscopy • Thermochemistry/ZPE • Dynamics

  4. Previous Theoretical Work Ab initio electronic structure R. Prosmiti, P. Villarreal, G. Delgado-barrio, (2001,2003) - DIM-fit PES H. Müller and W. Kutzelnigg, PCCP (2000) - CC-R12, stationary pts, De Y. Yamaguchi, J. F. Gaw, R. B. Remington, H. F. Schaefer III, (1987) - Dynamics I.Stich, D.Marx, M.Parinello, T.Terakura (1997) - PI/DFT W.P.Kraemer, V.Spirko, and O.Bludsk (1994) - Red Dim vibrations G. Moyano and M. Collins, (2003) - “GROW” QCT k(T)

  5. H5+ Potential Landscape Stationary Points

  6. H5+ Potential Landscape Stationary Points

  7. H5+ Potential Energy Surface (2005) • Ca 105ab initio energies [CCSD(T)/aug-cc-pVTZ] • Fit with a polynomial basis the is invariant wrt • any permutation of the 5 H atoms. • Many-body representation that gives the • fragments H3+ and H2 • Use a switching function to describe • long-range electrostatic interaction. • Z. Xie, B. J. Braams, and J. M. Bowman J. Chem. Phys. 122, 224307 (2005).

  8. 3 4 6 2 1 5 Permutational Invariance: H2CO Example H 4 H’ 3 6 5 1 2 H H’

  9. RMS Fitting Error

  10. H3+ Fragment

  11. H5+ Potential Energy Surface (2005) a Muller &Kutzelnigg, b Prosmiti et al. eMoyano & Collins

  12. Spectroscopy and Thermochemistry HD + H3+  [H4D+]H2+ + H2D+ Thermochemistry - get the ZPEs accurately. HO? Spectroscopy - detect reactant and products and maybe stabilizedH4D+ M. Okumura, L. I. Yeh, and Y. T. Lee (1988) - H5+

  13. Thermochemistry H5+ H3+ + H2 , D0= 6.9±0.3 kcal/mole Recall D0 = De+ DZPE ZPE H3++H2 ZPE H5+ De

  14. Thermochemistry H5+ H3+ + H2 , D0= 6.8±0.3 kcal/mol • The most accurate De = 8.58 kcal/mol • The present PES De = 8.30 kcal/mol • Using HO ZPEs PES gets D0 = 5.57 kcal/mol • (Not in good agreement with experiment)

  15. Quantum Diffusion Monte Carlo ZPEs Solution to the TDSE E0 is the exact ZPE Let t = it

  16. H5+ H3+ + H2 H3+ + H2 H5+ ZPE H5+ = 20.6 kcal/mol(= 2.48De) (Application of DMC requires a global PES)

  17. H5+ H3+ + H2 From the DMC ZPEs we get D0 = 6.33±.03 kcal/mol Exp* = 6.8±0.3 (HO = 5.57) *Exp1 = 6.6 ±0.3,Exp2 = 7.0 ±0.1 Present Deis low by 0.28 compared to most accurate ab intio value So, our estimate would be 6.6 kcal/mol

  18. More DMC-based Energetics H4D+ H3+ + HD D0 = 6.63 kcal/mol  H2D+ + H2 D0 = 6.37 kcal/mol H3+ + HD  H2D+ + H2 , E = -90 cm-1 (-0.26 kcal/mol)

  19. Dynamics and Reaction Rates HD + H3+ H2+ + H2D+

  20. HD + H3+ H4D+H2+ + H2D+ Structure of the Global Minimum Three distinct localized locations for D

  21. HD + H3+ H4D+H2+ + H2D+ Structure of the Global Minimum Three distinct localized locations for D

  22. HD + H3+ H2+ + H2D+ Ecoll= 95 K

  23. HD + H3+  H4D+H2 + H2D+ ( H’D + H3+) Statistical expectations Always form a “collision complex” - Langevin xsection Classically 60% to H2 + H2D+, P(b) = 0.6 and40% to H’D+ H3+ withP(b) = 0.3 for H’≠H P(b) = 0.1 H’=H

  24. HD + H3+  H4D+H2 + H2D+ ( H’D + H3+) Virtually no exchange, P(b) 0.05

  25. Reaction Cross Sections Vs. Collision Energy Ecoll= 95 K

  26. A sample direct trajectory H3+(J=1)+HD, Ecoll = 100 cm-1 Ecoll= 95 K

  27. Start with ZPE/2

  28. Thermal Rate Constant Calculation and Exp

  29. Summary So Far • Global PES done - PI, dissociates, VLR ad hoc • DMC calcs of ZPEs and Do • QCT calculations of xsection and rate constant • (Not statistical, mostly proton hopping) To Do • Quantum calculations of vibrational energies • and IR spectrum. (This is feasible with Multimode.) • Quantum calculation of the rate constant. (This is • very hard to do in full dimensionality.)

  30. CH5+ CH3+ + H2 CH5+ Like H5+ there are 5! equivalent Minima, saddle points. Fit to 36173 CCSD(T)/aug-cc-pVTZ Does CH5+ have a structure? • Oka’s unassigned spectrum • Marx and Parinello • Schaefer, Scheiner, Schlyer • Klopper and Kutzelnigg

  31. Science 6 January 2006:Vol. 311. no. 5757, pp. 60 - 63 LIR - Asvany, Schlemmer

  32. A. Brown, B. J. Braams, K. Christoffel, Z. Jin, and J. M. Bowman, J. Chem. Phys., 2003, 119, 8790. - fit and MD spectrum A. Brown, A. B. McCoy, B. J. Braams, Z. Jin, and J. M. Bowman, J. Chem. Phys., 2004, 121, 4105. - fit and DMC A.B. McCoy, B .J. Braams, A. Brown et al., J. Phys. Chem. A, 2004, 108, 4991. - DMC isotopmers

  33. DMC Calculation of the ZPEs CH3++H2 CH5+

  34. CH4D+ CH3+ + HD, CH2D+ + H2 Close to statistical and independent of initial geometry

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