recoil from the ionization step, and the result
isshownasthegreencurve.TheGaussianfit-
ting parameters were varied until the best fit
to the experimental data was obtained. Two
Gaussian functions provided a better fit to
experiment than any other model distribution
(see the section on experimental data model-
ing in the supplementary materials).
The speed distributions for the H 2 (7,4) and
(6,3) states in the bottom two rows of Fig. 1 now
contain contributions from CO(v= 1,2) because
the H 2 internal energy is commensurately
lower. Each distribution was very well fit by
two components to the rotational state distri-
bution in each vibrational state, as shown by
the stick spectra. Here, again, the blue and red
sticks represent the lower- and higher-jcom-
ponents, respectively, and the green curve
shows the convolution with the instrumental
function. The CO rotational state distributions
determined from the Gaussian fits are shown
in the right column of Fig. 1 for CO(v= 0).
Double Gaussian rotational distributions were
fit to 50 speed distributions for three initial
H 2 CO states and H 2 product states spanning
v=6to9andj=0to12(fig.S3).Inmostcases,
the low-jcomponent dominates; in a few cases,
the high-jcomponent is too weak to fit or lies
underneath the low-jcomponent of a higher-
lying vibrational state.
The meanjof the low- and high-j(CO) fitted
Gaussians—which are shown as blue and red,
respectively, in Fig. 1 and fig. S2—was con-
verted to CO rotational energy. This energy, for
CO(v= 0), is plotted as a function of available
energy in Fig. 2A. Each component shows a lin-
ear trend withErot(CO) for the first 7000 cm−^1
of available energy, perhaps reaching a pla-teau at the highest available energies. The
slope of each line represents the fraction of
available energy found in CO rotation for each
component, which reveals that 8 ± 1 and 28 ±
2% of the available energy is found, on aver-
age, in the low- and high-j(CO) components,
respectively.
As described in the experimental data mod-
eling section of the supplementary materials,
conservation of angular momentum, coupled
with very low H 2 CO and H 2 angular momen-
tum, ensures thatj(CO)≈L=mvb, whereLis
the orbital angular momentum,mis the re-
duced mass,vis the recoil velocity in the cen-
ter of mass (COM) frame, andbis the impact
parameter of the recoiling H 2 and CO frag-
ments. This relationship allows an approxi-
mate impact parameter to be determined for
the center of each fitted Gaussian component
(Fig. 2B), plotted as a function of available
energy. Further analysis is given as supple-
mentary materials, with limiting impact pa-
rameters shown in fig. S4. Figure 2B shows
that the low-j(CO) component corresponds to
an impact parameter of≈0.7 Å, and the high-j
component corresponds to≈1.3 Å. There is a
weak trend toward lower impact parameters
acrossthe1-eVdifferenceinavailableenergy.
The consistency of derived impact parameters,
across a wide range of available energy, arising
from 50 different combinations of H 2 CO ini-
tial states and H 2 product states is indicative
of a consistent feature in the dynamics of the
reaction,soweturntoQCTsrunonanaccu-
rate ab initio PESs for further insight.QCT results
The 52,800 QCTs calculated in ( 29 ) were re-
analyzed. These trajectories were run on a high-
quality PES ( 30 ) at a total energy of 36,223 cm−^1
relative to the bottom of the H 2 CO well, which
corresponds to excitation of the H 2 CO 2^143
state. Of the 42.8% of the trajectories that
gave H 2 + CO products, 13.5% produced H 2
withv≥6 and were classified as roaming.
These roaming trajectories were then exam-
ined and analyzed in detail. For each trajec-
tory, the final orbital angular momentum and
impact parameter were recorded along with
the angular momentum and the vibrational
and rotational energy of each of the CO and H 2
products. The classical results were converted to
quantum numbers using standard (histogram)
binning, with the exception of the H 2 vibra-
tional energy, for which we used Gaussian bin-
ning ( 31 ). Although Gaussian binning reduced
the effective number of trajectories for each
H 2 (v) (fig. S5), it describes the action asso-
ciated with each quantum state markedly
better and, hence, performs better in terms
of conservation of energy and gives minimal
blurring of other distributions ( 31 ). Further
details are provided in the computational meth-
ods section of the supplementary materials.1594 25 SEPTEMBER 2020•VOL 369 ISSUE 6511 sciencemag.org SCIENCE
Fig. 2. CO rotational energies
and impact parameters as
a function of available energy.
(A) Average CO rotational
energy (Erot) determined from
the mean of the Gaussian
components shown in Fig. 1
and fig. S2. (B) Approximate
impact parameter (see text for
details) between recoiling
CO and H 2 fragments,
calculated from the mean
of each Gaussian component.
In both panels, the red and
blue lines indicate the higher-
and lower-j(CO) Gaussian
components, respectively.
Eavail / cm<^10 2000 4000 6000 80000.00.40.81.21.6500100015000b / ÅE
rot(CO) / cm<^1AB2000slope = 0.08 ± 0.01slope = 0.28 ± 0.02Fig. 3. Two-dimensional slices of the H + HCO PES.(A) Potential experienced by a roaming H atom for
HCO in its equilibrium geometry. (B) Potential experienced by the H bound to CO at the critical point where it
bonds to the roaming H. Energies are with respect to the H 2 CO minimum.
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