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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 H5+, vibrational zero-point,

and reaction dynamics of H3+ + HD

JMB, Bas Braams, Zhen Xie,

Emory University,

NationalScience Foundation, Office of Naval Research


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)


Challenges for Theoretical Chemistry

  • Potential energy surfaces

  • Spectroscopy

  • Thermochemistry/ZPE

  • Dynamics


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)


H5+ Potential Landscape

Stationary Points


H5+ Potential Landscape Stationary Points


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).


3

4

6

2

1

5

Permutational Invariance: H2CO Example

H

4

H’

3

6

5

1

2

H

H’



H3+ Fragment


H5+ Potential Energy Surface (2005)

a Muller &Kutzelnigg, b Prosmiti et al. eMoyano & Collins


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+


Thermochemistry

H5+ H3+ + H2 , D0= 6.9±0.3 kcal/mole

Recall D0 = De+ DZPE

ZPE H3++H2

ZPE H5+

De


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)


Quantum Diffusion Monte Carlo ZPEs

Solution to the TDSE

E0 is the exact ZPE

Let t = it


H5+ H3+ + H2

H3+ + H2

H5+

ZPE H5+ = 20.6 kcal/mol(= 2.48De)

(Application of DMC requires a global PES)


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


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)


Dynamics and Reaction Rates

HD + H3+ H2+ + H2D+


HD + H3+ H4D+H2+ + H2D+

Structure of the Global Minimum

Three distinct localized locations for D


HD + H3+ H4D+H2+ + H2D+

Structure of the Global Minimum

Three distinct localized locations for D


HD + H3+ H2+ + H2D+

Ecoll= 95 K


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


HD + H3+  H4D+H2 + H2D+

( H’D + H3+)

Virtually no exchange, P(b) 0.05



A sample direct trajectory

H3+(J=1)+HD, Ecoll = 100 cm-1

Ecoll= 95 K




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.)


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


Science 6 January 2006:Vol. 311. no. 5757, pp. 60 - 63

LIR - Asvany,

Schlemmer


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



CH4D+ CH3+ + HD, CH2D+ + H2

Close to statistical and independent of initial geometry