Initial vibrational level distribution of HCN[X1Σ+(v10v3)] from the CN(X2Σ+)+H2→HCN+H reaction

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 109, NUMBER 11

15 SEPTEMBER 1998

˜

1

؉

Initial vibrational level distribution of HCN†X ⌺ „v 0v …‡

1

3

2

؉

from the CN„X ⌺ …؉H ˜HCN؉H reaction

2

a)

b)

G. A. Bethardy, F. J. Northrup, G. He, I. Tokue, and R. Glen Macdonald

Argonne National Laboratory, Chemistry Division, 9700 South Cass Avenue, Argonne, Illinois 60439

͑

Received 30 January 1998; accepted 15 June 1998͒

The reaction of the cyano radical ͑CN͒ with hydrogen was studied by time-resolved infrared

absorption spectroscopy of individual rovibrational states of HCN. The initial vibrational level

distribution of HCN(v 0v ) was determined by plotting the time dependence of the fractional

1

3

population of a vibrational level and extrapolating these curves to the origin of time. The

experiments were carried out at two temperatures, 293 and 324 K, with similar results. It was

estimated that about 50% of the available reaction exothermicity was deposited as vibrational

excitation of the HCN product. Surprisingly, the HCN͑101͒ vibrational level received a signiﬁcant

fraction of the observed vibrational population, implying that the CN vibration was not really a

spectator bond in the reaction dynamics. Furthermore, the observed HCN(v 0v ) vibrations only

1

3

account for about 27% of the initial HCN population produced in the title reaction. A signiﬁcant

fraction of the product HCN molecules must have been produced with the bending mode excited,

͓

S0021-9606͑98͒02735-4͔

I. INTRODUCTION

Rate constants for this reaction have been measured over a

wide temperature range by a number of workers.⁶

–10

Bair

The CNϩH reaction

2

and Dunning used ab initio quantum chemistry methods to

k

R1

probe the stationary regions on the PES for the CNϩH sys-

1

2

CNϩH ——→ HCN͑v ,v ,v ͒ϩH

2

1

3

11

tem, primarily to study the reverse reaction, HϩHCN.

Ϫ1

͑

⌬H ϭϪ21.6Ϯ2.1 kcal mole

͒

͑R1͒

These calculations were reﬁned and extended by Wagner and

Bair in order to obtain a theoretical estimate of the thermal

0

is a prototypical reaction system for the study of the detailed

dynamics of four atom systems. As such, a great deal of

effort has been put forth to provide both an experimental and

theoretical description of this reaction in order to elucidate

new dynamical features that can arise in four atom

12

^r^a^t^e^c^oⁿ^s^t^aⁿ^t^,^kR1

.

Using the theoretical predictions for the

properties of the saddle point and conventional transition

state theory to calculate the thermal rate constant, good

agreement with the available experimental values was ob-

tained by reducing the theoretically predicted barrier height

1

–3

systems.

In comparing the dynamics of three and four

Ϫ1

atom systems, not only does the number of internal degrees

of freedom increase from three to six, but the number of

arrangements of the four atoms into bound intermediates and

product channels also can increase. For the CNϩH reaction,

there are several atomic conﬁgurations that are bound, H CN

and HCNH and two product channels HCNϩH and HNCϩH

that become accessible with increasing energy. The unravel-

ing of how these intermediates and multiple product chan-

nels inﬂuence the reaction dynamics will occur only from the

from 6.0 kcal mole to 4.1 kcal mole . The theoretical cal-

culations indicated that the transition state was linear, located

in the entrance channel with an extended H–CN bond, and

was characterized by one very low frequency bending mode.

More experimental conﬁrmation about the appropriateness of

this theoretical description for the transition state came from

the correct predictions of the kinetic isotope effect.⁷

2

,9,13

The determination of product state distributions has

played an important role in the ﬁeld of reaction dynamics.¹⁴

Although there has not been a direct observation of the HCN

product state distribution from reaction R1, there have been

strong indications of substantial vibrational excitation in the

HCN product; for example, an infrared chemical laser, based

on reaction R1, has been created¹⁵and infrared chemilumi-

4

close interaction between theory and experiment. The ﬁrst

step along this path is to determine a global potential energy

surface ͑PES͒ that can describe all the possible interactions

in this system.

Thermal rate constants are a very sensitive measure of

the properties of the transition state region of a PES. For this

reason, the kinetics of the CNϩH reaction has received a

great deal of scrutiny, and has recently been summarized.

2

nescence from vibrationally excited HCN has been

observed.16 _A_r_u_n_a_n_e_t_a_l_.17 also measured the initial vibra-

5

tional distribution of HCN from the reaction of the CN radi-

cal with a a wide variety of H atom donors, and found sub-

stantial vibrational excitation in the HCN H–C stretch as

well as the bend-H–C stretch manifolds.

^a^͒Also at: Department of Chemistry, Northwestern University, 2145 Sheri-

dan Dr., Evanston, IL 60208-3113.

Also at: Department of Chemistry, Niigata University, Faculty of Science,

b͒

Niigata 950-21, Japan.

