Rotational and vibrational state distributions of HNC(0 v21 0) from the hot H atom reaction: H + (CN)2 → HNC + CN

Article abstract of DOI:10.1021/jp0010583

The reaction dynamics of the five-atom system, H + (CN)₂, was investigated by probing the minor product channel producing the transient HNC molecule. The complete initial energy disposition, translation, rotation, and vibration was determined for the HNC(0 v₂¹ 0), v₂¹= 0°, 1¹, product. The reaction was studied under bulk conditions and was initiated by energetic H atoms with a mean translational energy of 92 kJ mol^-1. The HNC molecule was monitored by time- and frequency-resolved absorption spectroscopy with sub-Doppler resolution. The initial rotational state distribution of each HNC(0 v₂¹ 0) vibrational level was measured and found to be well-described by a Boltzmann distribution. Only two vibrational levels were detected so that the initial HNC product vibrational level distribution was determined as well. The absolute reaction cross section for the title reaction was measured to be 2 × 10^-18 cm² for H atoms with a nominal translational energy of 113 kJ mol.^-1

Full text of DOI:10.1021/jp0010583

10202
J. Phys. Chem. A 2000, 104, 10202-10211
Rotational and Vibrational State Distributions of HNC(0 v12 0) from the Hot H Atom
Reaction: H + (CN)2 f HNC + CN†
R. Glen Macdonald*
Argonne National Laboratory, Chemistry DiVision, 9700 South Cass AVe., Argonne, Illinois 60439
ReceiVed: March 20, 2000; In Final Form: June 1, 2000
The reaction dynamics of the five-atom system, H + (CN)2, was investigated by probing the minor product
channel producing the transient HNC molecule. The complete initial energy disposition, translation, rotation,
and vibration was determined for the HNC(0 v21 0), v12) 00,11, product. The reaction was studied under bulk
conditions and was initiated by energetic H atoms with a mean translational energy of 92 kJ mol-1. The HNC
molecule was monitored by time- and frequency-resolved absorption spectroscopy with sub-Doppler resolution.
The initial rotational state distribution of each HNC(0 v12 0) vibrational level was measured and found to be
well-described by a Boltzmann distribution. Only two vibrational levels were detected so that the initial HNC
product vibrational level distribution was determined as well. The absolute reaction cross section for the title
reaction was measured to be 2 × 10-18 cm2 for H atoms with a nominal translational energy of 113 kJ mol.-1
I. Introduction
Much of our understanding of the energy disposition into the
polyatomic product comes from theoretical studies of four atom
systems, using both quasiclassical trajectory calculations14 or
approximate quantum scattering methods.15,16 The problem of
dealing with nine internal degrees of freedom from first
principles is still an intractable computational problem for exact
quantum scattering calculations, but progress is rapidly being
made.3 A recent review summarizes the details of the compari-
son between theory and experiment for four atom systems.17
An example of the complexity of a global PES involving four
atoms is provided by the HClCN system, for which Harding
calculated 9 transition states and 14 minima.18
The details of the energy disposal in three atom systems have
greatly added to our understanding of reaction dynamics. Indeed,
the interaction between theoretical predictions and experimental
observations have resulted in the emergence of some very useful
global concepts.1,2 The current status of atom + diatom systems
is such that it now almost possible to completely determine the
reaction dynamics between atoms and molecules composed of
first row elements using first principles, i.e., using the calculation
of an ab initio potential energy surface (PES) and a complete
quantum mechanical treatment of the scattering dynamics.3
Naturally, there has been a significant trend over the past
few years to extend the detailed study of reaction dynamics into
systems involving more than three atoms. For those studies
interested in probing reaction dynamics by investigating the
energy disposal into the reaction products, with a few exceptions,
the studies have concentrated on probing the diatomic product
in a state-specific manner. Efforts to probe the internal state
distribution of the polyatomic reaction product are hampered
by the large number of internal states, rotational and vibrational,
that are accessible to a polyatomic molecule and a general
difficulty in applying state-specific laser techniques to poly-
atomic species. To circumvent these difficulties, most investiga-
tors probing the energy disposition into a polyatomic reaction
product have concentrated on determining the vibrational level
distribution only and not the determination of the initial
rotational state distribution. All polyatomic molecules have
active infrared absorptions so either infrared absorption or
chemiluminescence have been the experimental method of
choice to detect the vibrational level distribution of the
polyatomic product.4,5,6,7,8,9,10, The CN + O2 f NCO + O is
the only four-atom system in which the vibrational11,12 and
rovibrational state distributions13 in the polyatomic product have
been probed by laser-induced fluorescence.
An excellent example of the interplay between theory and
experiment to elucidate the reaction dynamics in a polyatomic
system is provided by the OH + HBr f H2O + Br reaction
and its istopomers.10 The vibrational energy distributions of the
various possible H2O isotopomers were determined by infrared
chemiluminescence measurements. Quasiclassical trajectory
calculations19 were carried out on a model PES and were used
to elucidate the mechanism for vibrational energy disposition
into the H2O product. The calculations suggested several
methods for producing the large bending excitation observed
experimentally, and further illustrated that kinematic effects for
a H + L - H (where H and L are heavy and light masses,
respectively) mass combination expected for triatomic systems
were valid in the tetratomic case as well.
In the present work, the reaction dynamics of the pentatomic
reaction system H + (CN)2 f HNC(0 v12 0) + CN were
explored by determining the rotational state distribution of the
HNC product in its ground and first excited bending vibrational
level. The vibrational population distributed between these two
levels was also determined. No other rovibrational transitions
were detected, so these measurements likely determine the
vibrational level distribution in the HNC product. As a further
probe into the reaction dynamics of this system, the center of
mass (COM) translational energy disposition was also measured.
† Part of the special issue “C. Bradley Moore Festschrift”.
* To whom correspondence should be addressed. E-mail: macdonald@
anlchm.chm.anl.gov.
The reaction was initiated by photolyzing CH3SH at 248 nm
creating energetic H atoms that reacted with (CN)2 at low
10.1021/jp0010583 CCC: $19.00 © 2000 American Chemical Society
Published on Web 07/11/2000

Hot H Atom Reaction
J. Phys. Chem. A, Vol. 104, No. 45, 2000 10203
pressures under bulk conditions. The HNC rovibrational popula-
tion was probed by time- and frequency-resolved infrared
absorption spectroscopy with sub-Doppler frequency resolution.
The experiments reported here are closely related to other studies
of H + XCN f HX + CN, where X ) Br, Cl, or CN, from
this laboratory.20 In these experiments, the COM translation
energy release and rotation state distribution of the CN(0, J)
product were determined.
the photolysis laser pulse, and the other three recorded absorp-
tions at observation times of 0.3, 0.6, and 20 µs following the
initiation of the reaction. The gates of the boxcars monitoring
the transient absorptions were 0.1 µs wide, centered on the
nominal observation time. After 20 µs, the HNC was in thermal
equilibrium with the reagent gases, and the transient absorption
signals slowly decreased due to diffusion and flow. The
experiment was controlled by a laboratory PC that provided
the necessary timing pulses to initiate the experiment and control
voltages to scan the frequency of the color center laser.
