JOURNAL OF CHEMICAL PHYSICS
VOLUME 120, NUMBER 18
8 MAY 2004
Reaction of formaldehyde cation with molecular hydrogen:
Effects of collision energy and H2 CO¿ vibrations
Jianbo Liu and Scott L. Andersona)
Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
共Received 29 December 2003; accepted 12 February 2004兲
The effects on the title reaction of collision energy (E col) and five H2 CO⫹ vibrational modes have
been studied over a center-of-mass E col range from 0.1 to 2.3 eV. Electronic structure and Rice–
Ramsperger–Kassel–Marcus calculations were used to examine properties of various complexes
and transition states that might be important. Only the hydrogen abstraction 共HA兲 product channel
is observed, and despite being exoergic, HA has an appearance energy of ⬃0.4 eV, consistent with
a transition state found in the electronic structure calculations. A precursor complex-mediated
mechanism might possibly be involved at very low E col , but the dominant mechanism is direct over
the entire E col range. The magnitude of the HA cross section is strongly, and mode specifically
affected by H2 CO⫹ vibrational excitation, however, vibrational energy has no effect on the
appearance energy. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1695311兴
the 1 A 2 (3p x ) Rydberg state.10 For this study, H2 CO⫹ was
generated in its ground state, or with one quantum in one of
the following vibrational modes: ␯ ⫹
2 共CO stretch, 0.208 eV兲,
⫹
⫹
␯ 3 (CH2 scissors, 0.143 eV兲, ␯ 4 (CH2 out-of-plane bend,
⫹
0.114 eV兲, ␯ ⫹
5 (CH2 asymmetric stretch, 0.337 eV兲, and ␯ 6
(CH2 in-plane rock, 0.101 eV兲. For notational simplicity, we
⫹
⫹
will denote these states as the ground state, ␯ ⫹
2 , ␯3 , ␯4 ,
⫹
⫹
␯ 5 , and ␯ 6 .
Under even low-intensity REMPI conditions, ground
electronic state H2 CO⫹ is readily photodissociated to HCO⫹
and CO⫹ . To remove these fragment ions from the beam, the
ions were generated inside a short radio frequency 共rf兲 quadrupole ion guide that focused the ions through a pair of ion
lenses into a conventional mass-selecting quadrupole. At the
exit of the mass filter, the ions were collected and collimated
by a lens set equipped with variable apertures, and a split
lens pair used to time gate the ion pulse. The combination of
controlled collection radius and time gating produces a massselected beam with narrow kinetic energy spread (⌬E
⬇0.1 eV).
The mass-, vibrational state-, and kinetic energy-selected
primary beam was injected into a system of eight-pole radio
frequency ion guides.11 In the first segment of the guide, ions
pass through a 10 cm long scattering cell, containing D2 at
⬃1⫻10⫺4 Torr. Deuterium 共Cambridge Isotope Lab,
99.6%兲 was used without further purification, and the scattering cell pressure was measured with a capacitance manometer. Product ions and unreacted primary ions were collected by the ion guide, passed into a second, longer guide
segment for time-of-flight 共TOF兲 analysis, then mass analyzed and counted.
Our procedures for cross-section measurement have
been described previously.6,12 Briefly, the ion guides were
operated at high rf amplitude and with a ⬃1 V potential drop
between the scattering and TOF segments of the guide, to aid
in the collection of slow ions. Integral cross sections were
calculated from the ratio of reactant and product ion intensi-
I. INTRODUCTION
We report a vibrationally state-selected scattering study
of the reaction of H2 CO⫹ ( ␯ ⫹ ) with D2 . Both H2 CO⫹ and
molecular hydrogen are important in the chemistry of interstellar clouds, comets, and planetary atmospheres of reducing compositions,1– 4 where nonequilibrium conditions make
vibrational effects important. Several exoergic reactions, including simple H atom transfer, are possible, yet no reaction
is observed at 300 K,3,5 raising the possibility of an energy
barrier in excess of the reactant energy. Such barriers are
unusual for exoergic ion–molecule reactions requiring only
simple atom transfer. For exoergic reactions, we might expect the barrier共s兲 to be early enough on the reaction coordinate that the reactants still ‘‘remember’’ their initial vibrational state. As a consequence, probing the effects of
different reactant vibrational modes on the reaction probability should provide insight into the barrier crossing dynamics.
We are able to probe the effects of five different vibrational
modes, along with collision energy over the 共center-of-mass兲
range from 0.1 to 2.3 eV. The experimental measurements
will serve as a stringent test for a direct dynamics trajectory
study of this reaction, currently underway.
II. EXPERIMENTAL AND COMPUTATIONAL DETAILS
The guided ion beam tandem mass spectrometer used in
this study has been described previously,6,7 along with the
operation, calibration, and data analysis procedures. The
H2 CO precursor was generated by heating a mixture of
paraformaldehyde 共Aldrich 95%兲 and anhydrous MgSO4
共Merck兲 to 60 °C,8 and sweeping the resulting H2 CO into a
pulsed molecular beam valve using a flow of helium at ⬃1
atm, giving a H2 CO concentration of ⬃5%.9 H2 CO⫹ can be
generated in selected vibrational states by REMPI through
a兲
Author to whom correspondence should be addressed. Electronic mail:
anderson@chem.utah.edu
0021-9606/2004/120(18)/8528/9/$22.00
8528
© 2004 American Institute of Physics
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
ties, and the calibrated target gas pressure–length product.
Differential cross sections were not measured for this system, because the product ion–neutral mass combination is
unfavorable for extracting ion velocity distributions.
Because we are measuring subtle effects, it is important
to minimize systematic variations in experimental conditions
that might be caused by drifting potentials, changes in laser
intensity or focal position, etc. For each state, we cycled
through the series of E col values several times. As a check on
reproducibility, we measured the cross-sections for the
ground state at the beginning and end of each complete experimental run. Finally, the entire set of experiments was
repeated several times to check the reproducibility. The kinematics of this system are such that the usual uncertainties
arising from product collection and mass spectrometer transmission efficiencies are negligible. Based on the reproducibility of the measurements, we estimate that the relative
error 共e.g., uncertainty in comparing data for different vibrational states or E col) is less than 10%. The uncertainty in the
absolute scale of the cross-sections is the greater of 20% or
0.1 Å2.