0021-9606/98/109(11)/4224/13/$15.00

4224

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1

J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

4225

Other dynamical information on the CNϩH reaction

has come from the study of the reverse reaction, HϩHCN

variations were explored using full dimensional quasiclassi-

cal trajectory calculations. The PES labeled surface 3 by ter

Horst et al.³¹gave the best agreement with experiment for

the temperature dependence of the calculated k_R₁, and will

be labeled the THS surface for reference purposes, here. This

new global PES for reaction R1 describes all the features of

the CNϩH2 and HϩHCN interactions with near chemical

accuracy in some regions.

2

and probing the CN(v,J) product distribution. In these ex-

periments, energetic H atoms¹

8,19

or a combination of ther-

mal and energetic H atoms with mode speciﬁc excitation of

the HCN reactant,²

0,21

were used to induce the reaction.

Some of these experiments provided evidence that the CN

vibration participated in the reaction dynamics, and did not

behave as a pure spectator bond.²¹

In the present work, one unexplored experimental aspect

of the reaction dynamics of the CNϩH2 reaction is ad-

dressed, namely, the determination of the initial vibrational

level distribution of HCN. Time-resolved infrared absorption

spectroscopy was used to monitor individual rotational states

The notion of vibrational adiabaticity and the coupling

of vibrational modes to the reaction coordinate have long

22

been a question central to reaction dynamics. Early, evi-

dence that the nonreacting CN vibration behaved as a spec-

0

tator bond in the CNϩH reaction came from the theoretical

of the HCN(v10 v3) (v1ϭ0, 1 and v3ϭ0, 1, 2͒ vibrational

2

12

calculations of Wagner and Bair, who found the CN vibra-

tional frequency almost constant along the reaction path.

This notion was reinforced experimentally because the rate

levels. These measurements will be compared to the theoret-

ical predictions based on full-dimensional quasiclassical tra-

jectory calculations³²and four-dimensional quantum scatter-

ing calculations using an extension of the rotating bond

approximation treatment ͑RBA-4D͒.³³In both these theoret-

ical studies, the dynamics were carried out on the global

THS surface.

of reaction for CN(vϭ1)ϩH was found to be only slightly

2

6,7

larger than for CN(vϭ0). Reduced dimensional quantum

dynamical calculations have been conducted to probe various

aspects of the CNϩH reaction dynamics using model

2

9

,23–26

HCN is a linear triatomic molecule characterized by two

LEPS-type PESs.

A common theme among these treat-

stretching vibrations, ␷ primarily the C–N stretching mo-

ments was that the CN vibrational motion did not participate

in the reaction dynamics.

1

^tⁱ^oⁿ^,^␷3 ^p^rⁱ^m^a^rⁱ^l^y^t^h^e^H^–^C^s^t^r^e^t^c^hⁱⁿ^g^m^o^tⁱ^oⁿ^,^aⁿ^d^␷2 the

doubly degenerate bend, with angular momentum about the

The most detailed experimental information on the dy-

namics of reaction R1 has been provided by the work of Liu

3

4

internuclear axis, lϭv , v Ϫ2,...,1 or 0. Unless explicitly

2

l

27–30

needed, the l designation, v , will be suppressed in referring

and co-workers on the related CNϩD reaction.

These

2

to the HCN bending vibrational levels.

experiments were carried out in crossed molecular beams

with both time-resolved and Doppler-resolved multiphoton

ionization of the D atom product to determine velocity and

angle-resolved differential cross sections as a function of col-

lision energy. As expected for a direct abstraction reaction,

II. EXPERIMENT

The experimental apparatus³⁵^,³⁶has been described in

detail previously; however, several improvements have been

made for the present set of experiments, and for complete-

ness, a brief description is given here. The transverse ﬂow

reactor ͑TFR͒ consists of a rectangular stainless steel cham-

ber containing a Teﬂon box of dimensions 100ϫ100

ϫ5 cm. The TFR was evacuated by a liquid nitrogen trapped

25 c.f.m. mechanical pump to a base pressure of a few

mTorr, and had a leak rate of less than 1 mTorr per minute.

A separate high vacuum system supplied known ﬂows of

Ar, H , and (CN) to the TFR. The partial pressure of each

2

7,28

Che and Liu

found that the D atom product was predomi-

nately backscattered with respect to the incident D beam;

2

however, there was also signiﬁcant forward and side scat-

tered product. Also, the excitation function for the CNϩD₂

reaction was measured,²⁸and reaction was found at collision

Ϫ1

energies below the 4.1 kcal mole barrier height predicted

by Wagner and Bair.¹²Che and Liu suggested that a barrier

Ϫ1

height of 3.0 kcal mol was more consistent with their ob-

servations. In an even more exciting set of experiments, Lai

2

9

et al. were able to measure the doubly resolved differential

cross section for D atoms that corresponded to DCN with

different amounts of internal energy. The D atom correlating

to the product DCN with the more internal energy was found

to be more forward scattered. Recently, Wang et al.³⁰carried

out very careful studies of the angular distribution of the

2

component was calculated from their known ﬂow rates and

the total pressure in the TFR. Both the Ar and H , research

2

grade, 99.9995% pure, were supplied by AGA Gas. The

(CN) was Matheson grade, 98.5% pure, and was used with-

2

out further puriﬁcation, except for pumping on at Ϫ78 °C.