The HNC molecule is a moderately light, linear hydride so
that the spacing between rovibrational levels is several wave-
numbers compared to a 293 K Doppler width of only 0.008
wavenumbers. This large spacing between absorption features
precluded long frequency scans and only individual absorption
features were scanned. The laser frequency was incremented
in about 10 to 20 MHz steps. At each step, the excimer laser
was fired for 20 to 50 pulses, and the signal from each boxcar
recorded and averaged. The color center laser cavity was
adjusted from line-to-line so that the calibration factor relating
the scan voltage to the absolute frequency of the laser also
varied. The probe laser frequency scale was calibrated by
simultaneously monitoring the output from the high resolution
CF-500 Etalon. A scan consisted of about 8 to 10 Etalon fringes.
As noted, the probe laser was scanned in discrete frequency
increments, and the occasional Etalon fringe would be missed.
However, this situation was readily apparent over a complete
scan. The calibration factor relating control voltage to laser
frequency was determined from a linear least-squares fit to the
accumulated Etalon frequency measurement and control voltage
with an uncertainty of about ( 1%.
II. Experimental Section
The basic experimental apparatus has been described in
previous work,21 but for completeness, a brief description is
given here. The reaction chamber consisted of a vacuum-tight
stainless steel chamber containing a Teflon box of interior
dimensions of 100 × 100 × 5 cm. The chamber was evacuated
by a liquid nitrogen trapped mechanical pump to a pressure of
a few mTorr with a leak rate of less than 0.5 mTorr per minute.
Equal flow rates of (CN)2 and CH3SH (both gases supplied by
Matheson) were delivered from separate vacuum systems and
continuously flowed through the apparatus. The partial pressures
of the reagents were calculated from their known flow rates
and total chamber pressure, which was between 0.090 and 0.100
Torr.
The photolysis laser was a Lambda Physik Compex 205
excimer laser operating at 248 nm. A portion of the excimer
laser radiation transmitted through the apparatus was monitored
by a Molectron J-50 power meter. This measurement was used
to correct the data for variations in the photolysis laser intensity
caused by pulse-to-pulse fluctuations and a gradual decrease in
intensity due to a build-up of a UV absorbing deposit on the
optical surfaces exposed to the UV radiation.20
Individual rovibrational levels of HNC were detected by time-
and frequency-resolved infrared absorption spectroscopy. The
continuous wave infrared laser source was a Burleigh Model
20 single mode color center laser. The HNC rovibrational line
positions were taken from Burkholder et al.22 and data from
this laboratory.23 The absolute frequency of the infrared laser
was determined by a Burleigh Model WA-20IR wavemeter to
an accuracy of about 200 MHz, and a Model CF-500 high
finesse Etalon with a free spectral range of 150 MHz.
As described previously,21 the infrared probe laser was
multipassed through the photolysis zone using White cell optics.
Both the probe and photolysis laser beams were aligned
collinearly using a UV-IR dichroic mirror mounted on the
optical axis of the White cell at Brewster’s angle, with respect
to the IR laser beam.
The transmitted intensity of the infrared probe laser was
monitored by a liquid nitrogen cooled InSb detector. The
frequency response of the detector and associated electronics
was better than 7 MHz. The largest source of noise in the
experiment was caused by low-frequency fluctuations of the
probe laser intensity. To suppress this noise source, a portion
of the probe laser intensity was monitored by a second liquid
nitrogen cooled InSb detector. The output of this detector was
used as the reference for a Cambridge Research optical
modulator that controlled the optical power from the Krypton
ion laser used to pump the color center laser. This closed-loop
feedback system resulted in reduced fluctuations of the probe
laser intensity. To further suppress low-frequency noise, the
transient absorption signal was passed through an electronic high
pass filter.
For each vibrational state, a single transition near the peak
in the rotational state distribution was used to normalize the
data. After 3 to 5 rotational states were scanned, the normaliza-
tion level was rescanned. This procedure allowed scans recorded
on separate days to be related to each other and corrected for
possible drifts in experimental parameters.
III. Results
A. Analysis. The reaction sequence initiated by the transla-
tionally energetic H atoms is given by:
CH3SH 248nm8 CH3S + H,
H + (CN)2 f HCN + CN,
(1)
(2a)
f HNC + CN,
(2b)
(3a)
CN + CH3SH f HCN + CH3S/CH2SH,
f HNC + CH3S/CH2SH
(3b)
All species were lost by diffusion, but over the observation time
of several ten’s of µs, the diffusion was not important. The
branching fractions into the HCN and HNC channels for
reactions 2 and 3 are currently under investigation.24 Preliminary
data indicate that the thermal rate constant for reaction 3 is
nearly gas kinetic, and that the branching fraction, kib/(kia
+
kib) ∼ 0.1, for both reactions 2 and 3, where ki is the thermal
rate constant for reaction i.
The H atom translational distribution from reaction 1 was
calculated from the measured distribution25 from the 243.1 nm
photolysis of CH3SH and the known photochemistry26 and
photodynamics27 occurring at 248 nm. The H atoms produced
in reaction 1 have a Gaussian distribution with a mean
Four Stanford model SR-250 boxcar integrators were used
to record the transient absorption signal. One boxcar was used
to record the initial laser intensity, Io, measured at 100 µs before

10204 J. Phys. Chem. A, Vol. 104, No. 45, 2000
Macdonald
-1
H
translational energy, EhT, of 92 kJ mol and a fwhm of 38 kJ
mol-1. The H atom distribution is initially orientated with a â
parameter near -1; however, Park et al.28 have measured the
relaxation of a similarly orientated H atom distribution produced
from the photolysis of H2S at 193 nm. As previously argued,20
elastic reorientation collisions have a much larger cross section
than inelastic collisions, and at the relatively long delay time
of 0.3 µs, the H atom distribution should be isotropic.
Even though the photolysis laser was unpolarized, the
collinear propagation of the probe and photolysis lasers elimi-
nated the possibility of experimentally detecting any anisotropy
in the HNC speed distributions. Furthermore, even if the COM
differential cross section for the HNC product were highly
directional, the nearly isotropic and broad H atom speed
distribution, multiple correlated CN(0,J) product states, and
initial thermal (CN)2 speed distribution, would all contribute to
blur the observation of any anisotropy. Hence, it was assumed
that the HNC product speed distribution was isotropic, and the
area of an absorption feature determined the population in the
absorbing level.
For an absorption between two states j r i, the absorption
coefficient at frequency ν, σ(ν), is related to the integrated line
strength, Sji, for the transition by the normalized line shape
function, g(ν), as σ(ν) ) Sji g(ν). The absorbance at ν, A(ν), is
given by the Beer-Lambert law as29
Io(ν)
I(ν)
g
A(ν) ) ln
) 1 σ(ν) [Ni] - i[Nj]
(4)
(
)
(
)
gj
where Io(ν) and I(ν) are the incident and transmitted light
intensities at ν, l is the path length, gi is the degeneracy of level
i, and [ Ni] is the total concentration of absorbers in level i.