To aid in reaction coordinate interpretation, ab initio calculations were performed at the MP2/6-311⫹⫹G**,
B3LYP/6-311⫹⫹G** and G3 levels of theory, using
13
14
GAUSSIAN 98 and GAUSSIAN 03. Energies for stationary
points were also calculated at CCSD共T兲/cc-pVDZ using
MP2/6-311⫹⫹G** optimized geometries, giving results
similar to the G3 energies. We note that the G3 approach is
not suitable for describing transition structures on reaction
pathways involving a change in the number of electron
pairs.15 Fortunately, none of the transition structures in the
present system belong to this category. All of the transition
states 共TSs兲 found were verified to be first-order saddle
points by frequency calculations. When necessary, intrinsic
reaction coordinate 共IRC兲 calculations were used to determine which minima are connected by a particular TS. Rice–
Ramsperger–Kassel–Marcus 共RRKM兲 rate and density of
states calculations were done with the program of Zhu and
Hase,16 using its direct state count algorithm, and energetics
and scaled frequencies calculated at the G3 and MP2/6-31G*
levels, respectively.
III. RESULTS
A. Integral cross-sections
The H2 CO⫹ ⫹D2 isotope combination was used in the
experiment, to look for possible atom scrambling during the
reaction. For this system, product ions are observed only at
m/z 32, corresponding to simple D abstraction from D2 . We
will refer to this channel generically as hydrogen abstraction
共HA兲. The literature value for the exoergicity of the HA reaction for H2 is ⫺0.20⫾0.02 eV,17,18 and we calculate that
the exoergicity is ⬃0.01 eV larger for D2 , because of zeropoint effects. In reaction with D2 , no signal is seen for m/z
33, indicating that HA is not accompanied by hydrogen atom
scrambling. In principle, the m/z 32 product ion could be
D2 CO⫹ , from double H/D exchange. We discount this pos-
Reaction of formaldehyde cation with hydrogen
8529
FIG. 1. Cross-sections for the reaction of H2 CO⫹ ( ␯ ⫹ ) with D2 .
sibility because if double H/D exchange were significant, we
would expect to see the signal for single H/D exchange
(HDCO⫹ ) as well.
The integral cross-section for the reaction of ground
state H2 CO⫹ with D2 is given in Fig. 1, over the center-ofmass E col range from 0.1 to 2.3 eV. Our results indicate an
appearance energy 共AE兲 on the order of 0.4 eV, consistent
with the absence of reaction at thermal energies (kT
⫽⬃0.03 eV at 300 K兲.3,5 To extract the true threshold energy, it is necessary to correct for experimental broadening
factors, and this analysis is discussed below. Note that reaction efficiency ( ␴ reaction / ␴ collision) rises slowly with increasing E col , reaching only ⬃2% at E col⫽0.88 eV and ⬃12% at
our highest energy ( ␴ collision is taken as the greater of the
ion-induced-dipole capture and hard sphere cross-sections兲.
The experimental energy dependence is consistent with an
energetic barrier to reaction, but does not rule out the existence of a barrierless pathway strongly inhibited by dynamical constraints at low collision energy.
B. Ab initio results
The ab initio results for H2 CO⫹ ⫹H2 are summarized in
Figs. 2 and 3, and Table I. Table I compares the product
channel and intermediate complex energies calculated at
various theoretical levels, with experimental results, where
available.17 Because experimental results are not available
for the deuterium-labeled system, the values given in the
table are for the all-H system. For comparison, the G3 column also gives energetics for the reaction with D2 in parentheses. Note that the zero-point effects are quite small. In the
case of the HA channel, the MP2 method overestimates the
exoergicity by ⬃0.37 eV, while the B3LYP method underestimates it by 0.29 eV. The G3 results are in reasonable agreement with experiment. Not surprisingly, the binding energies
of productlike complexes 共relative to reactants兲 are also overestimated by MP2 and underestimated by B3LYP. The reaction path energetics in Fig. 2, including the transition states,
are from the G3 calculations. Our calculations at the G3 level
are in good agreement with previous calculations at the G1
and G2 levels by Ma et al.19
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8530
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
J. Liu and S. L. Anderson
FIG. 2. Schematic reaction coordinate for H2 CO⫹ ⫹H2 . Energies are derived from G3共0 K兲 calculations.
There are two isomers for the HA product, hydroxymethyl cation (H2 COH⫹ ) and methoxy cation (CH3 O⫹ ). In
accord with the thermochemical literature17 and earlier ab
initio work,20,21 the singlet H2 COH⫹ structure is the most
stable, giving ⌬ r H⫽⫺0.202 eV for the HA reaction. Singlet
CH3 O⫹ rearranges without activation to H2 COH⫹ , while
triplet CH3 O⫹ is ⬃3.4 eV higher in energy than singlet
H2 COH⫹ . Over our energy range, therefore, singlet
H2 COH⫹ is the only energetically accessible HA product.
Four weakly bound complexes 共A–D, Fig. 2兲 and two
covalently bound complexes (CH3 OH⫹ and CH2 OH⫹
2 ),
were found with CH4 O⫹ stoichiometry. Complexes A and B
are electrostatically bonded with no covalent or hydrogen
bonding. The potential is quite flat with respect to rotation of
the H2 CO⫹ and H2 moieties, as shown by harmonic hindered
rotor frequencies of just 16 and 51 cm⫺1, respectively, and
the fact that complex A converges to different geometries
when optimized at MP2/6-311⫹⫹G** and B3LYP/6311⫹⫹G** levels of theory 共inset in Fig. 2兲, respectively.
For the available energies relevant to the HA reaction, the
H2 CO⫹ and H2 moieties in these reactantlike complexes are
best considered to be nearly free rotors. Complexes C and D
are productlike, and bound by only ⬃0.1 eV with respect to
the HA products. No significant barrier separates the reactantlike complexes from reactants, or the productlike complexes from products.
