The right column of Fig. 1 shows the CO
rotational state distributions forv(CO) = 0,
derived from QCT calculations, for the four
(H 2 )(v,j) experimental states shown. The QCT
distributions are compared with the low- and
high-j(CO) Gaussians obtained by modeling
the experimental H 2 speed distributions. First,
the range ofj(CO) states is reproduced well
by the QCT calculations. Second, each QCT
distribution shows evidence of a bimodal ro-
tational distribution that strongly resembles
the experimentally derived distributions. The
qualitative agreement between the bimodal
experimental and QCT distributions leads us to
forensically investigate the trajectories and the
PES to seek an explanation. QCT speed distri-
butions corresponding to all experimental data
can be found in the supplementary materials.
Discussion
The nature of the PES
A bimodal distribution of product state pop-
ulations is often indicative of two reaction
mechanisms or two pathways to products on a
PES. To test whether there are two distinct re-
gions of H 2 CO phase space, we closely followed
the set of 208 trajectories that led to H 2 (v=
7,j= 3) products. HavingEavail= 6372 cm−^1 ,
this state is approximately in the middle of the
range of H 2 vibrational and rotational states
and available energies.
Figure 3A shows a slice of the PES expe-
rienced by the roaming H atom for in-plane
interaction with a free HCO moiety—that is,
with HCO bond lengths and bond angle equal
to those of the isolated radical. The origin is
defined as the COM of the CO moiety through-
out, and we define thexaxis as perpendicular
and theyaxis as parallel to this bond. The deep
H 2 CO well lies at a negativexdistance and is not
shown. A shallower well lies almost along the
CH bond. As the roaming H atom approaches
the bound H atom, the PES changes substan-
tially. There is a critical distance of approach
of the roaming H atom, at which point the in-
ternal H atom becomes unbound to the C atom.
Figure 3B shows a two-dimensional slice of this
critical point from the perspective of the bound
H atom. The energy plateau between the inner
HbeingboundtoCandboundtoHisshown
by orange shading. As the inner H moves away
from CO, it experiences a large attractive force
toward the free (roaming) H atom, forming the
H 2 molecule. This large force leads to exten-
sive H 2 vibrational excitation, which is a well-
known signature in H 2 CO roaming. After the
critical point for each trajectory, the PES con-
tinues to change substantially. There is a strong
repulsion between the COMs of the nascent
CO and H 2 fragments (fig. S6).Two roaming mechanisms
We examined all 208 trajectories leading to
H 2 (v= 7,j= 3). In every case, there is a well-
defined, critical point at which the internal H
atom transfers to the roaming H atom. The H
atom is never transferred back to CO. The CO
and H 2 fragments recoil directly away from each
other along the exit channel and form products,
with little further complex interaction (fig. S6).
Figure 4A shows these critical points for all
trajectories in the H 2 (v= 7,j= 3) set pro-
jected onto thexy(HCO) plane. The dots repre-
sent projections of the H 2 COM and are color
coded according to the finaljstate of the recoil-
ing CO, as shown in the legend. Although not ab-
solute, most low-jtrajectories have critical points
that lie in a cis-like O–C–H···H geometry, where-
as high-jtrajectories have critical points that lie
more frequently in a trans O–C–H···H geometry.
Figure 4B shows how the trajectories propa-
gate in the exit channel after the critical point—again showing the H 2 COM position relative
to the CO COM. The stationary reference frame
of the CO causes the trajectories to be curved,
and higher curvature reflects higher final CO
angular momentum. Trajectories are color
coded in the same way as they are in Fig. 4A.
The low-jtrajectories starting in cis geometries
mostly moved up in the figure and had a smaller
final impact parameter between H 2 and CO.
Trajectories with highj(CO) starting from
trans geometries, on the other hand, headed
downward in the figure, with larger resultant
impact parameters. Figure S7 shows that final
j(CO) is approximately proportional to orbital
angular momentumLand hence impact pa-
rameterb. The scatter about the linear rela-
tionship is a result of nonzeroj(H 2 ) = 3.
The correlation between cis and trans crit-
ical point geometries and finalj(CO) is shown
in Fig. 4C, where the H 2 COM of the trajectory
critical points—color coded for finalj(CO)—
have been projected onto theqOCHandqCHH
angular coordinates, describing the breaking
and forming bonds and superimposed on PES
contours. In Fig. 4C, cis and trans critical points
haveqCHH<0andqCHH> 0, respectively. The
trajectory critical points have been binned with
respect toqCHHon the right-hand side of the
panel, with the overall distribution (black) sep-
arated into low- and high-j(CO)—blue and red
symbols—defined asj(CO)≤21 andj(CO) > 21,
respectively. Figure 4C shows that cis critical
points strongly correlate with low-j(CO) pro-
ducts, and trans critical points are strongly
correlated with high-j(CO) products.
The QCTs also revealed a mechanistic differ-
ence between the low-jand high-jtrajectories.
As the roaming H atom approaches the bound
H of HCO, there is a strong attractive force
(Fig. 3A). From the point of view of abstraction
reactions, a cis O–C–H···H configuration leadsSCIENCEsciencemag.org 25 SEPTEMBER 2020•VOL 369 ISSUE 6511 1595
A BOCHDistance (Å)Distance (Å)OCHDistance (Å)COCH angle (deg)CHH angle (deg)110 120 130 140255075< 25< 50< 750Low jHigh j(^340003300032000)
34000
34000
33000
Fig. 4. CO + H 2 roaming exit channel.(A) Plot of position of H 2 COM at the
critical point on the PES (see text for details). (B) Trajectories of H 2 COM in the
stationary frame of CO after crossing the critical point. (C)H 2 critical point
COM projected onto theqOCHandqCHHcoordinates describing the breaking and
forming bonds superimposed on PES contours, with respect to the H 2 CO
minimum, for H–H, C–H, and C–O distances of 2.000, 1.200, and 1.1838 Å,
respectively, and all atoms in plane. Trajectories and critical points are color
coded to finalj(CO), as indicated. On the far right, the overall distribution
of critical pointqCHH(black squares), separated into low-j(CO) (blue circles)
and high-j(CO) (red triangles) components, is noted.
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