Provided that the population in the upper level, j, is zero,
integration of eq 4 over frequency relates the concentration, [Ni],
to the area under an absorption line and the integrated line
strength, Sji, by
Figure 1. Absorption line profiles for R(11) of the HNC(1000) r
HNC(0000) transition obtained at various observation times following
the initiation of reaction 2b. The solid lines are Gaussian frequency
profiles fit to the data, and the residues are indicated by the crosses.
At a delay time of 20 µs, Panel (c), the HNC product had equilibrated
to the temperature of the reaction chamber, 293 K. The conditions of
the experiment were PCH3SH ) 0.050 and P(CN)2 ) 0.050 Torr for a
KrF laser energy of 300 mJ/pulse. At 293 K, the Doppler width for
the R(11) transition is 262 MHz.
-∞∞A(ν)
∫
[Ni] )
(5)
1
-∞∞σ(ν)dν
∫
passes the probe laser made through the photolysis zone; hence,
the absorption measurements provided an absolute determination
of the HNC concentration produced in reaction 2b.
where the integral in the denominator is given by Sji.
Only two HNC vibrational levels were detected in the present
experiments, the ground-state HNC(00°0) and the first excited
bending state HNC(0110). Both levels were probed using the
fundamental H-NC ∆ν1 ) 1 vibrational transition as the active
chromophore. The transition moment for the HNC (1000) r
(0000) fundamental transition has recently been measured30 so
that the Sji for the rovibrational transitions probed in the present
experiment can be calculated from31
B. Rotational State Distributions of HNC(0000) and
HNC(0110). Typical absorbance profiles for the three observa-
tion times are shown in Figure 1 for the HNC(1000) r (0000)
R(11) transition and for the HNC(1110) r (0110) Rf(11)
transition in Figure 2. The solid line in each figure is a Gaussian
frequency profile fit to the data, i.e., A(ν) ) Apkexp(-((ν-νo)/
a)2). The three parameters describing the Gaussian profile were
determined by a nonlinear least squares procedure based on
Mardquart’s method,33 and the area under each absorbance
8π3
3hc
Aji
2
Sji )
νjji | j|µ|i |
HW
(6)
2J + 1
feature was determined from the nonlinear least squares
where c and h have their usual meanings, νjji, is the wavenumber
of the transition, | j | µ| i | is the vibrational transition moment,
Aji is the appropriate Ho¨nl-London factor, and HW is the
Herman-Wallis factor, accounting for the interaction between
rotation and vibration. The HW factor can be expressed as (1
+ A1m + A2m2)2 where m is J + 1 for an R branch and -J for
a P branch. For the HNC(1000) r (0000) transition, the HW
have been determined;32,23 however, they have not been
measured for the HNC(1110) r (0110) transition. The optical
path length was defined by the distance between the UV-IR
dichroic mirror and the UV beam absorber and the number of
∞
x
parameters as ∫-∞A(ν)dν ) Apka π. The crosses in Figures 1
and 2 indicate the difference between the experimental absorb-
ance and the calculated profile. Note that the distribution of
the residuals is uniform across the profile indicating that the
Gaussian functional form adequately described the data. As will
be discussed in Section D, the fwhm of the absorbance profiles
for the first two boxcar delays are broader than the Doppler
width describing a thermal (293 K) distribution so that the HNC
products in the (0000) and (0110) vibrational states are initially
produced with excess translational energy.

Hot H Atom Reaction
J. Phys. Chem. A, Vol. 104, No. 45, 2000 10205
Figure 3. The rotational state distributions for HNC(0000) produced
in reaction 2b measured at three different times following the initiation
of the reaction. The initial rotational state distribution was that given
at the shortest observation time panel (a). The distributions were
measured relative to HNC(0000) R(9) at t ) 0.3 µs assigned a value of
1.
Figure 2. Same as Figure 1 except the Rf(11) absorption line for the
HNC(1110) r HNC(0110) transition.
As noted earlier, pulse-to-pulse variations in the excimer laser
power were monitored by recording a portion of the photolysis
laser that was transmitted through the apparatus, Pt. As well,
the gradual attenuation of the photolysis laser power by a deposit
formed on the optical surfaces exposed to the UV laser radiation
was accounted for by normalizing the absorbance data according
tions obtained under similar experimental conditions. The scale
factor in each panel in Figure 3 relates the [HNC(0000; J ) 9)]
at the different times to each other with this average population
at 0.3 µs given a value of 1. The error bars in Figure 3 indicate
an uncertainty of one standard deviation ((1σ) in the average
of at least 4 independent measurements. For some rotational
states, the uncertainty is smaller than the symbol size plotted
in the figure.
to an experimentally determined power law, A(ν)
Pt0.6, as
described previously.20 The rotational state distributions in the
HNC (0 v12 0) vibrational levels were determined by scanning
over the R-branch of the HNC(1 v12 0) r (0 v21 0) transitions.
Only a few rotational levels were obscured by atmospheric
absorptions. The use of P-branch transitions resulted in poorer
signal-to-noise because the sensitivity of the apparatus decreased
at longer wavelengths due to an increase in infrared absorption
by the UV-IR dichroic mirror. One or two transitions for each
vibrational level, R(9) for HNC(000) and Re/f (9) or Re/f (10)
for (0110), were chosen to normalize the data collected over
different time periods for each vibrational level. Also, some of
these measurements, which were taken under identical ex-
perimental conditions, were used to determine the vibrational
state distribution and will be discussed further in the next
section.
The rotational state distributions shown in Figure 3 are plotted
as Boltzmann plots in Figure 4. If the distribution can be
described by a rotational temperature, Trot, the Boltzmann plot
is linear with slope equal to -1/kTrot and the intercept equal to
ln([N(ν)]tot/Qrot), where the brackets [ ] indicate concentration,
[N(ν)]tot is the total concentration in the probed vibrational level
ν, i.e., [N(ν)]tot ) ∑J[N(ν; J)], and Qrot is the rotational partition
function. As is evident from Figure 4, the rotational distributions
were well-described by a temperature. The results of a linear
least-squares analysis to determine Trot and [N(ν)]tot are sum-
marized in Table 1.
The rotational state distributions for the HNC(0000) ground
state measured at the three observation times of 0.3, 0.6, and
20 µsec are shown in Figure 3. The rotational state distributions
shown in Figure 3 are the average of several distributions
obtained under a variety of different experimental configurations
such as photolysis laser power and optical path length. The
different distributions were normalized to the population
calculated for the [HNC(0000; J ) 9)] state at each observation
time using the measured rotational temperature for two distribu-
The Trot measured at an observation time of 20 µs was in
good agreement with 293 K temperature of the reaction
chamber. For an HNC molecule at a total pressure of 0.090
Torr, a time of 0.3 µs corresponds to about one-quarter of the
hard sphere collision rate. As is evident from Table 1, some
rotational relaxation has occurred from a reaction time of 0.3
to 0.6 µs; however, the relaxation was not extensive, implying
that the Trot determined at the initial observation time provided

10206 J. Phys. Chem. A, Vol. 104, No. 45, 2000
Macdonald
Figure 4. Boltzmann plot of the rotational state distributions shown
in Figure 3. The linear least squares parameters are summarized in Table
1.