In addition to the weakly bound complexes, there are
two covalent complexes with CH3 OH⫹ and CH2 OH⫹
2 structures. From the experimental observation that there is no
H/D exchange 共no HDCO⫹ or d 2 -H2 COH⫹ ), we can conclude that the CH3 OH⫹ complex cannot form to a significant
extent, because breakup of such a complex, either to HA
products or back to reactants, would necessarily be accom-
panied by H/D scrambling. The participation of H2 COH⫹
2 as
an intermediate complex cannot be ruled out from the experimental results, however, the calculations suggest that it unlikely to be mechanistically significant, at least for low E col .
One might think that H2 COH⫹
2 could form from reactants
with little or no activation barrier, however, the perpendicular attack of H2 on the oxygen end of H2 CO⫹ is calculated to
become strongly repulsive at short O–H2 distances, resulting
in a barrier to the direct formation of H2 COH⫹
2 . We were not
able to locate the transition state connecting H2 COH⫹
2 directly to reactants, but a relaxed potential energy scan along
the approach coordinate results in a barrier in C 2 v geometry
of 3.9 eV. There is a lower-energy pathway to H2 COH⫹
2 via
TS5, however, TS5 connects H2 COH⫹
2 to the productlike
complex C, and such productlike geometries are more likely
to go on to HA products rather than cross TS5 to H2 COH⫹
2 .
forms,
we
calculate
an
⬃1.7
Furthermore, even if H2 COH⫹
2
eV activation barrier 共TS5兲 for the separation of H2 COH⫹
2 to
H2 COH⫹ ⫹H, even though this corresponds to a reverse activation barrier for an ion–radical recombination. The barrier
is related to the fact that H2 COH⫹ is closed shell, and must
undergo a significant geometry change to bond the additional
H atom. In sum, we conclude that the covalent CH3 OH⫹ and
H2 COH⫹
2 species do not participate significantly in the
H2 CO⫹ ⫹H2 reaction.
The calculations suggest that the main pathway leading
to H2 COH⫹ ⫹H products at low collision energy is via TS1,
0.358 eV 共0.370 eV for D2 ) above reactants at the G3 level.
The fact that the experimental threshold energy 共see below兲
for HA is in reasonable agreement with the TS1 energy suggests that the threshold results from this energy barrier, rather
than from some dynamical bottleneck. This pathway may be
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
Reaction of formaldehyde cation with hydrogen
8531
to HCOH⫹ in reaction with D2 would also result in H/D
exchange, and no such products were observed.
C. Vibrational effects
Figure 1 also shows the dependence of the HA cross
sections on H2 CO⫹ vibrational states. The vibrational fre⫹
⫹
quencies are ␯ ⫹
2 ⫽0.208 eV, ␯ 3 ⫽0.143 eV, ␯ 4 ⫽0.114 eV,
⫹
⫹
␯ 5 ⫽0.337 eV, and ␯ 6 ⫽0.101 eV, respectively. Clearly, all
modes of H2 CO⫹ vibrational excitation inhibit the reaction,
i.e., the effects of vibration and E col are opposed, and, in
addition, the vibrational effects are strongly mode specific.
To show the mode effects more clearly, Fig. 4 shows the
vibrational inhibition factor 关␴共␯兲/␴共gs兲兴 plotted as a function
of vibrational energy, where each energy corresponds to one
of the six states studied, and ␴共gs兲 is the ground state cross
section. If the effects depended only on vibrational energy,
the points for each E col would fall on a smooth curve. Note
that the vibrational effects are strong and mode-specific, but
with a very weak dependence on collision energy.
IV. DISCUSSION
A. HA mechanism
FIG. 3. Potential energy contour maps for the reaction calculated at
MP2/6-31G**. 共a兲 Plotted against DO distance and DOC angle near TS1;
and 共b兲 plotted against DO distance and D–OC–H dihedral angle near TS1.
The numbers are the potential energy 共eV兲 relative to the reactants.
mediated by the weakly bound complexes A–C, particularly
at very low collision energies.
Figure 3 shows cuts through the potential energy surface
in the region of TS1, calculated at the MP2/6-31G** level of
theory with all coordinates other than those plotted optimized at each point. The saddle points on the contour maps
correspond to TS1, which is 0.38 eV above the reactants at
this level of theory. The dotted lines on the maps are the
minimum energy paths connecting TS1 to reactants and
products, taken from the IRC calculations. The two cuts
show how energy varies with the DO distance 共i.e., reaction
coordinate兲 and DOC angle and D–OC–H dihedral angle,
respectively.
A potential issue relevant to H2 CO⫹ chemistry is the
existence of the trans-HCOH⫹ isomer, which could conceivably form during a reaction, and would significantly affect
both the reaction mechanism and energetics. The involvement of trans-HCOH⫹ is unlikely, because it is calculated7
to be ⬃0.32 eV above H2 CO⫹ , with a ⬎1.9 eV barrier to the
isomerization. Furthermore, most pathways that might lead
As will be shown in the next section, the threshold energy found in the experiments is consistent with the calculated TS1 barrier energy, and the absence of any other pathway with similar or lower activation barrier suggests that
TS1 controls the exoergic HA reaction. The lowest-energy
HA pathway is formally: reactants→complex A→TS1
→complex C→H2 COD⫹ ⫹D, where the mechanistic significance of the weakly bound complexes A and C is unclear. As
noted, complexes A and B are very floppy, and at the available energies in our experiments, these complexes are better
described as two local minima in the potential governing the
dynamics of a reactantlike precursor complex with no fixed
geometry. The mechanistic importance of such a complex
depends on its lifetime. If long enough lived, such a precursor complex can allow repeated encounters between the reactants, increasing the probability of eventually finding the
low-energy pathway to products. Analogous complexes play
an important role in the reaction of H2 CO⫹ with methane,
for example.22
To estimate the precursor lifetime, we used the RRKM
program of Zhu and Hase16 to calculate the lifetime of complexes A and B as a function of E col . The rotational quantum
number K was treated as active in evaluating the RRKM
unimolecular rate constant,23 and the distribution of orbital
angular momentum J was estimated from the reaction crosssection 共giving the magnitude of the impact parameter兲 and
collision energy. Because complexes A and B probably interconvert, we take the lifetime, ␶ complex , as the average of the
RRKM values for A and B. We also calculated the lifetime of
complex C to evaluate the possibility that trapping in such a
geometry might increase the reaction time. For each complex, all decomposition channels indicated by lines in Fig. 2
were included. For the decay of A and B back to reactants,
and of complex C to HA products, we assumed orbiting transition states.24 Because the kinematics in this system are poor
for product recoil velocity measurements, the recoil energies
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8532
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
J. Liu and S. L. Anderson
TABLE I. Experimental and ab initio energies 共eV兲 relative to reactants H2 CO⫹ ⫹H2 .
