“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

Cl + HD D+HCl, H+DCl 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 Cl 2 + H 2  2HCl chain reaction.

Studies of the Cl + H 2 reaction Experimental studies: –Rate constants for Cl + H 2 and D 2 reactions over the temperature range 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

The “G3” potential energy surface G3 surface was constructed by Truhlar et al. in It’s based on the so-called GQQ surface, which has been shown to give good agreement with experiment on Cl + H 2 and D 2 reactions. G3 surface improves on the GQQ surface in the region of Cl-H-H bending potential. Linear saddle point geometry: R HCl (Å) = R HH’ (Å) = R H’Cl (Å) = V (kcal/mol) = 7.88

G3 Success Cl + H 2 Cl + D 2

Failure of the G3 surface Branching ratio determined in cross-beam experiment as a function of collision energy for HD(j=0). K. Liu (1999) Collision energy (kcal/mol)

Contour Plot of G3 Surface ClCl H H  R r Jacobi Coordinates

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.

G3 surface and Bian-Werner surfaces

Theory and Experiment Manolopoulos Science (1999)

G3 and BW surfaces Cl H D H D Prob to form HCl reduced On BW relative to G3

Conclusion Van der Waals well (very shallow) in Cl+HD has a significant effect on branching ratio for Cl + HD(j=0) but not on rate constant

The O( 3 P)+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...

RATE CONSTANT FOR O( 3 P)+ HCl ON S4 S.Z.B.A.T.L.R.G.L JPC (2001)

The exact expression for k(T) N(E) is the Cumulative Reaction Probability

(Variational) Transition State Theory

TST Derivation

POTENTIALS FOR O( 3 P)+ HCl REACTION

The O( 3 P)+HCl Reaction

OH Cl OH OH kcal -5.2

The O( 3 P)+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(J=0) =

The O( 3 P)+HCl Reaction Xie, Wang, Bowman, Manolopoulos (2002)

The O( 3 P)+HCl Reaction

Bound states Quasi-bound states

Resonances and density of states Resonances are therefore like bound states in some respects, or bound states are resonances with zero widths. Eth

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

The (quasi) bound state approach Resonances are quasibound eigenstates with complex energy eigenvalues, E r,n - i  n  /2 H C = H - i U(R)

Quasibound State calculations A primitive basis of twenty Legendre functions, Eight vibrational functions of HCl for O+HCl (range: 1.6 a 0 to 3.3a 0 ) and 8 OH vibrational functions for Cl + OH (range 1.2a 0 to 3.6a 0 ) and 100 sine functions in R for each arrangement Ranges of R are [3.4a 0,10.2a 0 ] for the O+HCl channel and [3.2a 0, 8.0a 0 ] for the C+lOH channel. Length of the absorbing potential: 2.0a 0 A contraction scheme was used to reduce the direct product basis from to 16,000 to of the real wavefunctions used to construct complex H-matrix. The range of was to 0.5 h, in steps of 0.01 h.

Quasibound State calculations

Comparison of resonance energies and quasibound State energies of VdW wells (eV)

Comparison of resonance energies and quasibound state energies of VdW wells (eV) Overlap = quasibound density in the saddle point region

Assignment of resonances

Quasibound state wavefunctions O-HCl state at eV

Quasibound state wavefunctions Cl-HO state at eV

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?

Other examples

OH+HNO 3 Negative T-dependence indicates fairly complex and positive T-dependence indicates a barrier, as usual.