Almost all the experiments reported on here were carried at a

total pressure of 4 Torr.

Ϫ1

DCN product at a collision energy of 5.8 kcal mole and

compared these results to theoretical predictions.

A great advance was made in the understanding of the

dynamics of reaction R1 by the construction of a global PES.

This surface was based on a large number of high quality ab

initio points. Almost the complete molecular conﬁguration

space was explored using high quality ab initio molecular

orbital methods based on multireference conﬁguration inter-

action ͑MR-CI͒ wave functions for various levels of com-

plete active space ͑CAS͒ references. These ab initio points

were ﬁt to give several global PESs with slightly different

transition state properties, and some consequences of these

A Lumonics model 740 excimer laser, operating at a

wavelength of 193 nm and a power density of 10–20

mJ/cm, was used to generate a small concentration of CN

2

3

1

radicals from the photolysis of (CN) . Most of the data were

2

collected at a laser repetition rate of 5 Hz, but no difference

in the results was observed if the repetition rate was varied

between 1 and 10 Hz.

The complete time dependence of individual rovibra-

tional levels of HCN created in the CNϩH reaction was

2

followed by time-resolved infrared absorption spectroscopy.

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

The laser source was a single mode Burleigh Instruments

model FCL-20 Color Center laser. This laser is completely

tunable throughout the 2.6–3.4 ␮m range, and has an intrin-

sic bandwidth of better than 1 MHz. The laser frequency was

continuously monitored using the appropriate etalons to en-

sure that it was operating in a single mode, and was deter-

mined to an absolute accuracy of Ϯ150 MHz using a Bur-

leigh model WA-20IR wavemeter. Amplitude ﬂuctuation

noise was suppressed using a differential detection scheme,

as described previously.³⁵The overall frequency response of

the detection electronics was better than 5 MHz.

Two modiﬁcations to the apparatus were made in order

to increase the signal-to-noise ratio for the study of reaction

R1. One, was to add the ability to vary the temperature of the

reaction chamber, and the second, was to increase the ab-

sorption path length. The temperature variation was accom-

plished using a Neslab model EX-251HT bath to circulate

hot silicone oil through copper tubing embedded in the top

and bottom of the Teﬂon box. Only a modest increase in

temperature is needed to increase k_R₁, and hence, the con-

centration of the HCN product per unit time. The absorption

path length was increased by adding multipass White cell

optics to the TFR.³⁷

The rectangular-shaped ArF laser beam (ϳ1.5ϫ5 cm)

propagated through the TFR with the short dimension paral-

lel to the nominal ﬂow direction and the long dimension

parallel to the height of the TFR. Both the ArF and infrared

laser beams were overlapped using a dichroic UV-IR mirror

inserted onto the White cell optical axis at Brewster’s angle

with respect to the polarization of the infrared laser radiation.

The White cell mirrors were arranged so that the probe laser

images on the White cell mirrors followed the long dimen-

sion of the ArF laser beam. This arrangement allowed the

infrared laser to pass through the photolysis zone a total of

enough to conﬁdently tune the frequency of the infrared laser

to the peak of an absorption feature; however, the determi-

nation of the peak position was imperative in order to obtain

reliable data. As in previous work, the tuning of the laser

frequency was aided by maximizing the signal from a box

car averager whose gate was set at the maximum signal from

the temporal proﬁle for the transition under study.³⁵The fre-

quency of the infrared laser was then manually kept at this

value while the signal averaged proﬁle was acquired. If the

frequency for the peak of the transition under study could not

be reliably determined, then no data were collected for that

particular rovibrational level. As a result, very little data

could be gathered for the HCN͑200͒ level or for HCN with

any bending excitation.

As will be discussed in Sec. III C, the time dependence

of both the CN reactant and the HCN product enter into the

determination of the initial vibrational level distribution of

HCN. The CN radical was detected by time-resolved absorp-

tion spectroscopy using rotationally resolved transitions of

2

ϩ

the CN red system A ⌸← ⌺ (2,0) band near 790 nm. The

probe laser source was an Environmental Optical Sensors

tunable external cavity diode laser. Both the red and infrared

laser beams were overlapped, and propagated along with the

ArF photolysis laser so that the time dependence of both CN

and HCN could be followed on the same laser pulse. Further

details of this detection scheme will be presented in another

work.³⁸

The addition of the diode laser detection of CN was

made after the HCN vibrational level distribution data had

been gathered. However, the same experimental conditions

were duplicated, and the rate constants describing the time

dependence of CN(vϭ0) in the absence of H were mea-

2

sured ͑see Sec. III C 2͒.