Reaction channels
H2 COH⫹ ⫹H
CH3 O⫹ ⫹H
CH3 OH⫹ ⫹H
CH2 OH⫹
2 ⫹H
complex A
complex B
complex C
complex D
TS1
共complex A–C兲
TS2
共complex B–CH3 OH⫹ )
TS3
(CH3 OH⫹ –complex D兲
TS4
(CH3 OH⫹ – CH2 OH⫹
2 )
TS5
共complex C–CH2 OH⫹
2 )
G3共0K兲a
⫺0.113共⫺0.126兲
3.486共3.482兲
⫺0.839共⫺0.919兲
⫺1.174共⫺1.271兲
⫺0.066共⫺0.073兲
⫺0.051共⫺0.057兲
⫺0.229共⫺0.247兲
⫺0.184共⫺0.200兲
0.358共0.370兲
1.904共1.859兲
⫺0.181共⫺0.211兲
B3LYP/6-311⫹⫹G**b
MP2/6-311⫹⫹G**c
CCSD共T兲/cc-pVDZd
Experimentale
0.085
3.206
⫺1.024
⫺1.091
⫺0.041
⫺0.024
⫺0.037
¯
0.100
⫺0.573
3.247
⫺0.917
⫺1.509
⫺0.030
⫺0.013
⫺0.609
⫺0.570
0.366
⫺0.253
3.266
⫺0.884
⫺1.389
⫺0.099
⫺0.064
⫺0.308
⫺0.266
0.340
⫺0.20⫾0.02
3.43
⫺0.99
⫺1.30
¯
¯
¯
¯
0.40⫾0.05f
1.808
1.802
1.765
¯
⫺0.486
⫺0.219
¯
¯
0.255共0.196兲
0.293
0.037
0.168
¯
0.560共0.524兲
0.395
0.480
0.515
¯
a
Parenthetical values are values for the reaction with D2 .
Including zero-point energy calculated at B3LYP/6-311⫹⫹G** and scaled by 0.9804.
c
Including zero-point energy calculated at MP2/6-311⫹⫹G** and scaled by 0.9646.
d
Single-point calculation using MP2/6-311⫹⫹G** optimized geometries.
e
For all H systems 共Refs. 17 and 18兲.
f
This work. Fitted from the reaction cross-section.
b
needed to calculate the orbiting TS properties were estimated
using the statistical model of Klots.25 At E col⫽0.55 eV,
␶ complex is ⬃0.35 ps, dropping to ⬃0.2 ps as E col increases to
1 eV. For comparison, the classical rotational period of the
precursor complex 关estimated using average angular momentum 具 l 典 ⫽ ␮ • v rel• 具 b 典 , where ␴ (E col)⫽ ␲ 具 b 典 2 ] is around
0.3–0.4 ps—comparable to the RRKM lifetime. We can also
compare ␶ complex with an estimate of the direct reaction time,
taken here as the time for undeflected reactants to fly past
each other a distance of 2 Å. This fly-by time ranges from
only 0.04 ps at E col⫽0.55 eV to 0.03 ps at E col⫽1.0 eV. The
complex A/B lifetime, though short, is significantly longer
than the fly-by time, thus a precursor complex could conceivably have some mechanistic significance if it forms effi-
ciently. In contrast, the RRKM lifetime of complex C is less
than 0.1 ps at all E col , i.e., once the D2 bond is broken, the
system separates promptly to products.
As expected, RRKM predicts that the precursor complex
decays predominantly back to reactants, with the decay over
TS1 accounting for at most one percent in the E col range
below 1.0 eV. Similarly, complex C is predicted to decay
predominantly to HA products, with less than 1% transitioning back over TS1 or over TS5 to CH2 OH⫹
2 . These results
support the conclusion that TS1 crossing is the rate-limiting
step and that CH2 OH⫹
2 does not play a significant role.
If reaction occurred only by statistical decay of the precursor complex, the net reaction efficiency would simply be
the product of the precursor complex formation probability
and the branching ratio for crossing TS1. Taking the ioninduced-dipole capture cross section as an upper limit on
complex formation, we can estimate that the upper limit on
the complex-mediated contribution to the HA cross-section
ranges from 0.002 Å2 at E col⫽0.51 eV, to 0.03 Å2 at E col
⫽1.11 eV. The experimental HA cross-sections are about ten
times larger than this upper limit, indicating that complexmediated HA is, at most, a minor channel, i.e., direct reaction
dominates even at threshold. At high energies, the RRKM
complex lifetimes are too short for there to be any complex
contribution to the mechanism.
B. Threshold energy dependence
and the effects of vibrational energy
FIG. 4. Vibrational inhibition factors vs H2 CO⫹ E vib , for different E col .
One interesting question is how different vibrational
modes and collision energy compare in their ability to drive
reaction over the TS1 activation barrier at threshold. To extract the true threshold energy, E 0 , it is necessary to fit the
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
Reaction of formaldehyde cation with hydrogen
TABLE II. Integral cross-section fit results using the modified line-of-center
model with E 0 ⫽0.4 eV.