Figure 5. Similar to Figure 3 except the rotational state distributions
for the HNC(0110) vibrational state at three observation times. The
initial rotational state distribution is given in panel (a). The distributions
were measured relative to HNC(0110) Re/f (9) at t ) 0.3 µs assigned a
value of 1.
TABLE 1: Summary of the Linear Least Squares
Parameters Obtained from the Boltzmann Plots Shown in
Figure 4 for the Rotational State Distribution for HNC(00°0)
and in Figure 6 for the Rotational State Distribution for
HNC(0110) Produced in the H + (CN)2 Reactiona
HNC vibrational
state
boxcar delay
[HNC(0 v1 0]tot
(arb units)
2
relate to the other times. A comparison of the absorbance profiles
in Figures 1 and 2 shows that the signal-to-noise was less for
the HNC(0110) level and resulted in the increased scatter for
the HNC(0110) rotational state distributions. Note that the
populations in HNC(0000) and HNC(0110) were not directly
related to each other by these measurements.
The doubly degenerate bending vibration of HNC has a
fundamental frequency22 of ν2 ) 464.2 cm,-1 and at 293 K,
16.5% of the HNC population is in the ν2 ) 1. This is reflected
in the measurement of the [HNC(0110)] at 20 µs, as will be
discussed further in Section III C.
The dependence of Trot on the reaction times for the
HNC(0110) vibrational level was similar to that found for
HNC(0000), (see Table 1). The Trot measured at an observation
time of 0.3 µs. was only slightly higher than that measured at
0.6 µs, and the increase in [HNC(0110)]tot was small. Again,
this indicates that the Trot measured at a reaction time of 0.3
µs. was a good measure of the initial rotational state distribution
of HNC(0110) produced in reaction 2b. The fact that both
vibrational levels increased by nearly the same fraction is strong
evidence that both vibrational levels are produced in the same
reaction.
C. Vibrational Level Distribution for HNC. The enthalpies,
∆H°, for reaction 2a and 2b are summarized in Table 2. A large
source of uncertainty comes from the ∆fHo for the CN radical.
From the work of North and Hall34 on the photodissociation
dynamics of (CN)2, a value of ∆fHo equal to 431.9 ( 4.2 kJ
mol-1 was calculated. The value for ∆fHo for HCN was taken
(µs)
T
rot (K)
HNC(000)
0.3
0.6
20.0
0.3
0.6
20.0
506 ( 26
428 ( 22
298 ( 6
446 ( 77
393 ( 38
271 ( 20
18.9 ( 2.0b
22.0 ( 2.6
45.4 ( 2.6
34.4 ( 7.6c
35.4 ( 4.6
28.2 ( 1.9d
HNC(0110)
a The initial rotational state distribution was taken as that measured
at the earliest observation time of 0.3 µs. The uncertainties for TRot are
(1σ from the least squares fit and for [HNC(0v2l 0]Tot. They include
both the (1σ from the least squares fit and the calculated QRot.
b The
[HNC(000; J ) 9)] measured at a delay of 0.3 µs was assigned a value
of 1 au c The [HNC(0110, J ) 9,e or f] measured at a delay of 0.3 µs
was assigned a value of 1 au. d The data were analyzed using the room
temperature, 293 K.
a good description of the initial rotational state distribution in
HNC(0000) produced in reaction 2b.
The rotational state distributions for the first bending vibration
HNC(0110) are shown in Figure 5 for each observation time,
and are presented as Boltzmann plots in Figure 6. The
determinations of Trït and [HNC(0110)]tot from a linear least-
squares analysis are also summarized in Table 1. Similar to the
presentation of the rotational state distribution for HNC(0000),
the rotational state distributions for HNC(0110) were normalized
to the [HNC(0110; J ) 9] population calculated from the
measured rotational temperature of two experiments recorded
under identical conditions. The calculated [HNC(0110; J ) 9]
for the Trot obtained at an observation time of 0.3 µs was
assigned a value of 1, and the arbitrary unit factors in Figure 5

Hot H Atom Reaction
J. Phys. Chem. A, Vol. 104, No. 45, 2000 10207
TABLE 3: Determination of the HNC Vibrational State
Distribution from the H + (CN)2 f HNC + CN Reaction
[HNC(000,J ) 9)] [HNC(000)]tot [HNC]tot
× 10-9
× 10-10
× 10-10
boxcar
delay
(molecule
(molecule
(molecule [HNC(000)]tot/
cm-3
)
cm-3
)
cm-3
)
[HNC]tot
0.3
0.6
20.0
1.8
2.5
6.7
3.3
4.1
9.3
5.9
6.9
11.
0.44
0.41
0.16
[HNC(010,J ) 9,e)]
× 10-8
[HNC(010)]tot
× 10-10
(molecule cm-3
)
(molecule cm-3
)
0.3
0.6
20.0
6.7
8.2
6.2
2.6
2.8
1.8
a The initial vibrational level distribution of HNC was given by the
distribution determined at the observation time of 0.3 µs. The
l
uncertainty in the average of three measurements for [HNC(0v2 0,J )
9)] populations was about (10%.
indicated that only the most energetic H atoms react to form
HNC.
Only the transitions originating from HNC(000) and
HNC(0110) were detected in the present work. The exact
frequencies for other rovibrational transitions have been recorded
in this laboratory,23 but scans over the wavelength regions
corresponding to several low J transitions originating from the
HNC(020,20) and HNC(001) vibrational levels were unsuccess-
ful.
Figure 6. Boltzmann plot of the rotational state distributions shown
As noted previously, the [HNC(0000; J ) 9)] and [HNC-
(0110; J ) 9, 10] populations were used to normalize the
population data obtained at various times and experimental
conditions. Furthermore, the absorption technique results in an
absolute determination of the population in each HNC rovibra-
tional state. The initial vibrational population can be determined
from the initial rotational state distribution for each vibrational
level combined with the measurement of the population in a
single rotational state for the various vibrational levels obtained
under the same experimental conditions. The initial rotational
state distributions for HNC(0000) and (0110) were taken as that
measured at an observation time of 0.3 µs., Figures 3 and 5,
and were described by the Trot given in Table 1.
The results for the determination of [HNC(0000)]tot and
[HNC(0110)]tot are summarized in Table 3. As is evident from
the last column in Table 3, the fraction of the observed HNC
produced in reaction 2b that was found in the HNC(0110) level
was constant as the observation time increased from 0.3 to 0.6
µs, indicating that vibrational relaxation was negligible over
this time interval. After 20 µs, the HNC vibrations had
equilibrated to the temperature of the reaction chamber as
indicated by the measured fraction of HNC that was in the
HNC(0110) bending vibration. Even though the uncertainty in
the determination of the population in an individual rotational
state was estimated to be about (10%, the excellent agreement
with the expected thermal value provides confidence in the initial
vibrational distribution measurement.
in Figure 5.
