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From product pair correlation to mode-specific reactivity

From product pair correlation to mode-specific reactivity. Cl + CHD 3 reactions. Ground state CHD 3 : 張柏林博士 Bend-excited CHD 3 : 張柏林博士 C-H Stretch-excited CHD 3 : 楊軒.吳彥典.岳現房. Cl + CH 4  HCl + CH 3. A slightly endothermic reaction, H 0 = +1.21 kcal/mol.

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From product pair correlation to mode-specific reactivity

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  1. From product pair correlation to mode-specific reactivity Cl + CHD3 reactions Ground state CHD3:張柏林博士 Bend-excited CHD3:張柏林博士 C-H Stretch-excited CHD3 : 楊軒.吳彥典.岳現房

  2. Cl + CH4  HCl + CH3 A slightlyendothermicreaction, H0= +1.21kcal/mol Kinetically, k (298 K)= 1.0  10-13cm3/moleculesec A pronouncednon-Arrhenius temperature dependency with the Afactor ~ 1.1  10-11cm3/moleculesec and Earanging from 2.4 to 3.6 kcal/mol. Dynamically, a late-barrier reaction implies a preferential promotion of reactivity by vibrational excitations of CH4(Polanyi’s rule). But, which modes ?

  3. Polanyi’s rule for A + BC reactions : Barrier location Energy requirement Reactant vibration is more effective than translation in driving a reaction with a barrier located late along the reaction coordinate; & the reverse is true for reactions with early barriers. Energy disposal Earlybarrier preferentially leads to vibrationally excited products, whereas a late barrier yields translationally hot products. Polanyi ACR 5(1972)161; Science 236(1987)680

  4. Mode-specificity Zare: (v3=1)  30  (v=0) HCl(v=1) / HCl(v=0)  0.6 v=1: a prominent forward peak ; v=0: mainly back- & side-scattered, as the ground state, Cl+CH4(v=0), reaction. Similar findings for the CH4(v1=1)reaction ! Crim:(v1+v4 )  2 (v3+v4 )  20 (v=0) for Cl+CH3D, (C-H s.s.)  7 (C-H a.s) Vibrational adiabaticity ?

  5. Bond-selectivity For the isotopic variant reactions, such as Cl + CH3D, the excitation of the initial C-H(C-D)stretch leads almost exclusively to the HCl(DCl)products. (Zare and Crim etc.) Spectator paradigm

  6. A six-atom reaction with 12 internal degrees of freedom & with two molecular products ! How to unravel the complexity to gain deeper insights?

  7. Transition State (TS) Geometric Structure Energetic Vibrational Frequencies But, TS should be dynamic! (Wigner 1938) Need to go beyond the above static properties How to reveal the collective motions of all atoms in TS ?

  8. What to measure? Product-Pair Correlation How to achieve that? Exploiting conservations of energy and momentum

  9. Joint probability matrixP(n,m) P(n) = P(n,m) P(m) = P(n,m) Two limiting cases Uncorrelated :P(n,m) = P(n) P(m) Strictly correlated : sayn = m + i P(n,m) = P(n) n m 1 2 3 P(m) 10.1 0.3 0.2 0.6 20.3 0.1 0 0.4 30 0.1 0.2 0.3 P(n) 0.4 0.5 0.4 Pair-Correlated Distribution PCCP 9(2007)17

  10. Correlated product pair Concerted motions at transition state decode ?

  11. well-controlled tagged imaging REMPI For a given high-resolution velocity measurement of a state-taggedCD3 product yields the coincident information ofthe DF(v,j) co-products  pair-correlation F + CD4  DF + CD3 Conservation of energy Conservation of momentum Ec - H0 = Etotal Science 300(2003)966

  12. ? Conventional 2-D Ion Velocity Mapping

  13. Gee, how lucky ! Two birds with one stone (merely by conservation laws) How to realize the simple idea experimentally ?