Ionic state
E vib 共actual, eV兲
E vib 共fit, eV兲
n
Ground state
␯⫹
6 ⫽1
␯⫹
4 ⫽1
␯⫹
3 ⫽1
␯⫹
2 ⫽1
␯⫹
5 ⫽1
0
0.101
0.114
0.143
0.208
0.337
0 ⫾0.05
⫺0.04⫾0.05
0.01⫾0.05
⫺0.03⫾0.05
⫺0.02⫾0.03
⫺0.01⫾0.04
1.8 –2.2
2.0–2.5
2.0–2.4
2.0–2.4
2.0–2.3
1.9–2.3
experimental E col dependence, convoluting a model ‘‘true’’
␴ (E col) function with the appropriate experimental broadening distributions. For our ‘‘true’’ ␴ (E col) function, we have
taken the usual modified line-of-center model:26,27
␴ 共 E col兲 ⫽ ␴ 0
共 E col⫹E vib⫹E rot⫺E 0 兲 n
,
E col
共1兲
for (E col⫹E vib⫹E rot)⬎E 0 , otherwise ␴ (E col)⫽0. Here E vib
and E rot are the vibrational and rotational energy of the reactants, and ␴ 0 is a normalization factor, adjusted to match
the magnitude of the experimental cross section at some E col
well above threshold. The two fitting parameters are E 0 , the
‘‘true’’ threshold energy, and n, which controls curvature of
the cross-section function. E vib is the energy of the selected
state, and E rot is Boltzman 共300 K兲 for D2 , and negligible for
H2 CO⫹ because it is produced by the photoionization of a
supersonic beam. The main broadening factor is the distribution of E col , resulting from ion beam velocity spread 共measured by TOF at each nominal E col) and thermal motion of
the D2 target. The model ␴ (E col) function is run through a
Monte Carlo simulation of the experiment to factor in the
broadening functions, and the n and E 0 parameters are adjusted until the convoluted model function matches the experiment. E 0 and its uncertainty range are estimated by running fits for a series of E 0 values, with n freely adjusted at
each step, then noting the range of E 0 for which it is possible
to obtain fits within the experimental uncertainty.
For a reaction of the ground state H2 CO⫹ , the best fit
‘‘true’’ threshold energy (E 0 ) is 0.40⫾0.05 eV, and the corresponding n parameter is 2.0⫾0.2. This threshold energy is
consistent with the G3 energy of TS1 共0.37 eV for D2 ),
within the combined uncertainties of the experiment 共0.05
eV兲 and the G3 calculation 共⬃0.045 eV兲,28 consistent with
the conclusion that TS1 controls HA.
As shown by Eq. 共1兲, the usual threshold law explicitly
assumes that E vib and E col are equally effective in the nearthreshold region. To probe the actual effectiveness of E vib ,
we fit the vibrationally excited cross-sections, fixing E 0 at
the value obtained for ground state H2 CO⫹ , and treating E vib
as a fitting parameter 共along with n兲. The E vib parameters
thus extracted 共Table II兲 measure the effectiveness of each
vibrational mode at driving the HA reaction. The extracted
E vib parameters are all zero within the fitting uncertainty of
⬃0.05 eV, irrespective of the fact that the actual E vib is varying from 0 to 0.337 eV for the states studied. Note that the n
8533
parameters are all roughly equal, indicating that the crosssections have a similar near-threshold curvature for all vibrational states.
The complete absence of any vibrational effect on the
threshold energy is interesting. For collision energies above
the threshold, vibrational effects are determined by the average way in which vibration couples to the reaction coordinate, and vibration can enhance or inhibit reactivity. The
threshold energy, on the other hand, is not determined by
average behavior, but rather by whether there is any probability for coupling vibration to drive barrier crossing. We
might expect that for total energy near the threshold, there
should be at least some chance that vibrational energy can
drive a reaction, and thus that the threshold should just depend on E total . This assumption is inherent in Eq. 共1兲, which
has been used extensively to extract accurate energetics from
threshold fitting.27,29,30 It should be noted, however, that the
reactants in such experiments are thermal near room temperature, thus the results are not very sensitive to vibration,
especially for high-frequency modes of the sort probed here.
The handful of previous studies directly addressing the
effects of vibration on reaction thresholds can be classified
into two groups. The first is simple collision-induced dissociation 共CID兲, in collisions with inert targets. The dominant
CID mechanism for this type of system consists of an impulsive collision, where translational-to-internal 共T-to-V,R兲 energy transfer occurs, followed by dissociation if the resulting
internal energy exceeds the dissociation limit. To our knowledge, the only studies of vibrational effects on CID were our
studies of OCS⫹ ( ␯ ⫹ )⫹Ar and Xe,31 and H2 CO⫹ ( ␯ ⫹ )⫹Ne
and Xe.7 In the two examples known, it is found that for E col
above the threshold, CID is driven by reactant vibrational
energy more efficiently than by E col . This enhancement reflects the fact that, on average, collisional T↔V,R conversion is not 100% efficient; thus the energy in the reactant
vibration is more likely to end up as internal energy than an
equivalent amount of E col . 32 Note, however, that the thresholds, themselves, were found to depend only on E total , reflecting the fact that thresholds do not probe average behavior, but rather the extremes. In this case, E total scaling
indicates that there is at least some chance that a collision
with E total⫽E 0 results in 100% conversion to internal energy,
driving dissociation.
For chemical reactions, where potential surfaces are
complex and highly variable, vibrational effects on both reactivity and threshold energies do not fit a simple pattern.
