Cl + CH 4 HCl + CH 3 A slightly endothermic reaction, H 0 = kcal/mol Kinetically, k (298 K) = 1.0 cm 3 /molecule sec A pronounced non-Arrhenius temperature dependency with the A factor ~ 1.1 cm 3 /molecule sec and E a ranging from 2.4 to 3.6 kcal/mol. Dynamically, a late-barrier reaction implies a preferential promotion of reactivity by vibrational excitations of CH 4 (Polanyi’s rule). But, which modes ?
Polanyi’s rule for A + BC reactions 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 Early barrier preferentially leads to vibrationally excited products, whereas a late barrier yields translationally hot products. : Barrier location Polanyi ACR 5(1972)161; Science 236(1987)680
Mode-specificity Vibrational adiabaticity ? Zare: (v 3 =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+CH 4 (v=0), reaction. Similar findings for the CH 4 (v 1 =1) reaction ! Crim: (v 1 +v 4 ) 2 (v 3 +v 4 ) 20 (v=0) for Cl+CH 3 D, (C-H s.s.) 7 (C-H a.s)
Bond-selectivity Spectator paradigm For the isotopic variant reactions, such as Cl + CH 3 D, the excitation of the initial C-H (C-D) stretch leads almost exclusively to the HCl (DCl) products. (Zare and Crim etc.)
A six-atom reaction with 12 internal degrees of freedom & with two molecular products ! How to unravel the complexity to gain deeper insights?
Transition State (TS) But, TS should be dynamic ! (Wigner 1938) Need to go beyond the above static properties Geometric Structure Energetic Vibrational Frequencies How to reveal the collective motions of all atoms in TS ?
What to measure? Product-Pair Correlation How to achieve that? Exploiting conservations of energy and momentum
Pair-Correlated Distribution Joint probability matrix P(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 : say n = m + i P(n,m) = P(n) m P(m) P(n) n PCCP 9(2007)17
Concerted motions at transition state Correlated product pair decode ?
F + CD 4 DF + CD 3 Conservation of energy Conservation of momentum well-controlled imaging REMPI tagged For a given high-resolution velocity measurement of a state-tagged CD 3 product yields the coincident information of the DF(v,j) co- products pair-correlation E c - H 0 = E total Science 300(2003)966
? Conventional 2-D Ion Velocity Mapping
Gee, how lucky ! Two birds with one stone (merely by conservation laws) How to realize the simple idea experimentally ?
Cl CHD 3 Discharged Cl-beam Variable angles to control the collision energy hv (2+1) REMPI detection of CD 3 Cl + CHD 3 HCl + CD 3 Time-sliced velocity imaging of state- selective CD 3 + Ion optics & imager ( ) RSI 74(2003)2495
0 π (v′= 0) (v′= 1)* (v′= 1) 9.7 kcal/mol 0 π (v′= 0) (v′= 1)* (v′= 1) kcal/mol Cl/Cl* + CH 4 HCl(v’) + CH 3 (0) At 9.7 kcal/mol, both (v’=0) & (v’=1)* are mainly sideways, while (v’=1) is back-scattered. At kcal/mol, (v’=0) shifts slightly and (v’=1)* becomes sharply forward peaking, while (v’=1) is sideways scattered. Time-Sliced Raw Images JCP 122(2005)101102
Ground state product pair Progressive shift toward more forward with the increase in E c, Pair-correlated distribution CH 3 (0 0 ) + HCl(v’=1) pair Distinctly different & changing angular distributions!
Cl+CH 4 HCl( ’=1)+CH 3 (0 0 ) Cl+CH 4 HCl( ’= 0)+CH 3 (0 0 ) Direct pathway governed by large impact-parameter (peripheral) collisions Different mechanism from “pattern recognition” What and why ?? JCP 122(2005)101102
Resonance signatures For DCS: a rapidly evolving E c -ridge from backward to sideways, followed by sharp forward-backward peaking; A step feature in ICS. Characteristic patterns! Lessons from F + HD HF + D PRL 85(2000) E c (kcal/mol)
How reactive are the high frequency stretches and the low frequency ( bending & torsion) modes ? How adiabatic is reaction dynamics ? heat Cl + CH4(v=0) HCl (0) + CH3(0)
Pair-correlation crossed molecular beam technique Controlling E c Time-sliced imaging Conservation of energy & momentum REMPI probing Locking OPO
Scaling down I(θ) for IR-off by (1-n # /n 0 ) & subtracting it from that for IR-on leads to the genuine angular distribution for the HCl(v’=1) + CD 3 (0) product pair; & branching ratio (σ 1 / σ 0 ) # = 0.67 IR-off IR-on Inner rings Cl + CHD 3 HCl(v’) + CD 3 (0 0 ) E c = 4.6 kcal/mol PCCP 9(2007)250
Vibrational enhancement At the same E c, [c & d] Both modes show enhancements with different E c -dependences At the same Total E, [e & f] Little preferential enhancement for vibration! But, Product-like transition state structure Polanyi’s rule ? 8.6 kcal/mol 3.1 kcal/mol step! Science (2007)
(0, 0 0 ) s ECEC (0, 0 0 ) b ECEC (1, 0 0 ) g ECEC (0, 0 0 ) g ECEC (1, 0 0 ) s ECEC Evolution of pair-correlated angular distribution with E c Two distinct patterns The ground-state pairs (left): ridge structure implying a direct collision mechanism governed by peripheral dynamics. The excited pairs (right): Sharp forward (backward) peaking, suggesting a short- lived complex reaction mechanism Cl + CHD 3 (v) HCl(v’) + CD 3 (0 0 )
How about correlated vibrational branching ? Reaction with ground-state CHD 3 yields predominantly ground-state product pair; the same is true for bend- excited reactants. Reaction with C-H stretch- excited CHD 3 yields a 20-fold increase in the coincidently formed HCl(v’=1) products!
Duncan et al, JCP 103(1995)9642Corchado et al, JCP 112 (2000)9375 v 3 (t 2 ) v 1 (a 1 ) v 2 (e) v 4 (t 2 ) Cl+CH 4 v2v2 v4v4 v3v3 v1v1 HCl(v=1) HCl+CH 3 Curvature & Coriolis couplings of sym.stretch & umbrella modes The v 1 -vibration of CH 4 is an active mode, and adiabatically correlated to the HCl(v=1) + CH 3 (0 0 ) product pair
E total (1, 0 0 ) (0, 0 0 ) (0, 2 1 ) S (amu 1/2 bohr) Cl + CHD 3 HCl + CD 3 v 1 v3v3 v = 0 15 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 % 98% ~100% 55 %
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 ?