TABLE 2: Summary of the Energetics for the H + (CN)2 f
HCN/HNC + CN Reaction
a
∆H° reaction
(kJ mol-1
Eavail
reaction
)
(kJ mol-1
)
H + (CN)2b f HCNc + CN
41.0 ( 10.2
101 ( 14
+54.5
-6
f HNCd + CN
a Calculated for ETH ) 92 kJ mol-1 in eq 7. b ∆fH° (CN)2 ) 307.2
( 4 kJ mol-1. Ref: Chase, M. W., Jr. NIST-JANF Thermochemical
Tables; AIP; New York, 1998. c ∆fH° HCN ) 132.3 ( 4.2 kJ mol-1
ref 35. d ∆fH° HNC ) 192.6 ( 8.2 kJ mol-1. ref 36.
.
from the recent work of Berkowitz et al.,35 and the value for
∆fH° for HNC was taken from the theoretical calculation by
Lee and Rendell.36 The most probable energy available to the
HNC + CN product channel, Eavail is given by
Eavail ) -∆H° + ETH + RT + Etνherm
(7)
where EHT is the average COM translational energy of the
reacting H atoms, RT accounts for the reactant rotation energy,
and Etνherm accounts for the thermal excitation in the two
degenerate low-frequency bending modes of (CN)2 Eνtherm
)
1.1 kJ mol-1). The relative collision energy between the H atom
and (CN)2 is essentially given by the initial translational energy
of the H atoms because of the small mass of an H atom. For
this mass combination, the contribution of reactant thermal
motion to EHT can be ignored.37 As summarized in the last
column of Table 2, the HNC + CN product channel is calculated
to be 6 kJ mol-1 endothermic; however, the uncertainty in ∆Ho
and the broad distribution of the initial translational energy of
the H atoms (EhHT) ) 92, and fwhm ) 38 kJ mol-1) leads to a
relatively large uncertainty in the actual threshold energy for
the reaction. However, the fact that the products were observed
to be produced almost entirely during the first 0.3 µs (Table 1)
The total concentrations of HNC, [HNC]tot, observed in the
experiment at the various observation times are given in the
second last column of Table 3. The [HNC]tot increased by a
factor of 1.9 from the initial to the final observation time,
whereas it only increased by a factor of 1.17 for a factor of 2
increase in reaction time. The same trend is evident in the data
presented in Table 1 for each vibrational level. As noted earlier,
reaction 3b produces HNC, and the observed increase in [HNC]
at an observation time of 20 µs was due to this channel. The

10208 J. Phys. Chem. A, Vol. 104, No. 45, 2000
Macdonald
Figure 8. Similar to Figure 7 except for the HNC(0110) vibrational
level.
Figure 7. Summary of the determination of the laboratory translational
temperatures at three observation times for the rotational states in the
HNC(0000) vibrational manifold using the measured Doppler widths,
according to Equation 8. The dashed line is a linear least-squares fit to
the data, showing that there was no measurable correlation between
Ttrans and J.
TABLE 4: Summary of the Determination of EvT for
HNC(0 v12 0) Measured at Different Observation Times
vibrational
level
observation
time(µs)
v
T
T
trans (K)
E (kJ mol-1
)
fact that preliminary data24 indicate that the branching fractions
for the production of HNC in both reactions 2 and 3 are nearly
equal implies that the final concentration of HNC, after reaction
3b has gone to completion, should be twice the initial
concentration of HNC, as observed in Table 3.
D. Translational Energy Release for H + (CN)2 f HNC
+ CN. Inspection of the absorbance profiles shown in Figures
1 and 2 shows that the HNC product from reaction 2b was
formed with excess translational energy. It was argued in Section
III A that the HNC speed distribution should be isotropic or
nearly so. This, coupled with the fact that the absorbance profiles
exhibited a Gaussian dependence on frequency, indicates that
the laboratory speed distribution of HNC was described by a
Maxwell-Boltzmann distribution.38 The laboratory translational
temperature, Ttrans, is related to the fwhm of the absorbance
profile, νjD (cm-1), by
HNC(0000)
0.3
0.6
20.0
0.3
0.6
20.0
473 ( 68b
429 ( 57
297 ( 23
449 ( 89
415 ( 85
308 ( 49
11 ( 1.4
HNC(0110)
10 ( 2
a The vjD’s were obtained by non-linear least squares fits to the A(v)
profiles for each rotational state in the HNC(0000) and HNC(0110)
vibrational levels, and Ttrans determined from eq 8 b The uncertainty is
(1σ in the average Ttrans plotted in Figures 7 and 8.
The results are summarized in Table 4 as simple averages over
all the rotational states of the Ttrans at each observation time.
The dashed lines in Figures 7 and 8 are linear least-squares fits
to the data. As is clear from these figures, the data were too
scattered to exhibit any trends in the translational energy released
as a function of the HNC rotational state. The error bars result
from the repeated measurement of νjD for the same rotational
state. At the final observation time of 20 µs, the measured Ttrans
corresponded to the measured temperature of the reaction
chamber, 293 K, within experimental scatter, indicating that the
frequency scale was accurately calibrated by the Etalon fringe
measurements. The Ttrans determined at the observation time of
0.3 µs was taken as a measure of the translational energy release
in reaction 2b. The small change in Ttrans on going from an
observation time of 0.3 to 0.6 µs indicated that translational
relaxation was small under the conditions of the experiment,
and the initial Ttrans for reaction 2b must be close to that observed
M
8R ln 2
c2
Ttrans
)
νj2D
(8)
2
νjji
where M (grams) is the mass of the probed molecule, and R is
the gas constant (ergs/degree). The average translational energy
for the probed molecule in vibrational level ν, EνT , was taken
as 1.5 RTtrans
.
Plots of the measured νjD’s for the rotational states of the
HNC(0000) vibrational level at the three observation times are
shown in Figure 7, and for the HNC(0110) level in Figure 8.

Hot H Atom Reaction
J. Phys. Chem. A, Vol. 104, No. 45, 2000 10209
at 0.3 µs. A comparison of Tables 1 and 3 also reveals that Trot
and Ttrans were equilibrated with each other, within experimental
scatter.
of products, [HNC]tot. The kinetic rate equation describing the
loss of H atoms can be rearranged to give σR as
[HNC]tot
For a discussion of the dynamics of reaction 2b, the desired
quantity is the mean translational energy released in the COM
collision frame, ET . The conversion from the laboratory frame
to the COM frame requires knowledge of the differential cross
section, which is unknown. However, some idea of the COM
translational energy release can be obtained by taking advantage
of the near isotropic H atom distribution to relate the laboratory
and COM speed distributions of HNC. The laboratory velocity
of an HNC product molecule, WHNC, produced in a single reactive
collision is the vector sum of the COM velocity WCOM and the
COM velocity of HNC, uHNC, i.e., WHNC ) WCOM + uHNC. The
differential cross section determines the final angle between
σR )
(9)
VH [H]R [(CN)2]∆t
where ∆t is the observation time at which the [HNC]tot was
measured. Equation 9 implies a linear relationship between the
observation time and the accumulation of product; i.e., the
measurement of the number density is equivalent to the reactive
flux. Previously, this equivalence was demonstrated for reaction
2 using the same experimental apparatus and conditions, except
monitoring the CN(V ) 0; J) product.20 For reaction 2b, the
[HNC]tot was found to increase by 17% as the observation time
increased by a factor of 2; however, this is not due to a violation
of the equivalence between reactive flux and number density
but rather to the relaxation of the H atom translational energy
distribution. Only a small shift in the H atom energy distribution
to lower energies is needed to quench reaction 2b.