One subclass of reactions is endoergic charge transfer 共CT兲,
and vibrationally resolved thresholds are available for three
systems. In each case, reactant vibration does drive CT at the
threshold, however, the relative efficiencies of E col and E vib
vary among the three systems. As in the present study, the
thresholds were fit using Eq. 共1兲, and E vib was treated as a
fitting parameter. For CT of H2 CO⫹ with OCS (⌬ r H
⫽0.30 eV), the ratio E vib共fit)/E vib共actual) is large and decreases smoothly with increasing E vib共actual), from 100%
⫹
33
for ␯ ⫹
6 共101 meV兲, to 77% for ␯ 5 共337 meV兲. In contrast,
⫹
for CT of CH3 CHO with C2 D4 (⌬ r H⫽0.28 eV), the
E vib共fit)/E vib共actual) ratio was ⬃18%, irrespective of the vibrational state.34 Finally, for CT of OCS⫹ with C2 H2 (⌬ r H
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8534
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
J. Liu and S. L. Anderson
TABLE III. Estimated TS1 barrier height for vibrational excited H2 CO⫹ ⫹H2 . a
Reactant state and frequencies 共eV兲
Ground state
H2 CO⫹ ( ␯ ⫹
6 ⫽1)
H2 CO⫹ ( ␯ ⫹
4 ⫽1)
H2 CO⫹ ( ␯ ⫹
3 ⫽1)
H2 CO⫹ ( ␯ ⫹
2 ⫽1)
H2 CO⫹ ( ␯ ⫹
5 ⫽1)
H2 ( ␯ ⫽1)
¯
0.103
0.131
0.154
0.192
0.355
0.530
Corresponding
frequencies 共eV兲 in TS1
Barrier height 共eV兲
¯
0.129
0.139
0.166
0.193
0.370
imaginary
0.321
0.382共0.388兲b
0.338共0.338兲
0.360共0.345兲
0.320共0.316兲
0.351共0.351兲
none 共0.016兲
Barrier height change
共eV兲
0
0.061共0.067兲b
0.017共0.017兲
0.039共0.024兲
⫺0.001共⫺0.005兲
0.030共0.030兲
⫺0.321共⫺0.305兲
a
The calculations were done at MP2/6-311⫹⫹G**, zero-point energies are not included; calculated frequencies
are scaled by 0.9434.
b
The value in the parenthesis corresponds to the other turning point for the vibration state of interest.
⫽0.23 eV) the vibrational efficiency is quite mode-specific.
E vib共fit)/E vib共actual) is ⬃100% for ␯ ⫹
3 共C–S stretch, 87
meV兲, and essentially 0% for both ␯ ⫹
1 共C–O stretch, 256
12
共bend,
62
meV兲
excitation.
Clearly, the coumeV兲 and ␯ ⫹
2
pling of vibration to drive CT is complicated and system
dependent, and presumably depends on the CT mechanism.
One important factor in vibrational effects is competition
with other channels. We might expect that endoergic channels will generally tend to be enhanced by additional energy,
including E vib . The net enhancement may be reduced or
eliminated, however, if E vib also enhances competing channels. CT is always in competition with nonreactive scattering. In essence, collisions mix A⫹ ⫹B and A⫹B⫹ charge
states, and as the collision partners separate, the charge may
end up on either A or B. If the separation is slow 共i.e., adiabatic兲, the lower-energy reactant charge state will tend to
dominate, rather than CT. For a given total energy, therefore,
we might anticipate that partitioning energy into E vib , at the
expense of E col , would tend to reduce recoil speed, thus
tending to suppress CT. Perhaps more importantly, the systems mentioned have competing exoergic reaction channels
that are mediated by collision complexes at low E col .
Breakup of the complexes is dominated by the exoergic reaction channels, thus anything enhancing a complex formation will tend to inhibit CT. We have argued that partitioning
energy from E col to E vib reduces the amount of T→V,R transfer required to form complexes, thus enhancing the complex
formation.
The reaction under study here is an atom transfer process, and vibrationally selected thresholds have been previously measured for only two atom transfer reactions. The
proton transfer 共PT兲 reaction CH3 CHO⫹ ( ␯ ⫹ )⫹D2 O
→CH3 CHO⫹D2 OH⫹ (⌬ r H⫽0.11 eV) was studied for reactant vibrational states with E vib from zero to 439 meV.
Here, E vib exceeds the PT endoergicity by up to a factor of 4,
and is observed to enhance PT above the threshold. Nonetheless, the threshold itself was found to be vibrational stateindependent 关i.e., E vib共fit)/E vib共actual)⬇0].35 The absence of
E vib effects was rationalized in terms of competition between
endoergic PT, which was found to occur by a direct mechanism, and a complex-mediated mechanism leading to exoergic product channels, similar to the argument outline above
⫹
for CT. In contrast, the HA reaction C2 H⫹
2 ⫹CH4 →C2 H3
⫹CH3 (⌬ r H⬇0.05 eV) has strongly mode-specific effects
on both the cross-section magnitude and the threshold. The
excitation of ␯ ⫹
2 共CC stretch, 225 meV兲 results in no significant change in the threshold behavior 关i.e., E vib共fit)/
E vib共actual)⬇0], and increases the above-threshold crosssection by only about 50%. The excitation of an overtone of
the cis-bend (2 ␯ ⫹
5 , 155 meV兲 essentially eliminates the
threshold 关 E vib共fit/E vib共actual)⬇80%], and increases the
cross-section by up to a factor of 30 in the near-threshold
energy range. In that system, it was argued36 that the bending
vibration was the correct type of motion to drive passage
over a cis-bent transition state, while CC stretching was the
wrong type of motion, and thus was ineffective.
The present H2 CO⫹ ⫹D2 reaction differs from these previously studied examples in a number of ways. The only
channel observed, HA, is exoergic with a substantial activation barrier, rather than endoergic. As in several of the previous studies, the channel in question goes by a direct
mechanism, however, there are no other channels in competition, other than ‘‘no reaction.’’ There are strongly bound
complexes whose formation is formally in competition with
HA (CH3 OH⫹ and CH2 OH⫹
2 , Fig. 2兲, however, participation of these complexes in the reaction mechanism is blocked
by high-energy transition states 共TS2,TS5兲.
The vibrational and collision energy effects in this system are presumably associated with crossing TS1, i.e., with
breaking the D2 bond. If this were an impulsive reaction in
an A⫹BC system, we would try to analyze vibrational and
E col effects in terms of the early/late barrier notions introduced by Polanyi et al.37– 40 For a system with many degrees
of freedom 共12 in this case兲 and with vibrational motions that
are both faster and slower than the characteristic reactant
relative motion, it is not obvious how to apply such rules. To
try to gain deeper insight into the collision/vibrational dynamics, we are in the course of carrying out an extensive
direct-dynamics trajectory study of this reaction. Here we
will confine ourselves to some qualitative remarks.
