Van der Waals Wells are Important in Chemical Reactions

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Van der Waals Wells are Important in Chemical
Reactions
University of Florida, QTP Nov. 6, 2002
Acknowledgments Dunyou Wang (now at NASA/Ames),
Tiao Xie (Emory), David Manolopoulos (Oxford),
from US Dept. of Energy
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Cl HD DHCl, HDCl reaction

• Importance of this reaction
• It plays a central role in fundamental chemical
  kinetics, and has served as a critical test case
  for bimolecular reaction rate theory, especially
  transition-state and kinetic isotope effect. And,
  the theory of isotope effects was derived from
  it.
• This reaction is also a prototype for a host of
  Cl reactions that are in atmospheric chemistry
  and photochemical air pollution.
• This reaction is the rate determining step in the
  mechanism of the Cl2 H2 ? 2HCl chain reaction.

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Studies of the Cl H2 reaction

• Experimental studies
• Rate constants for Cl H2 and D2 reactions over
  the temperature range 296-3000 K.
• Branching ratio of Cl HD reaction has been
  studied in crossed molecular beam experiment.
• Theoretical studies
• Many potential energy surfaces have been
  constructed for this reaction, among which, the
  G3 surface most successful one.
• VTST have been used to calculate rate constants
  on these surfaces, and compared with experimental
  data. Truhlar and co.
• Quantum reactive scattering on G3 and a new pes
  Manolopous, Werner and co-workers

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The G3 potential energy surface

• G3 surface was constructed by Truhlar et al. in
  1996.
• Its based on the so-called GQQ surface, which
  has been shown to give good agreement with
  experiment on Cl H2 and D2 reactions.
• G3 surface improves on the GQQ surface in the
  region of Cl-H-H bending potential.
• Linear saddle point geometry
• RHCl (Å) 1.4011
• RHH (Å) 0.9896
• RHCl (Å) 2.3907
• V (kcal/mol) 7.88

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G3 Success
Cl D2
Cl H2
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Failure of the G3 surface
Branching ratio determined in cross-beam
experiment as a function of collision energy for
HD(j0). K. Liu (1999)
Collision energy (kcal/mol)
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Contour Plot of G3 Surface
Jacobi Coordinates
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G3 surface and Bian-Werner surface

• BW and G3 surface are broadly similar
• Barrier height (kcal/mol)
• 7.88 (G3) 7.61 (BW)
• Saddle point frequencies (cm-1)
• bending 581 (G3) 540 (BW)
• stretching 1358 (G3) 1360 (BW)
• Difference
• Imaginary frequency (cm-1)
• 1520i (G3) 1294i (BW)
• This indicates that G3 surface has a thinner
  barrier.
• BW has a Van der Waals well with a depth of 0.5
  kcal/mol at a T-shape equilibrium geometry.

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G3 surface and Bian-Werner surfaces
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Theory and ExperimentManolopoulos Science (1999)
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G3 and BW surfaces
Prob to form HCl reduced On BW relative to G3
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Conclusion
Van der Waals well (very shallow) in ClHD has a
significant effect on branching ratio for Cl
HD(j0) but not on rate constant
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The O(3P)HCl Reaction
A challenging reaction, non-linear saddle point,
heavy-light-heavy system.
Barrier height of KSG adjusted down by KSG to get
agreement with exp on k(T). Those calculations
were not converged so later calcs showed
disagreement with Experiment - barrier height too
small. New surface S4 by Ramuchandran, barrier
height is higher than KSG, but ...
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RATE CONSTANT FOR O(3P) HCl ON S4
S.Z.B.A.T.L.R.G.L JPC (2001)
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The exact expression for k(T)
N(E) is the Cumulative Reaction Probability
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(Variational) Transition State Theory
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TST Derivation
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POTENTIALS FOR O(3P) HCl REACTION
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The O(3P)HCl Reaction
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The O(3P)HCl Reaction
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The O(3P)HCl Reaction
S. Skokov, T. Tsuchida, S. Nanbu, J. M. Bowman,
and S. K. Gray, J Chem. Phys(2000). K. Nobusada,
H. Nakamura, Y. Lin, B. Ramachandran, J. Chem.
Phys. (2000)
CRP(J0)
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The O(3P)HCl ReactionXie, Wang, Bowman,
Manolopoulos (2002)
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The O(3P)HCl Reaction
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The O(3P)HCl Reaction
Quasi-bound states
Bound states
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Resonances and density of states
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Resonances are therefore like bound states in
some respects, or bound states are resonances
with zero widths.
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Resonances and lifetimes
The more conventional relationship is given as
follows
This is unimolecular decay of an (isolated)
resonance, with a decay rate equal to
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The (quasi) bound state approach
Resonances are quasibound eigenstates with
complex energy eigenvalues, Er,n-iG n /2 HC H -
ilU(R)
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Quasibound State calculations
A primitive basis of twenty Legendre functions,
Eight vibrational functions of HCl for
OHCl (range 1.6 a0 to 3.3a0) and 8 OH
vibrational functions for Cl OH (range 1.2a0 to
3.6a0) and 100 sine functions in R for each
arrangement Ranges of R are 3.4a0 ,10.2a0 for
the OHCl channel and 3.2a0 , 8.0a0 for the
ClOH channel. Length of the absorbing
potential 2.0a0 A contraction scheme was used to
reduce the direct product basis from to 16,000
to 4770. 400 of the real wavefunctions used to
construct complex H-matrix. The range of l was
0.001 to 0.5 h, in steps of 0.01 h.
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Quasibound State calculations
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Comparison of resonance energies and
quasibound State energies of VdW wells (eV)
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Comparison of resonance energies and
quasibound state energies of VdW wells (eV)
Overlap quasibound density in the saddle point
region
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Assignment of resonances
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Quasibound state wavefunctions
O-HCl state at 0.2496 eV
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Quasibound state wavefunctions
Cl-HO state at 0.2414 eV
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CONCLUSIONS
Resonances in the tunneling region due to Van der
Waals minima. Important effect on k(T) -
increasing, why? a) Resonances prepare
complexes b) Non-adiabaticity? Recall
Question bend zpe. Do wells destroy bending
Adiabaticity?
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Other examples
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OHHNO3 Negative T-dependence indicates fairly
complex and positive T-dependence indicates a
barrier, as usual.