  14. Cl + CHD3 HCl + CD3 Variable angles to control the collision energy  Ion optics & imager ( ) hv  (2+1) REMPI detection of CD3 Time-sliced velocity imaging of state-selective CD3+  RSI 74(2003)2495 Cl CHD3 Discharged Cl-beam

  15. 9.7 kcal/mol (v′= 0) (v′= 1)* (v′= 1) 0 π 14.74 kcal/mol (v′= 0) (v′= 1)* (v′= 1) 0 π Time-Sliced Raw Images Cl/Cl* + CH4  HCl(v’) + CH3(0) At 9.7 kcal/mol, both (v’=0) & (v’=1)* are mainly sideways, while (v’=1) is back-scattered. At 14.74 kcal/mol, (v’=0) shifts slightly and (v’=1)* becomes sharply forward peaking, while (v’=1) is sideways scattered. JCP 122(2005)101102

  16. CH3(00) + HCl(v’=1) pair Distinctly different & changing angular distributions! Pair-correlated distribution Ground state product pair Progressive shift toward more forward with the increase in Ec,

  17. Cl+CH4HCl(’=1)+CH3(00) Cl+CH4HCl(’= 0)+CH3(00) Direct pathway governed by large impact-parameter (peripheral) collisions Different mechanism from “pattern recognition” What and why ?? JCP 122(2005)101102

  18. 0 1 2 3 Ec (kcal/mol) Lessons from F + HD  HF + D Resonance signatures For DCS: a rapidly evolving Ec-ridge from backward to sideways, followed by sharp forward-backward peaking; A step feature in ICS. Characteristic patterns! PRL 85(2000)1206

  19. heat HCl (0) + CH3(0) Cl + CH4(v=0) How reactive are the high frequency stretches and the low frequency ( bending & torsion) modes ? How adiabatic is reaction dynamics ?

  20. Pair-correlation crossed molecular beam technique Conservation of energy & momentum Time-sliced imaging REMPI probing Controlling Ec Locking OPO

  21. IR-on IR-off Cl + CHD3  HCl(v’) + CD3(00) Ec = 4.6 kcal/mol Inner rings Scaling down I(θ) for IR-off by (1-n#/n0) & subtracting it from that for IR-on leads to the genuine angular distribution for the HCl(v’=1) + CD3(0) product pair; & branching ratio (σ1/ σ0)# = 0.67 PCCP 9(2007)250

  22. step! 8.6 kcal/mol 3.1 kcal/mol Vibrational enhancement At the same Ec , [c & d] Both modes show enhancements with different Ec-dependences At the same Total E, [e & f] Little preferential enhancement for vibration! But, Product-like transition state structure  Polanyi’s rule ? Science (2007)

  23. (0, 00)s (0, 00)g EC EC   (1, 00)s (1, 00)g EC EC   (0, 00)b EC  Evolution of pair-correlated angular distribution with Ec Two distinct patterns The ground-state pairs (left):ridge structure implying a direct collisionmechanism governed by peripheral dynamics. The excited pairs (right): Sharp forward (backward) peaking, suggesting a short-lived complex reactionmechanism Cl + CHD3(v)  HCl(v’) + CD3(00)

  24. How about correlated vibrational branching ? Reaction with ground-stateCHD3yields predominantly ground-state product pair; the same is true for bend-excited reactants. Reaction with C-H stretch-excitedCHD3 yields a 20-fold increase in the coincidently formed HCl(v’=1) products!

  25. HCl+CH3 v3 v1 HCl(v=1) v4 v2 Duncan et al, JCP 103(1995)9642 Corchado et al, JCP 112 (2000)9375 Cl+CH4 v3(t2) Curvature & Coriolis couplings of sym.stretch & umbrella modes v1(a1) v2(e) v4(t2) The v1-vibration of CH4 is an active mode, and adiabatically correlated to the HCl(v=1) + CH3(00) product pair

  26. Cl + CHD3HCl + CD3 Etotal 15 v1 10 (1, 00) 5 v3 (0, 21) v = 0 (0, 00) 0 S(amu1/2bohr) -1.5 -1.0 -0.5 0 0.5 1.0 1.5 Visulizing the reaction pathways Ground-State Reaction A vibrationally adiabatic process Bend-Excited Reactants A non-adiabatic pathway, funneling bending energy into product rotations and translations C-H Stretch-Excited Reactant Bifurcated pathways, one direct path mediated by couplings to S, and the other complex-forming path governed by Feshbach (reactive) resonance 45 % 2 % ~100% 98% 55 %

  27. Summary Contrary to the current perception, while reactant vibration exerts enormous influences on dynamical attributes, it is NOT more efficient than translation in promoting the reaction rate. Aided by ab initio results, product pair correlation measurement enables us to visualize the cooperative motions of atoms in the transition state region. How to generalize Polanyi’s rule to polyatomic reactions ?

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