One way of thinking about vibrational effects is in terms
of the effects of vibration distortion on the effective TS1
barrier height. Clearly, distortion away from the equilibrium
共or TS structure兲 increases the energy of both reactants and
TS, but if the increase is larger for reactants than in the TS
geometry, then the vibrational energy effectively lowers the
barrier height. The energies of reactants and TS1 were calculated with the H2 CO⫹ moiety distorted to the classical
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
turning points of each vibrational mode, and the results are
summarized in Table III. Note that none of the H2 CO⫹ vibrations lower the effective TS1 barrier, as might be expected because the H2 CO⫹ geometry is only distorted by
1%–2% in TS1. In contrast, for vibrationally excited D2 , the
barrier vanishes, reflecting the fact that this is a high-energy
vibration of the bond being broken at the TS1. 共The D2 bond
is extended ⬃10% in the TS1.兲 This result is similar to what
was found in the HCl⫹1,3-butadiene addition reaction by
Klenerman and Zare et al.,41 where the reaction is exoergic,
but with an energy barrier. Internal excitation of the 1,3butadiene, on its own, was inefficient at overcoming the barrier, and the excitation of HCl vibration or collision energy
or both are required to promote the addition reaction.
C. Above threshold vibrational effects
As shown in Fig. 4, all H2 CO⫹ vibrations inhibit the HA
reaction above threshold, with effects that are strongly dependent on the mode of excitation, i.e., the excitation of ␯ ⫹
4
共out-of-plane bend兲 or ␯ ⫹
5 共asym. CH stretch兲 results in
smaller-than-average inhibition 共per unit energy兲, while ␯ ⫹
6
⫹
(CH2 in-plane rock兲, ␯ ⫹
3 (CH2 scissors兲, and ␯ 2 共CO stretch兲
cause larger-than-average inhibition. As discussed above, the
HA reaction is dominated by a direct mechanism, even at
low E col . Therefore, the vibrational inhibition cannot be ascribed to E vib-induced reduction in the precursor complex
lifetime. Rather, the effects must reflect the dynamics of the
direct collision event.
In thinking about mechanisms for vibrational effects,
two physical limits come to mind. If the collision time scale
is short compared to the vibrational period共s兲, then each collision will take place at fixed vibrational phase. In this limit,
the primary vibrational effect must result from vibrationinduced distortion of the reactants. The other limit corresponds to collisions slower than the vibrational time scale,
and here distortion cannot be an important effect because
each collision averages over several vibrational periods. Instead, vibrational effects must depend on the vibrational velocities of the reactant atoms, which exceed the relative velocity in this limit. In most reactions, vibrations are fast
compared to collision times, however, in this system the reduced mass of the reactants is small, resulting in high relative velocities. For the E col range above the reaction threshold, the relative velocity ranges from ⬃5000 m/sec to
⬃12,000 m/sec. If we take 2 Å as a characteristic distance
defining some sort of reaction time, then the times vary from
⬃40 fsec at threshold to ⬃17 fsec at E col⫽2.5 eV. For comparison, the classical vibrational periods for the various
H2 CO⫹ vibrations vary from 12 to 40 fsec, with associated
maximum atomic velocities in the range from 5000– 8000
m/sec. Over the range of conditions studied, the relative and
vibrational velocities and time scales are comparable, and
both velocity and distortion effects might be significant.
In this context it is interesting to note that the vibrational
mode effect pattern 共Fig. 4兲 is quite similar over the entire
E col range studied, even though the relative velocity is
changing by a factor of two. Even more interesting is the fact
that a nearly identical mode effect pattern is also observed in
Reaction of formaldehyde cation with hydrogen
8535
the analogous HA reaction with methane: H2 CO⫹ ⫹CD4
→H2 COD⫹ ⫹CD3 , and again the effects are nearly
E col-independent.22 For both systems, the controlling transition state can be characterized as reactant-like with respect to
the geometry of the H2 CO⫹ moiety, while the neutral reactant is significantly distorted at the TS. It is the breaking of
the D-CD3 or D-D bond that results in the barrier, and the
similarity of H2 CO⫹ mode effects suggests that the dynamics at the critical point must be quite similar for the two
systems. The major differences between these two system are
that for H2 CO⫹ ⫹CD4 , HA proceeds with no activation energy, and the reduced mass of the reactants is 3.4 times
greater. Taken together, we find a nearly constant pattern of
H2 CO⫹ mode effects for relative velocities ranging from
⬃1300 m/s (CD4 at 0.1 eV兲 to 12 0000 m/s (D2 at 2.5 eV兲,
i.e., for collision time scales ranging from considerably
longer than to about the same as the vibrational periods.
The direct dynamics trajectory study underway will presumably shed more light on the origin of the mode-specific
vibrational effects. Here we merely note a few obvious
points. The contour maps in Fig. 3 show cuts through the
TS1 portion of the PES corresponding to D2 approaching the
O end of H2 CO with D2 in the favorable end-on orientation
共see Fig. 2 for the structure of TS1兲. The top shows the
dependence on the DO distance and the DOC angle, and the
bottom shows the dependence on the DO distance and
D–OC–H dihedral angle. The minimum energy reaction
path is shown as a dashed line. These figures show that TS1
is geometrically quite restricted. The favorable orientation is
for D2 to approach in the H2 CO plane, with a DOC angle of
about 112°, and a D–OC–H angle near 0°. The energy rises
rapidly if either angle is varied by more than 10°–20°, i.e.,
the TS1 is quite tight. As shown in Table III, H2 CO⫹ vibrational distortion does not affect the effective barrier height
significantly, but vibrational distortion might significantly affect the tightness of the TS1. It is not feasible to explore the
effects of each vibrational mode on a high dimensionality
PES, however, we did do some exploration of this issue. As
shown in Fig. 4, ␯ ⫹
2 共CO stretch兲 excitation causes the largest
inhibition. To examine the effects of ␯ ⫹
2 excitation on TS
tightness, we carried out two-dimensional relaxed PES scans,
similar to those used to generate Fig. 3, but with the CO
bond fixed at lengths corresponding to the classical turning
points of the H2 CO⫹ ␯ ⫹
2 vibration. It was found that when
the CO bond is compressed, the TS1 energy is more strongly
dependent on the DOC angle by ⬃15%, suggesting that vibrational tightening of the reaction bottleneck might be a
factor in the vibrational inhibition. We note that the other
modes that give larger-than-average inhibitions per unit en⫹
ergy ( ␯ ⫹
6 and ␯ 3 ), also involve changes in the CO bond
length 共⬃25 and ⬃50% of the changes for ␯ ⫹
2 ). In contrast,
)
and
CH
asymmetric
stretch
the out-of-plane bend ( ␯ ⫹
2
4
),
which
both
cause
less
inhibition
than
expected
from
(␯⫹
5
their energies, involve relatively little CO bond distortion.
