to a rebound reaction with a small impact pa-
rameter, whereas a trans configuration leads
to a stripping reaction with a large impact
parameter. Thus, trans critical point configura-
tions produced more CO rotation. Four typical
rebound and stripping trajectories are shown
in fig. S8 and movies S1 to S4.
The origin of bimodality
The QCT results reproduced the range of final
j(CO). They showed that reactions that produce
low-j(CO) have predominantly cis critical point
geometries and demonstrate a rebound-type ab-
straction reaction. High-j(CO) trajectories, on the
other hand, typically have trans critical point ge-
ometries and exhibit a stripping-like reaction
with a large impact parameter. We can also de-
scribe the energetics of the roaming reaction to
produce H 2 + CO. In the entrance channel, there
is a substantial well near a linear C–H···H geom-
etry (Fig. 3A). At the critical geometry, the CH
bond breaks on a high-energy plateau (Fig. 3B)
such that the H 2 product is formed with high
vibrational energy, and then, in the exit channel,
thereisarepulsiveforceleadingtothefinalmo-
lecular products (fig. S6).
Figure 4C shows the importance ofqCHH.
Our hypothesis of the origin of the bimodality
is that this coordinate may be considered to be
a bending coordinate of the roaming H atom
about the breaking CH bond. The coordinate is
crucial because the roaming H atom must roam
from the H 2 COwellontheoppositesideofthe
molecule to the critical roaming configuration.
This necessarily involves large-amplitude mo-
tion in—and hence velocity associated with—
theqCHHcoordinate. Abstraction of the bound H
atom takes place when the roaming H reaches
a critical H···H distance of ~2 Å (Fig. 3B).
Figures 3A and 4C also show that the mini-
mum energy geometry has near-linear C–H–H,
and theqCHHbending potential is approxi-
mately harmonic. As shown in Fig. 4C, the
critical points for abstraction occurred more
often when the H atom had slowed to a stop
at the classical turning points of theqCHH
potential—i.e., at cis and trans geometries,
which will occur in resonance with the classi-
calqCHHangular frequency. There is also a
minimum in the distribution of trajectory crit-
ical points at the near-linear C–H–H angle,
which corresponds to the minimum energy
PES well shown in Fig. 4C. Thus, abstraction
was less probable when the roaming H atom
passed through the minimum energy configu-
ration with substantial velocity. This is classical
behavior, and it explains why the QCTs could
qualitatively reproduce the distinct impact pa-
rameter distribution and hence the bimodality
in thej(CO) distribution.
There is a commensurate quantum me-
chanical explanation, which arises straight-
forwardly from quantum-classical correspondence.
As the roaming H atom starts an oscillation in
theqCHHcoordinate, a bound wave function is
transiently established. All bending wave func-
tions exceptv= 0 have maxima at the ex-
tremities. In this case, the minimum inqCHHis
close to linear, so the extremities correspond
to cis and trans geometries. This bending wave
function—likely a mix of many different quanta
of the van der Waals bending vibration, but not
v=0—is projected onto the final CO product
state distribution. The projection of a bending
wave function in the parent molecule onto the
final product rotational state distributions of
the products is known as the rotation reflection
principle ( 32 , 33 ), and the bimodal CO rotation-
al distribution can be considered to arise from
resonances of theqCHHpartial wave expansion.Summary and outlook
Detailed velocity-mapped imaging measure-
ments of the H 2 product of H 2 CO dissociation
have made it possible to measure the cor-
relations between individual vibrational and
rotational states of the H 2 and individual vi-
brational and rotational states of the CO pro-
ducts. Although previous results ( 29 ) have
shown that the roaming and TS pathways to
molecular products have different CO rota-
tional distributions, our results—obtained by
focusing on high-vibrational (v≥6) levels of
the H 2 —demonstrate that the CO rotational
distribution for the roaming pathway is itself
also bimodal. The measurement and the asso-
ciated QCT calculations provide additional
insights into the roaming process: The high
rotational states of CO from roaming come
from a trans O–C–H···H critical configuration,
whereas the low rotational states come from a
cis configuration. A simple physical picture is
that the former leads to a large impact param-
eter stripping abstraction of the H in HCO by
the roaming H atom, whereas the latter leads
to a small impact parameter rebound abstrac-
tion. We hypothesized that the bimodality
arises from a reflection of the wave function
for bending theqCHHcoordinate.
Large-amplitude motion in the bending coor-
dinate comprising the breaking and forming
bonds is a prerequisite for roaming reactions.
This motion arises precisely because of the
roaming mechanism. We therefore expect bi-
modality to be a feature of all roaming reac-
tions. Testing this hypothesis will be a challenge
for theoretical and experimental chemistry. The
quantitative reproduction of the state-specific
experimental correlations would be an extreme-
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ACKNOWLEDGMENTS
Funding:The University of New South Wales and University of
Sydney work was supported by the Australian Research
Council (DP190102013). M.S.Q. was supported by an Australian
postgraduate award. J.M.B. thanks the Army Research Office,
DURIP grant (W911NF-14-1-0471), for funding a computer cluster
where the trajectory calculations were performed.Author
contributions:M.S.Q. performed all experiments and data
analysis. K.N. assisted with experiments and performed detailed
analysis of PES. M.J.T.J. supervised aspects of computational and
experimental data analysis. J.M.B. directed construction of PESs
and trajectory code. P.L.H. supervised and carried out trajectory
calculations. S.H.K. conceived and directed the project and
supervised experiments. All authors contributed to the drafting
of the manuscript.Competing interests:The authors have no
competing interests to declare.Data and materials availability:
All data needed to evaluate the conclusions in the paper are
present in the paper or the supplementary materials. Raw data are
available at the Australian Research Data Archive ( 34 ).SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/369/6511/1592/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S8
Tables S1 and S2
References ( 35 – 38 )
Movies S1 to S4
23 April 2020; accepted 19 July 2020
Published online 6 August 2020
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