The cross section for absorption of CH3SH and the quantum
yield for H atom production at 248 nm have been measured to
be 3.0 × 10-19 cm2 molecule-1and 1, respectively.26 The
photolysis laser energy was measured directly in front of the
entrance window of the reaction chamber, but the actual laser
energy that traversed the apparatus was not measured directly.
Estimates of the loses on the entrance window and UV-IR
dichroic were made to determine the actual photolysis laser
energy irradiating the photolysis zone. Using the measurement
of the [HNC]tot at an observation time of 0.3 µs provided in
Table 3 and eq 9, the σR for reaction 2b was calculated to be
2.0 × 10-18 cm2 for an ETH of 113 kJ mol-1. The uncertainty
in determining σR was estimated to be about a factor of 2
primarily because of the uncertainty in determining the [H]R
atoms.
W
COM and uHNC. Even though the most probable initial25 H atom
speed is high, 1.4 × 106 cm s-1, its mass is only 1.9% of the
mass of (CN)2, and WCOM is only slightly deviated from the initial
(CN)2 velocity; thus, the approximation WCOM ≈ W(CN)2 is
reasonable. Furthermore, W(CN)2 has an isotropic Maxwell-
Boltzmann distribution. The velocity of HNC in the COM
system can be approximated by uHNC ≈ WHNC - W(CN)2, where
both WHNC and W(CN)2 are given by isotropic Maxwell-Boltz-
mann distributions. To determine the COM translational energy
release in reaction 2b, the squared distribution of uHNC is needed.
This is obtained from two Maxwell-Boltzmann distributions
related by uHNC2 ) VHNC2 + V(CN)22 - 2 VHNC
V(CN)2cosθ, where
θ is the angle between WHNC and W(CN)2. This situation is identical
to that described by Dagdigian et al.39 These workers determined
the relative speed-squared distributions for collisions of gases
at two temperatures and found that the most probable speed
squared was given by the sum of the most probable speeds
squared for each gas, i.e., uj2HNC ) VjH2 NC + Vj(2CN)2, where the bar
indicates the most probable speed and VjX2
)
2kT/m , for
x
x
molecule X. The conservation of linear momentum in the COM
frame allows the most probable relative translational energy in
the COM frame, ET , to be given by ET ) 1/2 mHNC/mCN(mHNC
IV. Discussion
+ mCN) uj2
.
HNC
The measurements of the present work provide a compre-
hensive look at the complete energy disposition into the HNC
product from reaction 2b by detailing how the reaction energy
was shared among all the degrees of freedom: translation,
rotation, and vibration. Unfortunately, the energetics were not
well-defined because of the initial broad H atom translational
energy distribution. Assuming EHT to be 113 kJ mol-1(see
The last column in Table 4 gives the measured ET as
determined after 0.3 µs. Even though the HNC(0110) vibrational
level is 5.55 kJ higher in energy than the ground state the
translational energy release is similar within experimental error
for each vibrational level.
E. Absolute Reaction Cross Section for H + (CN)2 f
HNC + CN. As summarized in Table 3, the measurements
reported in this work provide a determination of the absolute
concentration of the HNC product and can be used to determine
an estimate of the reaction cross section, σR, for reaction 2b
provided some estimate of the concentration and speed of the
reacting H atoms can be made. This was done by making the
following approximations. Above the reaction threshold, σR was
assumed to be independent of the H atom collision energy, and
the reaction threshold was taken to occur for H atoms with
translational energy greater than the reaction endothermicity,
i.e., 98 kJ mol-1 (Table 2). The concentration of H atoms with
translational energy greater than the reaction threshold, [H]R,
corresponds to 0.23 of the total number of atoms created in the
photolysis of CH3SH. The reaction rate constant, k2b, can be
estimated from k2b ) σR VH , where VH is the average speed
Section III D), Eavail can be calculated to be 18.5 kJ mol-1
.
Another estimate for Eavail can be made using the measure-
ments of the HNC product state distribution and the COM
translational energy release. The most energetic rotational state
observed for each vibrational level can be identified from Figure
3 for HNC(0000) and Figure 5 for HNC(0110) to be J ) 22 and
J ) 18, respectively. Using the (EvT for each vibrational level
(Table 4), the maximum energies available to the HNC(0000)
and (0110) product states are 20.1 and 21.7 kJ mol-1, respec-
tively. Of course, this is a crude estimate of Eavail insofar as
more energetic states were not detected because of signal-to-
noise limitations, and the CN(V ) 0, J) coproduct must be
assumed to be in J ) 0. Nevertheless, the estimates of Eavail
using the two methods are in reasonable agreement. Because
the product state distribution estimate relied on a value of ETv
that is clearly an overestimate of the translational energy of the
most thermodynamically allowed product state, a value of Eavail
) 19 kJ mol-1 was taken as a reasonable estimate. With this
value of Eavail , HNC bending vibrations up to ν2 ) 3 could
have been excited.
of the H atoms that can react, and was calculated from VH
)
∞
∫
Eth VP(V)dV ) 1.5 × 106 cm s-1, where P(V) is the normalized
Gaussian speed distribution of the H atoms.
Under near single collision conditions, such as the case here,
the H atoms lost by reaction are equal to the total production

10210 J. Phys. Chem. A, Vol. 104, No. 45, 2000
Macdonald
TABLE 5: Summary of the Estimates for the Complete
Energy Disposition into Vibration, Rotation, and Translation
for the H + (CN)2 f HNC + CN Reaction
TABLE 6: Summary of the Global Fraction of EAvail that
Appeared as Product Translation, Rotation, and Vibration
for Reaction 2bl
vibrational level
reaction
fT
fR
fV
(000)
19
0.57
0.22
0.20
(0110)
13.4
0.75
0.27
∼0
H +(CN)2fHNC + CN
0.56
0.32
0.13
Eavail - EV (kJ mol-1
f Tv
f HRNC(v)
f VR,CN(0)
)
(Eavail ≈ 19 kJ mol-1
)
H + F2fHF + Fb
0.39
0.54
0.03
0.09
0.58
0.37
(Eavail)427 kJ mol-1
)
H + Cl2fHCl + Clc
(Eavail)203 kJ mol-1
)
a The EAvail was estimated to be 19 KJ mol-1. Only HNC(0v2 0)
l
a For comparison, the energy disposition for the related H + X2
for V2 ) 00 and 11 were detected experimentally.
reactions are included, where X is F or C. b Ref 40. c Ref 41.
The rotational energy content of the CN fragment, produced
along with HNC in reaction 2b is unknown; however, the
combined average rotational energy for CN produced in both
difference between the polyatomic and the triatomic case is the
linear or nearly linear nature of the reactive configurations in
the triatomic situation. The PESs for both H + HCN43 and H
+ ClCN18 were found to be highly repulsive for linear H-N
configurations, and it is presumed that reaction 2 proceeds
through bent configurations.
The PES describing the HNCCN system has not been
explored in as much detail as that available for the HClCN
system; however, Yang et al.44 have described several stationary
points on the HNCCN surface at the BAC-MP4 level of theory.
These workers found that an NC(H)CN adduct was bound by
about 130 kJ mol-1 with respect to the H + (CN)2 asymptote.
It is clear from the average energy disposition, Table 6, that
the product state distribution is highly nonstatistical so that the
formation of a long-lived complex, in which the energy in the
internal degrees of freedom are completely randomized, appears
unlikely. The presence of a deep potential minimum on the
HNCCN surface could facilitate the occurrence of secondary
encounters, however.
One major difference between the polyatomic and triatomic
reaction systems (Table 6) is the large fraction of the internal
energy that appears as product rotation compared to vibration
in the polyatomic case. To excite rotational motion in a
molecule, a torque must be applied about its COM. For the
triatomic systems, this is difficult because the reaction exother-
micity is released repulsively between the diatomic fragment
in linear or near linear configurations. Furthermore, the COM
of the diatomic product lies close to the halogen atom, making
rotational excitation again unfavorable. However, for the H +
(CN)2 system, near-linear configurations are highly repulsive,
and the reaction must proceed through bent configurations.
Under such circumstances, the COM of the new HNC product
molecule is not collinear with the direction of the repulsive
energy release between the two C atoms, and a large torque
can be applied to the departing fragments, HNC and CN. Also,
the anisotropy of the PES between a diatomic and linear
triatomic molecule should be greater than that between an atom
and a diatomic hydride molecule. Both of these factors favor
rotational excitation in the polyatomic product case.
Another difference between reaction 2b and the H + halogen
reactions is the small amount of energy available to the products
for the former reaction (Table 6). For reaction 2b, this small
value of Eavail results in the rather small value for the relative
velocity between the diatom and triatom fragments so that there
is a high likely hood that secondary encounters can occur. In
fact, for an HNC(0 v12 0) molecule, with J at the peak of the
rotational state distribution, the CN and HNC fragments only
separate 0.3 Å before HNC completes one rotational period.
Such trajectories might be responsible for the conversion of
initial bending vibrational motion into product rotation.
The reaction of energetic H atoms with XCN compounds,
where X is Br, Cl, or CN, has been recently studied20 by
reactions 2a and 2b has been measured20 to be 7.4 kJ mol-1
.
Reaction 2a is 60 kJ mol-1 more exothermic than reaction 2b
and accounts for about 90% of the total reaction rate. The
rotational excitation of CN produced in reaction 2b should not
be more than that of the HNC(0000) and (0110), products, 4.2
and 3.7 kJ mol-1, respectively. The average rotational energy
content of the CN coproduct can be estimated from the
conservation of energy equation:
Eavail ) ETV + EHRNC(V) + EHV NC + ERHNC(V)
(10)
where EVR,X ) RTrot is the average rotational energy content
of species X in vibrational level V, and EHV NC is the vibrational
energy of level V.
The results are summarized in Table 5 expressed as the
fraction of the available energy in vibrational level v that
appeared as COM translational energy and rotational energy of
HNC or CN. The EHRNC(V) was determined from the Trot
measured at the earliest observation time listed in Table 1, and
EVT is given in Table 4. It has been argued previously20 that
on purely kinematic grounds, the EHRNC(V) should be similar to
EVR,CN(0) for reaction 2. This is approximately true for the CN
produced along with the HNC(0000) level, but not so for CN
produced along with HNC(0110). The difference is attributed
to the large uncertainty in the estimate of Eavail and experi-
mental scatter in the determination of EVT . It is more likely
that EVR,CN(0) ≈ ERHNC(V) for all HNC vibrations.
An interesting aspect of the results in Table 5 is the increased
partitioning of the available energy into the translational energy
of the separating fragments on going from v2 ) 0 to v2 ) 1. As
noted above, there is considerable uncertainty in the determi-
nation of the translational energy (Table 4); however, this may
be a real trend as even fHRNC(v) is larger for v2 ) 1 than for v2 )
0.
Using the estimates for the energy partitioning summarized
in Table 5 and the observed vibrational state distribution, the
global energy disposition for each degree of freedom was
calculated, expressed as a fraction of the Eavail that appears in
a particular degree of freedom summed over the vibrational
population. The results are summarized in Table 6 along with
similar results for related triatomic reaction systems: H + F2
f HF + F40 and H + Cl2 f HCl + Cl.41
Both the mass and electron affinity42 of the CN radical lie
between those of the F and Cl atom; however, the global
dynamical features appear to be quite similar to the H + Cl2
reaction system (Table 6). It appears that the global features of
energy partitioning for a polyatomic reaction system can be
rationalized from the observations of triatomic systems of similar
mass combinations,1 i.e., L + H-H reaction systems. One

Hot H Atom Reaction
J. Phys. Chem. A, Vol. 104, No. 45, 2000 10211
References and Notes
monitoring the CN(0; J) product. Both the rotational state
distribution of CN and the COM translational energy distribution
were determined in these experiments. For reaction 2, the HCN
channel accounts for nearly 90% of the products24 and dominates
the HNC pathway; hence, the observed CN(0; J) distribution
can be attributed to the HCN channel. This channel is 60 kJ
mol-1 more energetic than the HNC channel; however, the fT
values are remarkably similar. The origins of these fT values
should be quite different in the two cases. He, Tokue, and
Macdonald argued that the large fT for the HCN channel arose
from the tendency for L + H-H reaction systems to channel
reactant translational energy greater than the barrier height into
product translational energy. This cannot be the case for reaction
2b because the H atoms that react must just have enough energy
to do so. It may be that the observed HNC molecules must have
sufficient translational energy to separate from the CN radical
otherwise the H atom could be transferred back to the departing
CN radical and form the more exothermic reaction product,
HCN.
(1) Polanyi, J. C. Science 1987, 236, 680.
(2) Holmes, B. E.; Setser, D. W. In Physical Chemistry of Fast
Reactions; Smith, I. W. M., Ed.; Plenum Press: New York, 1980; Vol. 2,
Chapter 2.
(3) Clary, D. C. Science 1998, 279, 1879.
(4) McDonald, J. D. Annu. ReV. Phys. Chem. 1979, 30, 29.
(5) Sugawara, K.; Fumiyuki, I.; Nakanaga, T.; Matsumura, C. J. Chem.
Phys. 1990, 92, 5328.
(6) Arunan, E.; Setser, D. W. J. Phys. Chem. 1991, 95, 4190.
(7) Frost, M. J.; Sharkey, P.; Smith, I. W. M. Faraday Discuss. Chem.
Soc. 1991, 91, 305.
(8) Suzuki, T.; Hirota, E. J. Chem. Phys. 1993, 98, 2387.
(9) Arunan, E.; Manke, G., II; Sester, D. W. Chem. Phys. Lett. 1993,
207, 81.
(10) Nizamov, B.; Setser, D. W. J. Phys. Chem. 1996, 100, 4853.
(11) Phillips, L. F.; Smith, I. W. M.; Tuckett, R. P.; Whitham, C. J.
Chem. Phys. Lett. 1991, 183, 254.
(12) Sauder, D. G.; Patel-Misra, D.; Dagdigian, P. J. J. Chem. Phys.
1991, 95, 1696.
(13) Macdonald, R. G.; Liu, K.; Sonnenfroh, D. M.; Liu, D.-J. Can. J.
Chem. 1994, 72, 660.
(14) Schatz, G. C. J. Phys. Chem. 1996, 100, 12 839.
(15) Clary, D. C. J. Phys. Chem. 1994, 98, 10 678.
(16) Bowmann, J. M.; Schatz, D. C. Annu. ReV. Phys. Chem. 1996, 46,
169.
V. Summary
The reaction dynamics of translationally energetic H atoms
with (CN)2 was investigated by determining the complete initial
rovibrational state distribution of HNC(0 v12 0), v21 ) 00, 11, the
minor product channel for reaction 2. The initial rotational state
distributions for each vibrational level, v12 ) 00, 11, were found
to be Boltzmann, with Trot ) 500 ( 30 and 440 ( 80 K,
respectively. The initial vibrational distribution was found to
have 44% of the observed HNC product in the first excited
bending vibration, Table 3. As well, the initial COM transla-
tional energy released in each vibrational level was determined
from the line width of the HNC absorption features, and the
Ttrans for each vibrational level was found to be 470 ( 70 and
450 ( 90 K, for v12 ) 0, 1, respectively, Table 4. Within the
scatter of the measurements the initial translational and rotational
temperatures were equilibrated. Several methods were used to
determine Eavail , and an estimate of 19 kJ mol-1 was used to
calculate the fraction of the available energy in a given
vibrational level that appeared as translation and rotation of both
HNC and CN. The results are summarized in Table 5. The global
disposition of the reaction energy is summarized in Table 6.
As anticipated from studies of triatomic systems, the kinematics
of L + H-H systems plays an important role in the global
dynamics for polyatomic systems, and a large fraction of the
energy released in the reaction appears as product translational
motion.
(17) Casavecchia, P.; Balucani, N.; Volpi, G. G. Annu. ReV. Phys. Chem.
1999, 50, 347.
(18) Harding, L. B. J. Phys. Chem. 1996, 100, 10 123.
(19) Nizamov, B.; Setser, D. W.; Wang, H.; Peslherbe, G. H.; Hase,
W. L. J. Chem. Phys. 1996, 105, 9897.
(20) He, G.; Tokue, I.; Macdonald, R. G. J. Chem. Phys. 2000, 112,
6689.
(21) Bethardy, G. A.; Northrup, F. J.; He, G.; Tokue, I.; Macdonald, R.
G. J. Chem. Phys. 1998, 109, 4224.
(22) Burkholder, J. B.; Sinha, A.; Hammer, P. D.; Howard, C. J. Mol.
Spec. 1987, 126, 72.
(23) Northrup, F. J.; Bethardy, G. A.; Macdonald, R. G. J. Mol. Spec.
1997, 186, 349.
(24) Decker, B. K.; Macdonald, R. G., in preparation.
(25) Rogers, L. J.; Ashfold, M. N. R.; Matsumi, Y.; Kawasaki, M.;
Whitaker, B. J. J. Chem. Soc., Faraday Trans. 1996, 92, 5181.
(26) Barone, S. B.; Turnipseed, A. A.; Gierczak, T.; Ravishankara, A.
R. J. Phys. Chem. 1994, 98, 11 969.
(27) Jensen, E.; Keller, J. S.; Waschewsky, G. C. G.; Stevens, J. E.;
Graham, R. L.; Freed, K. F.; Butler, L. J. J. Chem. Phys. 1993, 98, 2882.
(28) Park, J.; Shafer, N.; Bersohn, R. J. Chem. Phys. 1989, 91, 7861.
(29) Kroto, H. W. Molecular Rotational Spectra; Dover: New York
1992; p 69.
(30) He, G.; Macdonald, R. G. Chem. Phys. Lett. 1999, 301, 175.
(31) Smith, M. A. H.; Rinsland, C. P.; Fridovich, B. Molecular
Spectroscoy: Modern Research; Rao, K. N. Ed.; Academic Press: Orlando,
1985.
(32) Nezn, M.; Ammano, T.; Kawaguchi, K. J. Mol. Spect. 1998, 192,
41.
(33) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.
Numerical Recipes: The Art of Scientific Computing; Cambridge Univer-
sity: Cambridge, 1988; Chapter 14.
(34) North, S. W.; Hall, G. E. J. Chem. Phys. 1997, 106, 60.
(35) Berkowitz, J.; Ellison, G. B.; Gutman, D. J. Phys. Chem. 1994,
98, 2744.
(36) Lee, T. J.; Rendell, A. P. Chem. Phys. Lett. 1991, 177, 491.
(37) Zande, W. J.; Zhang, R.; Zare, R. N.; McKendrick, K. G.; Valentini,
J. J. J. Phys. Chem. 1991, 95, 8205.
(38) Gordon, R. J.; Hall, G. E. AdVances in Chemical Physics; Prigogine,
I., Rice, S. A., Eds.; John Wiley & Sons: New York, 1996; Chapter 1.
(39) Dagdigian, P. J.; Cruse, H. W.; Zare, R. N. J. Chem. Phys. 1975,
62, 1824.
Reaction 2b must occur through bent configurations so that
bending and rotational motions are excited as the reaction energy
is released between the departing C-C atoms. It was suggested
that secondary encounters between the separating HNC and CN
fragments could play an important role in determining the
observed internal state distribution of HNC especially because
of the small value for Eavail . Clearly, detailed dynamics
calculations on a PES that accounts for the interaction of the H
atom attacking the N atoms in (CN)2 will be needed to fully
understand the dynamics in this five atom system.
(40) Polanyi, J. C.; Sloan, J. J. J. Chem. Phys. 1972, 57, 4988.
Acknowledgment. The author wishes to thank Prof. I. Tokue
and Dr. G. He for their work in carrying out preliminary
experiments on the H + (CN)2 system. This work was supported
by the U.S. Department of Energy, Office of Basic Energy
Sciences, Division of Chemical Sciences, under Contract W-31-
109-ENG-38.
(41) Anlauf, K. G.; Horne, D. S.; Macdonald, R. G.; Polanyi, J. C.;
Woodall, K. B. J. Chem. Phys. 1972, 57, 1561.
(42) Tyler, J. K.; Sheridan, J. Trans. Faraday Soc. 1963, 59, 2661.
(43) ter Horst, M. A.; Schatz, G. C.; Harding, L. B. J. Chem. Phys.
1996, 105, 558.
(44) Yang, D. L.; Yu, T.; Lin, M. C.; Melius, C. F. J. Chem. Phys.
1992, 97, 222.