Supplementary information supporting Nature 454, 88−91 (2008)

Vibrational excitation through tug-of-war inelastic collisions.
Stuart J. Greaves, Eckart Wrede, Noah T. Goldberg, Jianyang Zhang, Daniel J. Miller, and Richard N. Zare.
Nature 454, 88−91 (2008).
  abstract   full text

See also the News & Views feature by Mark Brouard:
When molecules don't rebound.
Mark Brouard, Nature 454, 43−45 (2008).   full text

QCT movies of characteristic H + D2(v = 0, j = 0) → H + D2(v' = 3, j') inelastic collisions

We employ the quasi-classical trajectory (QCT) methodology as described in our two recent papers:
New, Unexpected and Dominant Mechanisms in the Hydrogen Exchange Reaction. JCP 128 164306 (2008).
A quasi-classical trajectory study of the time-delayed forward scattering in the hydrogen exchange reaction. JCP 128 164307 (2008).

5 million trajectories for H + D2(v = 0, j = 0) collisions were propagated at a collision energy of Ecol = 1.72 eV. Inelastically scattered trajectories for the D2(v' = 3, j' = 0,2,4,6,8) product quantum states were analysed in more detail for comparison with experimental data by Zare and coworkers.

The D2(v' = 3, j' = 0) product state

Figure 1 below [adapted from Figure 2 of Nature 454, 88−91 (2008)] shows the almost linear correlation of the impact parameter of the H atom before and the deflection angle of the H atom after the collision for the D2(v' = 3, j' = 0) product state. Trajectories with low impact parameter are backwards scattered (the H atom turns around) whereas trajectories with high impact parameter are forward scattered (the H atom carries on in the same direction). Most trajectories are scattered on the nearside, i.e. into the same hemisphere as the incoming H atom.

Click on the links below or on the numbered areas of Figure 1 to start the corresponding trajectory movies.

b / ÅΘ / deg
Traj 10.008-170.9
Traj 20.067156.1
Traj 30.130164.3
Traj 40.282134.4
Traj 50.302131.8
Traj 60.424107.3
Traj 70.603 73.5
Traj 80.716 55.9
Traj 90.804 42.1
Traj 100.813 40.2
Traj 110.999 1.8
Correlation between deflection angle and impact parameter for D2(v'=3, j'=0) products
Figure 1: Deflection angle, Θ, versus impact parameter, b, for D2(v' = 3, j' = 0) inelastically scattered products from QCT calculations of H + D2(v = 0, j =0) collisions at a collision energy of 1.72 eV.

The trajectory animations clearly show that the D-D bond is stretched due to the attractive forces between the incoming H atom and the nearest D atom in the molecule. The vibrational excitation of the D2 results from the "tug" of the H atom as it departs and not, as is common wisdom for inelastic collisions, by compressing the D-D bond upon impact. Thus, the vibrational excitation is the result of a "tug of war" between the H atom and the D2 molecule. These inelastic collisions are frustrated reactive scattering events in which the well between H and D never deepens enough to break the D-D bond to lead to HD products.

Remarks

The D2(v' = 3, j' = 4) product state

The same behaviour, i.e., that the product motion is set up by the final pull of the departing H atom, is seen in trajectories leading to higher rotational excitation. Figure 2 shows the scattering angle – impact parameter correlation for D2(v' = 3, j' = 4) products which exhibits the same linear trend as for j' = 0, although less well defined.

b / ÅΘ / deg
Traj 10.172137.8
Traj 20.43084.5
Traj 30.63137.7
Traj 40.171149.5
Traj 50.455110.5
Traj 60.63283.8
Traj 70.80855.9
Traj 80.82456.5
Traj 91.0360.4
Traj 101.123-15.9
Correlation between deflection angle and impact parameter for D2(v'=3, j'=4) products
Figure 2: Deflection angle, Θ, versus impact parameter, b, for D2(v' = 3, j' = 4) inelastically scattered products from QCT calculations of H + D2(v = 0, j =0) collisions at a collision energy of 1.72 eV.

Remarks


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Eckart Wrede, 28 June 2008