ACKNOWLEDGMENT
This work was supported by the National Science Foundation under Grant No. CHE-0110318.
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8536
J. Chem. Phys., Vol. 120, No. 18, 8 May 2004
A. Dalgarno and J. H. Black, Rep. Prog. Phys. 39, 573 共1976兲.
D. Smith and N. G. Adams, Astrophys. J. 217, 741 共1977兲.
3
W. T. Huntress, Jr., Astrophys. J., Suppl. Ser. 33, 495 共1977兲.
4
M. Y. Amin, M. S. El Nawawy, B. G. Ateya, and A. Aiad, Earth, Moon,
Planets 69, 127 共1995兲.
5
N. G. Adams, D. Smith, and D. Grief, Int. J. Mass Spectrom. Ion Phys. 26,
405 共1978兲.
6
Y.-H. Chiu, H. Fu, J.-T. Huang, and S. L. Anderson, J. Chem. Phys. 102,
1199 共1995兲.
7
J. Liu, B. Van Devener, and S. L. Anderson, J. Chem. Phys. 116, 5530
共2001兲.
8
R. Spence and W. Wild, J. Chem. Soc. 1935, 338.
9
F. S. Dainton, K. J. Ivin, and D. A. G. Walmsley, Trans. Faraday Soc. 55,
61 共1959兲.
10
J. Liu, H.-T. Kim, and S. L. Anderson, J. Chem. Phys. 114, 9797 共2001兲.
11
D. Gerlich, Adv. Chem. Phys. 82, 1 共1992兲.
12
Y.-H. Chiu, H. Fu, J.-T. Huang, and S. L. Anderson, J. Chem. Phys. 105,
3089 共1996兲.
13
M. J. Frisch, G. W. Tucks, H. B. Schlegel et al., GAUSSIAN 98, Gaussian,
Inc., Pittsburgh, PA, 1998.
14
M. J. Frisch, G. W. Trucks, H. B. Schlegel et al. GAUSSIAN 03, Gaussian,
Inc., Pittsburgh, PA, 2003.
15
L. A. Curtiss 共private communication兲.
16
L. Zhu and W. L. Hase, Quant. Chem. Prog. Exchange QCPE 644.
17
S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and
W. G. Mallard, J. Phys. Chem. Ref. Data 17, Suppl. 1 共1988兲.
18
S. G. Lias, in NIST Standard Reference Database Number 69, edited by P.
J. Linstrom and W. G. Mallard 共National Institute of Standards and Technology, Gaithersburg, MD, 2003兲, http://webbook.nist.gov
19
N. L. Ma, B. J. Smith, J. A. Pople, and L. Radom, J. Am. Chem. Soc. 113,
7903 共1991兲.
20
W. J. Bouma, R. H. Nobes, and L. Radom, Org. Mass Spectrom. 17, 315
共1982兲.
1
2
J. Liu and S. L. Anderson
21
L. A. Curtiss, L. D. Kock, and J. A. Pople, J. Chem. Phys. 96, 4040
共1991兲.
22
J. Liu, B. V. Devener, and S. L. Anderson, J. Chem. Phys. 119, 200 共2003兲.
23
L. Zhu and W. L. Hase, Chem. Phys. Lett. 175, 117 共1990兲.
24
M. T. Rodgers, K. M. Ervin, and P. B. Armentrout, J. Chem. Phys. 106,
4499 共1997兲.
25
C. E. Klots, J. Chem. Phys. 58, 5364 共1973兲.
26
M. B. Sowa-Resat, P. A. Hintz, and S. L. Anderson, J. Phys. Chem. 99,
10736 共1995兲.
27
P. B. Armentrout, Int. J. Mass. Spectrom. 200, 219 共2000兲.
28
L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A.
Pople, J. Chem. Phys. 109, 7764 共1998兲.
29
P. B. Armentrout, in The Encyclopedia of Mass Spectrometry. Volume 1:
Theory and Ion Chemistry, edited by P. B. Armentrout 共Elsevier, Amsterdam, 2003兲, p. 426.
30
P. B. Armentrout, in Ref. 29, p. 417.
31
B. Yang, Y. H. Chiu, H. Fu, and S. L. Anderson, J. Chem. Phys. 95, 3275
共1991兲.
32
J. Liu, K. Song, W. L. Hase, and S. L. Anderson, J. Chem. Phys. 119, 3040
共2003兲.
33
J. Liu, B. V. Devener, and S. L. Anderson, J. Chem. Phys. 117, 8292
共2002兲.
34
H.-T. Kim, J. Liu, and S. L. Anderson, J. Phys. Chem. A 106, 9798 共2002兲.
35
H.-T. Kim, J. Liu, and S. L. Anderson, J. Chem. Phys. 115, 1274 共2001兲.
36
S. J. Klippenstein, J. Chem. Phys. 104, 5437 共1996兲.
37
J. C. Polanyi and W. H. Wong, J. Chem. Phys. 51, 1439 共1969兲.
38
M. H. Mok and J. C. Polanyi, J. Chem. Phys. 51, 1451 共1969兲.
39
J. H. Mok and J. C. Polanyi, J. Chem. Phys. 53, 4588 共1970兲.
40
B. A. Hodgson and J. C. Polanyi, J. Chem. Phys. 55, 4745 共1971兲.
41
D. Klenerman and R. N. Zare, Chem. Phys. Lett. 130, 190 共1986兲.
Downloaded 07 May 2004 to 128.110.196.158. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp