Supplementary material for “Differential and integral cross sections
for the rotationally inelastic scattering of methyl radicals with H2 and
D2”
Ondřej Tkáč,1 Qianli Ma (马千里),2 Cassandra A. Rusher,3 Stuart J. Greaves,3 Andrew J. OrrEwing,1,a) and Paul J. Dagdigian2,b)
1
School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, UK
2
Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-2685,
USA
3
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS
UK
a)
Electronic mail: a.orr-ewing@bris.ac.uk
b)
Electronic mail: pjdagdigian@jhu.edu
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1. Density-to-flux transformation
The Monte Carlo program simulates an instrument function that determines a relative
detection efficiency of scattered molecules that depends on their final laboratory frame velocity.
The changes made to the Monte Carlo program include simulation of slicing of the central part of
the Newton sphere. For reliable use of the simulation program, values for various parameters
characterizing the experimental apparatus were carefully determined. These parameters included
the speed and angular divergence distributions, temporal profiles, and spatial widths of the two
molecular beams, as well as the temporal profile, the Rayleigh range and beam waist of the
focused probe laser. In addition, for diatomic molecules as a collision partner the Monte Carlo
simulation program requires their rotational constants as input parameters. The rotational
constants are B(H2) = 60.853 cm-1 and B(D2) = 30.443 cm-1. By sampling ~2 × 108 sets of initial
conditions from the distributions of molecular beam and laser beam properties, the Monte Carlo
program was used to simulate the instrument function. Since the k projection number is not
resolved in the REMPI spectra of methyl radicals, a set of instrument functions were simulated
for individual k projection numbers and weighted according to the 2-photon line strengths factors
for the given detection line. A final, corrected image was then obtained by dividing the raw
experimental image by this sum of instrument functions over k projection quantum numbers.
Figure S1 shows a raw DCS extracted from an experimental ion image for inelastic
scattering of CD3 with D2 for final level nk = 3123. The red line shows the part of the DCS that is
destroyed by the beam spot. This raw DCS is not symmetric. We divide this DCS by an angular
distribution of the simulated instrument function shown in Fig. S1(b). As a result we get a
density-to-flux corrected DCS, which is symmetric about 0º as shown in Fig. S1(c). The
symmetry of the final DCS can be considered as a test of the accuracy of the Monte Carlo
program.
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FIG. S1. (a) Raw DCS extracted from an uncorrected image measured for inelastic scattering of
CD3 with D2 for final level nk = 3123. (b) Angular distribution of the instrument function
simulated by the Monte Carlo program. (c) Corrected (symmetric) DCS acquired by the division
of the raw DCS by the angular distribution of the instrument function. The red lines in (a) and (b)
show the part of the DCS that is destroyed by the parent beam spot.
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2. Raw Images for Inelastic Scattering of CD3 by H2
Raw images for inelastic scattering of CD3 by D2 are presented in Fig. 6 of the main text.
We present here for completeness the raw images for scattering of CD3 by an H2 collision
partner.
FIG. S2. Raw images for inelastic scattering of CD3 radicals by H2 at a collision energy of 680
± 75 cm–1. The images are denoted by the symbol Y( n'k ' k ' ) for final rotational levels with n =
1
N
2 – 8 of the CD3, with unresolved final k projection levels as discussed in section II.C of the
main text. Y denotes the spectroscopic branch used in REMPI detection. The orientation of the
relative velocity vector vrel is indicated in one panel.
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3. Raw Images and DCSs for Inelastic Scattering of CH3 by D2 and H2
Collision energies for inelastic scattering of CH3 radicals with H2 and D2 were 665 ± 70
cm-1 and 615 ± 60 cm–1, respectively. The collision energies are slightly smaller than for CD3
because of the smaller reduced mass. Experimental images for inelastic scattering of CH3
radicals with H2 and D2 are shown in Fig. S3 for n = 2 and 3. Extracted experimental DCSs for
n = 2 and 3 are shown in Fig. S4. The experimental DCSs were normalized to their maximum
values.
FIG. S3. Raw images for inelastic scattering of CH3 radicals by H2 and D2 at respective collision
energies of 665 ± 70 cm–1 and 615 ± 60 cm–1. The images are denoted by the symbol
Y( n' k ' ... k ' ) for final rotational levels with n = 2 and 3 and unresolved final k projection levels. Y
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N
denotes the spectroscopic branch.
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FIG. S4. Experimental DCSs for inelastic scattering of CH3 radicals by H2 and D2 into final
rotational levels n = 2 and 3 at respective collision energies of 665 ± 70 and 615 ± 60 cm–1.
DCSs were determined from the measured images displayed in Fig. S3. The REMPI line
employed for detection is indicated in each panel, along with the range of k projection levels
contributing to the scattering. The experimental DCSs were normalized to their maximum
values.
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4. Computed state-resolved integral cross sections
We present in this section computed integral cross sections for transitions out of the
lowest CD3 rotational levels of A2 and E nuclear spin symmetry in collisions with D2.
FIG. S5. Computed integral cross sections for transitions out of the CD3 00 level (the lowest
level of the A2 nuclear spin modification) in collisions with D2 at a relative translational energy
of 640 cm–1. The rotational level of the diatomic collision partner is j2 = 0 (upper panel) and j2
= 1 (lower panel). The initial level is indicated with an open square.
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FIG. S6. Computed integral cross sections for transitions out of the CD3 11 level (the lowest
level of the E nuclear spin modification) in collisions with D2 at a relative translational energy of
640 cm–1. The rotational level of the diatomic collision partner is j2 = 0 (upper panel) and j2 = 1
(lower panel). The initial level is indicated with an open square.
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5. Computed state-resolved differential cross sections
The DCSs for transitions between specific initial and final levels of the CD3 radical and
the D2 or H2 molecule cannot be determined experimentally because of the nk state distribution
in the incident CD3 beam and our inability to resolve individual k levels by REMPI detection.
In this section, we present computed state-to-state DCSs in which the initial and final levels of
both collision partners are specified.
FIG. S7. Computed state-to-state DCSs for inelastic scattering of CD3 from the 00 rotational
level into final rotational levels with n ≤ 7 (indicated in the insets) in collisions with D2 at a
collision energy of 640 cm–1. The solid and dashed curves are DCSs for which the initial
rotational level j2 of the D2 collision partner equals 0 and 1, respectively, and is the same after
the collision. In each panel, the plots are displaced vertically for clarity.
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FIG. S8. Computed state-to-state DCSs for inelastic scattering of CD3 from the 10 rotational
level into final rotational levels with n ≤ 7 (indicated in the insets) in collisions with D2 at a
collision energy of 640 cm–1. The solid and dashed curves are DCSs for which the initial
rotational level j2 of the D2 collision partner equals 0 and 1, respectively, and is the same after
the collision. In each panel, the plots are displaced vertically for clarity.
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FIG. S9. Computed state-to-state DCSs for inelastic scattering of CD3 from the 11 rotational
level into final rotational levels with n ≤ 5 (indicated in the insets) in collisions with D2 at a
collision energy of 640 cm–1. The solid and dashed curves are DCSs for which the initial
rotational level j2 of the D2 collision partner equals 0 and 1, respectively, and is the same after
the collision. In each panel, the plots are displaced vertically for clarity.
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FIG. S10. Computed state-to-state DCSs for inelastic scattering of CD3 from the 11 rotational
level into final rotational levels with n = 6 and 7 (indicated in the insets) in collisions with D2 at
a collision energy of 640 cm–1. The solid and dashed curves are DCSs for which the initial
rotational level j2 of the D2 collision partner equals 0 and 1, respectively, and is the same after
the collision. In each panel, the plots are displaced vertically for clarity.
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