14 times, giving an absorption path length of 14 m. A beam

dump of KCl or ZnS was inserted onto the White cell optical

axis, again at Brewster’s angle, to attenuate the ArF laser

radiation and prevent damage to the White Cell mirrors. The

chambers containing the optics were ﬂushed by about 25%

of the Ar ﬂow to reduce the deposit of paracyanogen on the

optical surfaces exposed to the ArF laser radiation.

Time-resolved absorption signals of individual rovibra-

tional states of HCN were collected by tuning the infrared

laser to the peak of an absorption feature, and then signal

averaging for 1000 photolysis laser shots using a LeCroy

III. RESULTS

A. Initial energy distribution of CN

In order to compare the measurement of the initial HCN

vibrational product distribution with theoretical predictions,

it is important that the initial conditions for the translational

energy and the internal state distribution of the CN reactants,

be well deﬁned. The photolysis of (CN) at 193 nm produces

CN radicals that are translationally and internally excited,

2

39–41

9410 digital oscilloscope. A background trace was recorded

with about 13% in the CN(vϭ1) vibrational level.

The

with the infrared laser detuned several linewidths from the

peak of the probed transition. The two records,

signalϩbackground and background, were transferred to a

laboratory PC and subtracted to obtain the undistorted signal

proﬁle alone. This procedure was needed to account for an

instantaneous baseline shift that was largest directly follow-

ing the photolysis laser pulse, and was presumably caused by

a refractive index gradient induced in the dichroic mirror or

current experiments were carried out at a pressure of 4 Torr

so that at least the translational and rotational degrees of

freedom of CN could be thermalized before appreciable re-

action occurred. The kinetics for the rotational relaxation of

CN(vϭ2;J) in collisions with Ar have been studied by Fei

et al.,⁴²and many relaxation rates were found to be near gas

kinetic. Rotational relaxation rates should not depend dra-

matically on vibrational quantum number so that rotational

relaxation of CN(vϭ0;J) should be nearly as rapid.

beam dump. The initial infrared laser intensity, I , was re-

0

corded by a box car averager that sampled the laser intensity

several hundred ␮s before the excimer laser pulse.

For many of the HCN vibrational levels studied in the

present work the single shot signal-to-noise was not large

Both experimental and theoretical considerations indi-

cate that the kinetics of CN(vϭ1) are similar to those for

CN(vϭ0), and it was assumed that the HCN product distri-

bution was similar for these two reactant vibrational levels.

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Bethardy et al.

4227

B. Determination of the time dependence of the

HCN„v 0v … population

1

3

The absorption of radiation of frequency, v, for a tran-

sition from a lower rovibrational state i, with population n_i,

to an upper state j with population n , is given by the fol-

j

43

lowing form of the Beer-Lambert Law:

8

3

␲³

ln͓I ͑␷͒/I͑␷͔͒ϭ

␷ HW A_i_j͉␮_i_j͉

²g͑␷͒

0

ͭ

ͮ

hc

d_i

ϫ

ͩ

n_iϪ n_j

ͪ

l,

͑2͒

d_j

where the absorbance is deﬁned as ln͓I (␷)/I(␷)͔, the absorp-

0

tion cross section is deﬁned by the terms within the curly

brackets, ͕ ͖, h, and c have their usual meanings, HW is the

Herman–Wallis factor to correct for the interaction between

rotation and vibration,⁴⁴A_i_jis the Honl–London factor, ␮_i_j

is the vibrational transition dipole moment, g(␷) is a line

shape function, d is the degeneracy of level k, and l is the

k

path length. At a total pressure of 4 Torr, the effects of pres-

sure broadening are small, and g(␷) is well described by a

thermal Doppler proﬁle, independent of the HCN vibrational

4

3,45

level probed.

The population in all the vibrational levels

of HCN can be monitored using the ␷₃mode as a chro-

mophor in combination bands where the changes in vibra-

tional quantum number are ⌬v ϭ0, ⌬v ϭ0, and ⌬v ϭ1

1

2

3

changes. The transition moments for these excited vibra-

tional transitions, with ⌬v ϭ1, were taken form the calcu-

3

46

FIG. 1. Absorbance plots as a function of time for the HCN(00v ) mani-

lations of Botschwina et al., but were scaled to the experi-

3

_m_e_n_t_a_l_m_e_a_s_u_r_e_m_e_n_t_o_f_S_m_i_t_h_e_t_a_l_.₄7 for the fundamental

fold. The curves labeled by diff are the raw experimental absorbance pro-

ﬁles, and those labeled by pop the actual populations as determined by the

application of Eq. ͑2͒. The insets show an expanded view of the initial time

region for the raw data ͑diff͒. The conditions of the experiment were P_A_r

^ϭ³^.⁰⁷⁴^,^P(CN)₂^ϭ⁰^.⁰⁶⁷^aⁿ^d^PH₂ϭ0.960 Torr at a temperature of 324 K.

transition. The method of correcting the raw experimental

absorbance proﬁle for the measured degeneracy weighted

difference in population has been described previously.³⁵

Furthermore, none of the data depends on the absolute con-

centration of HCN(v 0v ), and all the population proﬁles

1

3

HCN͑201͒ and ͑102͒ were not detectable at all so that the

have been normalized to the peak absorption cross section

for the HCN͑000͒ R͑8͒ transition.

absorbance from these levels was estimated to be less than

Ϫ4

5

ϫ10.

Typical absorbance temporal proﬁles are shown in Figs.

1

At 293 K, the HCN(01 0) bending level accounts for

% of the equilibrium HCN population, and this was the

1

and 2 for single rotational states of the HCN(00v ) and

3

6

HCN(v 0v ) manifolds, respectively. The inserts show an

1

3

only bending vibrational level from which an absorption sig-

expanded view of the initial portion of each curve. As is

evident from Eq. ͑2͒, a negative absorbance can arise when a

population inversion occurs between the two probed quan-

tum states, e.g., Figs. 1͑b͒, 1͑c͒, and 2͑b͒. At 4 Torr total

pressure, the rotational relaxation of HCN for each vibra-

tional level should be as rapid as that for CN, and the rota-

tional states can be described by a Boltzmann distribution at

the temperature of the reaction chamber. Hence, a measure

of the HCN population in a single rotational state deﬁnes the

total population for that vibrational level. The absorbance

temporal proﬁles labeled by pop shown in Figs. 1 and 2

describe the complete time evolution for the population of

the HCN(v 0v ) vibrational levels relative to each other,

48

nal could be measured. The spectral regions in which sev-

1

2

eral excited HCN(0,v ,v ) levels should have transitions

3

were carefully scanned over, but the signal was either very

weak or not detectable. The small signal from the bending

manifolds can be attributed to several factors: the reduced

individual line strength due to l-type resonance, the partition-

ing of the HCN population in a given ␷ vibrational level

2

among the near degenerate multiple bending vibrations,

given by v , v Ϫl,...,1 or 0, and the rapid vibrational re-

2

laxation, both intra and inter, for the bending manifolds.

1

3

C. Determination of the initial HCN„v 0v …

1

3

outside of a small Boltzmann correction factor, which ac-

counts for the different rotational states probed. In only a few

experiments could signal be detected from the HCN͑200͒

distribution

1

. Kinetic model

Figures 1 and 2 represent the complete time dependence

of the relative vibrational population of HCN(v 0v ) pro-

level, but under higher pressures of H than in Figs. 1 and 2,

2

and is not shown. Other levels of the stretch manifolds,

1

3

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

k

R5

CNϩO ——→ NCOϩO,

͑R5͒

͑6͒

2

CN

k

diff

CN ——→ ,

HCN

k

diff

HCN ——→ ,

͑7͒

where reaction ͑5͒ was included to allow for the fact that the

CN may react with a background O . The solution of the

2

kinetic equations corresponding to this reaction scheme is

given by:

͓

CN͔ϭ͓CN͔ exp͑Ϫk^Јt͒,

͑8͒

0

CN

k_R₁͓H ͔͓CN͔₀

2

HCN

͓

HCN͔ ϭ

͕

exp͑Ϫk_d_i_f_ft͒Ϫexp͑ϪkЈ t͒

͖

,

CN

T

HCN

kЈ Ϫk

CN

diff

͑

9͒

CN

diff

where kЈ ϭk ͓H ͔ϩk ͓O ͔ϩk . At times greater than a

CN

H

2

O

2

few ms, vibrational relaxation of all the excited HCN mani-

folds was virtually complete ͑see the Appendix͒, and at a

long enough observation time, t, the ͓HCN͑000͔͒ provided a

direct measure of the ͓HCN͔ produced in the reaction, i.e.,

T

͓

HCN(000);t͔ϭ͓HCN;t͔ . This allows for the measure-

T

ment of the ͓CN͔ and the compete description of the time

0

dependence of ͓HCN͔ according to Eq. ͑9͒ if diffusion were

T

a simple ﬁrst order process. However, with the current ge-

ometry, diffusion is complicated, and must be considered in

detail before applying Eq. ͑9͒.

FIG. 2. Absorbance plots as a function of time for the HCN(v 0v ) mani-

1

3

fold. The labeling is the same as in Fig. 1. Note the large population inver-

sion between the HCN͑100͒ and HCN͑101͒. The conditions of the experi-

ment were the same as Fig. 1.

2. Diffusion

On the time scale for the diffusion of HCN from the

photolysis region, tens of ms, the creation of HCN can be

considered rapid, less than a few ms. This situation has been

considered by McDaniel for the diffusion of a species in-

stantaneously created with a uniform concentration in the

form of a rectangular parallelepiped. Under these circum-

stances, the time dependence of the diffusional process is

described by an inﬁnite series of decaying exponential terms

with exponential rate constants, k_i_j_k, for the various diffu-

sion modes ͑indexed by i, j, k͒, given by:

duced in the CNϩH reaction system. These population pro-

ﬁles could be converted into time dependent fractional popu-

2

49

lations, f (v v v ;t), expressed as:

v

1

2

3

f ͑v ,v ,v ;t͒

v

1

2

3

ϭ͓HCN͑v ,v ,v ;t͔͒

Ͳ

͓HCN͑v ,v ,v ;t͔͒

1 2 3

1

2

3

͚

v1,v2,v3

͑3͒

2iϪ1͒ ²͑2jϪ1͒ ²͑2kϪ1͒ ²

͑

if the total HCN product concentration could be determined,

k_i_j_k_ϭ_D_␲2

ͭ

ͫ

ͬ

ϩ

ͫ

ͬ

ϩ

ͫ

ͬ

ͮ

,

a

b

c

i.e., ͓HCN;t͔ ϭ⌺͓HCN(v ,v ,v ;t)͔, where the sum is

T

1

2

3

͑

10͒

over all vibrational levels and the square brackets, ͓ ͔, indi-

cate concentration. Extrapolation of the f (v v v ;t) curves

v

1

2

3

where D is the diffusion constant and a, b, and c deﬁne the

dimensions of the initial rectangular parallelepiped in which

the diffusing species was created. For the ArF laser beam

geometry used in the current experiments, these dimensions

were approximately aϷ1.5 cm, bϷ5 cm, and cϷ100 cm,

and an inspection of Eq. ͑10͒ shows that the following rela-

tionship approximately held for the lowest four diffusion

modes, k₁₁₁Ϸk₁₂₁Ϸk₁₁₂and k₂₁₁ϭ9 k₁₁₁. Higher order

modes were described by increasingly larger rate constants,

and were quickly attenuated.

to the time origin, f (v v v )^͉tϭ0 , would provide a measure

v

1 2 3

of the initial vibrational level distribution of HCN. The fol-

lowing model was used to determine the ͓HCN;t͔ ͑the ex-

T

plicit time dependence will be dropped͒.

In the CNϩH reaction system, the kinetics are straight-

2

5,7,9,13,38

forward, and the rate constant is well established.

The following set of reactions describe the time dependence

of the total CN and HCN populations:

1

93 nm

The ͓HCN͑000͔͒ proﬁles were ﬁt to a series of exponen-

tial terms ͑see the Appendix͒, and for times longer than a few

ms the decay was described by two terms with exponential

͑

CN͒ ——→ 2CN,

͑4͒

2

k

R1

Ϫ1

CNϩH ——→ HCNϩH,

͑R1͒

decay rates ranging from 150–250 s and 15–25 s , re-

2

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

4229

FIG. 4. The f (00v ) curves as a function of time are shown for the ﬁrst

v

3

200 ms for the experimental proﬁles in Fig. 1. The inset shows the extrapo-

lation to tϭ0 to determine the initial vibrational population. The maximum

in the f (00v ) plots was used to estimate the initial population in the

v

3

undetected levels as discussed in Sec. IV.

FIG. 3. The very long time behavior of HCN(000;Jϭ8) is shown to illus-

trate the titration experiments and the decay of CN. Two raw experimental

proﬁles for ͓HCN͑000͔͒ are shown: the heavy curve labeled

͓

HCN͔͑C H ϩH ͒ with the addition of 0.074 Torr C H and the lighter

evaluated at a long time, compared to the kinetics, if the use

2

6

2

6

curve labeled ͓HCN͔͑H ͒ no C H added. The very thin curve, labeled

2

6

of this equation were valid. The CNϩC H reaction rate

2

6

͓

HCN͔ , shows the results using Eq. ͑9͒ based on the measurement of

5

T

constant and vibrational relaxation of HCN(v v v ) by

1

2 3

HCN͑000͔͒ at tϭ7.0 ms from the ͓HCN͔͑H ͒ curve. The arrow, Calculated

2

35,50

C H are sufﬁciently rapid

that the CN radicals were

CN͔ , is close to the peak of the ͓HCN͔͑C H ϩH ͒ curve. The conditions

2

6

0

2

6

2

of the experiment with C H were P_A_rϭ3.796, P₍_C_N₎₂ϭ0.074, and P_H₂

scavenged by the C H , and relaxed to HCN͑000͒ before

2

6

2

6

ϭ0.184 Torr at Tϭ294 K. The inset shows the time dependence of the

CN(vϭ0) radical before recording the preceding ͓HCN͑000͔͒ time proﬁles

for the conditions: P_H₂ϭ0.0, P_A_rϭ3.913, P₍_C_N₎2^ϭ⁰^.⁰¹⁰¹^T^o^r^r^,^aⁿ^d^T

ϭ294 K. The nonlinear least squares parameters for the experimental curves

being lost by diffusion. Generally, the ͓HCN͑000͔͒ measured

in the titration experiments was within 5% of the ͓CN͔₀

determined by the application of Eq. ͑9͒. This was taken as

conﬁrmation that the approximation of ignoring the slow dif-

͑

see Appendix͒, in the form (A ,k ): for the ͓HCN͔͑H ͒, ͑Ϫ0.1160, 3.120

i

2

^f^u^sⁱ^oⁿ^p^r^o^c^e^s^s^w^a^s^r^e^a^s^oⁿ^a^b^l^e^aⁿ^d^t^h^a^t^t^h^eⁱⁿⁱ^tⁱ^a^l^͓^C^N^͔0

ϫ10 ), ͑0.047 48, 1.68ϫ10 ), and ͑0.062 07, 28.7͒, for the ͓HCN͔͑C H ͒,

2

6

3

2

͑Ϫ0.2045, 5.79ϫ10 ), ͑0.0702, 1.10ϫ10 ), and ͑0.085 96, 25.2͒, and for

could be determined using Eq. ͑9͒.

2

^C^N^d^e^c^a^y^wⁱ^t^h^PH₂ϭ0.0, ͑0.0547, 1.64ϫ10 ).

An example of the long time behavior of both the

͓

HCN͑000͔͒, the ͓CN͔, and the titration of CN by C H is

2 6

provided in Fig. 3. The inset in Fig. 3 shows the time depen-

spectively, in very close agreement with the ratio of k₁₁₁to

k₂₁₁predicted by Eq. ͑10͒. These time scales were well sepa-

rated from each other, and all other kinetic and relaxation

dence of CN(vϭ0;Jϭ8) in pure Ar, recorded using the la-

ser diode. In a nonpolar gas mixture such as Ar–H , the

2

CN

diff

diffusion rate for CN, k , should be similar to that for

HCN because of their similar masses. Hence, in the ab-

51

processes occurring in the CNϩH system. Under these cir-

2

cumstances, the slower diffusional process can be neglected,

and diffusion can be considered to be a ﬁrst order process.

Thus, the simple kinetic model, reactions ͑4͒ to ͑7͒, can be

sence of H , the ﬁrst order decay of CN should be equal to

2

HCN

k

. Generally, this was not the case, and the ﬁrst order

diff

HCN

decay of CN was about 30% larger than k_d_i_f_f, and resulted

applied to the data, and the time dependence of ͓HCN͔ is

in an uncertainty in the determination of the ͓HCN͔ proﬁle,

T

given by Eq. ͑9͒.

e.g., at a mole fraction of H of 0.05 this increase in k

2

CN

The appropriateness of this assumption was tested in

several experiments by titrating the CN radicals by the addi-

tion of a small partial pressure of C H and determining the

results in a 10% decrease in the calculate ͓HCN͔_Tproﬁle.

The cause of the larger rate for the CN decay was attributed

5

2

to the reaction, CNϩO , because this rate constant is large,

2

6

2

Ϫ11

3

Ϫ1 Ϫ1

͓

HCN͑000͔͒. This concentration should agree with the

k_R₅ϭ2.5ϫ10

cm molecule

s , and the background

CN͔ calculated using Eq. ͑9͒ for the ͓HCN͑000͔͒ proﬁle

pressure of O in the TFR apparatus could have been up to

0

2

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1

4230

J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

FIG. 5. Same as Fig. 4 except for the experimental proﬁles in Fig. 2.

2

ϫ10^Ϫ⁴Torr. In early experiments, there was no HCN de-

FIG. 6. The results for the initial level distribution, f (v10v3)͉tϭ0 , as a

v

function of H mole fraction. The upper panel for the HCN(00v ) manifold

tected without H present; however, those experiments were

not extensive, and in the most recent experiments, a back-

ground HCN signal was detected.

2

3

2

and the lower panel for the HCN(v 0v ) manifold. The dotted lines are

1

3

linear least squares ﬁt to the data for each vibrational level. The experiments

were carried out at a total pressure of 4 Torr and P₍_C_N₎₂Ϸ0.07 Torr at T

^T^h^e^tⁱ^m^e^d^e^p^eⁿ^d^eⁿ^c^e^o^f^͓^H^C^N^͔T was calculated using

ϭ293 K. The closed symbols were for the rotational sequence Jϭ8→9

→10 for increasing v3 , the open symbols for the Jϭ15→16→17 sequence

and the partially open symbols for Jϭ20→21→22 sequence. The plots

have been corrected for the variation in the rotational Boltzmann factor. The

plots show that the f (v 0v )͉_t_ϭ₀are independent of H partial pressure.

Eq. ͑9͒ with the measured decay for CN for P ϭ0.0 added

H

2

to the best estimate for k_R₁for a temperature of 293 K

Ϫ14

3

Ϫ1 Ϫ1

and 324 K, i.e., k ϭ2.5ϫ10

cm molecule

s

and

R1

v

1

3

2

Ϫ14

3

Ϫ1 Ϫ1

5,7,9,38

4

.3ϫ10

cm molecule

s , respectively.

3

. The f „v 0v … extrapolation

v

1

3

of rapid vibrational relaxation, the initial f (00v ) and

v

3

f (v 0v ) values were measured as a function of the H

The complete time dependence of the f (v 0v ) was

v

1

3

2

v

1

3

mole fraction, and are presented in Figs. 6 and 7 for the

temperatures of 293 and 324 K, respectively. The dotted

lines in Figs. 6 and 7 are linear least squares ﬁts to the data

for each vibrational level, and are intended only as a guide

for the eye. As is evident from Figs. 1 and 2, the HCN͑002͒

and ͑101͒ levels exhibited the fastest variation with time, and

hence, are most inﬂuenced by vibrational relaxation pro-

cesses ͑see the Appendix͒. The slopes of the linear least

determined according to Eq. ͑3͒ using Eq. ͑9͒ to describe the

time dependence of ͓HCN͔ under a given set of experimen-

T

tal conditions. The HCN͑000͒ time dependence was moni-

tored several times during an experimental run, and the data

were normalized to account for drifts in the experimental

conditions. The determinations of the f (v 0v ) versus time

v

1

3

plots for the population proﬁles shown in Figs. 1 and 2 are

presented in Figs. 4 and 5, respectively. The initial vibra-

tional level distribution was determined by extrapolating the

ﬁrst 5–10 ␮s to tϭ0, as shown in the insets in Figs. 4 and 5.

The ﬁrst few points were ignored in making these extrapola-

tions because the noise is larger ͑dividing an experimental

trace by a small number͒ and the ﬁrst few data points exhib-

ited the largest uncertainty due to the correction for the back-

ground instantaneous baseline shift induced by the ArF laser

pulse ͑see Sec. II͒. Similar results were obtained at a tem-

perature of 293 K.

squares ﬁts to f (002) and f (101) are essentially zero, in-

v

dicating that the determination of the initial fractional popu-

^l^a^tⁱ^oⁿ^w^a^sⁱⁿ^d^e^p^eⁿ^d^eⁿ^t^o^f^t^h^e^PH₂. This was the case for the

other vibrational levels as well, and the nonzero slopes for

these levels were attributed to their small values and hence,

experimental scatter. The ﬁnal determinations for the initial

vibrational level distribution were obtained by simply aver-

aging all the data presented in Figs. 6 and 7 for each tem-

perature, and are summarized in Table I.

In order to check for the systematic dependence of the

initial f (v 0v ) on the P , such as the potential inﬂuence

Computer simulations for the production and relaxation

of a model set of levels representing the HCN vibrational

v

1

3

H

2

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

4231

collected. Within the scatter, there was no obvious trend, and

it was concluded that the HCN was rotationally relaxed to

the temperature of the reaction, as would be expected.

IV. DISCUSSION

The observed initial population of HCN in the bendless

stretch manifolds accounts for only 27% of the HCN created

in reaction R1, see Table I; thus, 73% of the initial HCN

population must be created with bending vibrations excited,

likely in combination with the H–C stretching mode. Some

insight into the distribution of these undetected levels can be

gained by simple considerations of the maximum population

in the observed stretch levels.

The maximum in the f (v 0v ) plots, shown in Figs. 4

v

1

3

and 5, occurred relatively close to tϭ0 ͓especially true for

HCN͑002͒ and HCN͑101͔͒, before signiﬁcant depletion by

vibrational relaxation. To crudely account for vibrational re-

laxation while the maximum in a f (v 0v ) was being

v

1

3

reached, a simple exponential extrapolation back to tϭ0 was

made using an average relaxation rate constant calculated

from the appropriate phenomenological rate constants sum-

marized in Table IV. A summary of the measurements on the

maximum in the f (v 0v ) curves and an estimate of the

v

1

3

largest possible fraction of the HCN(v 0v ) population that

1

3

could pass through a given level is given in Table II.

Vibrational relaxation of polyatomic molecules is not

well characterized,⁵³but it would be expected that vibra-

tional energy should be removed from the lower frequency

bending vibrations in HCN combination levels before being

removed from the higher frequency stretching vibrations. If

this scenario has any validity, then the stretching manifolds

can be viewed as intermediate levels in which vibrational

energy is deposited as it ﬂows down through a vibrational

manifold. Taking the average of the data for the two tem-

peratures, 294 and 323 K, the last column in Table II can be

interpreted to imply that about 64% of the HCN molecules

FIG. 7. Same as Fig. 6 except for a temperature of Tϭ324 K.

manifold were carried out to verify the applicability of this

extrapolation procedure. These calculations were similar to

those described previously.³⁵As long as there are no very

rapid relaxation processes ͑none were detected in the present

work, as summarized in the Appendix͒, then the described

procedure is reliable.

Most of the data for the HCN(00v ) manifold were ob-

3

formed in the CNϩH reaction were created with vibrational

2

tained for rotational states with Jϭ8, 9, and 10, for v ϭ0, 1,

3

energy greater than or equal to the HCN͑001͒ vibrational

and 2, respectively, near the peak of the Boltzmann distribu-

tion; however, several experiments were carried out on more

energetic rotational states, Jϭ15, 16, and 17 and Jϭ20, 21,

and 22. The results of these experiments are indicated in Fig.

by the open symbols. Because of the poorer signal-to-noise

for these experiments, only a limited amount of data could be

Ϫ1

level ͑9.5 kcal mole ͒, and 27% were formed with energy

Ϫ1

greater or equal to the HCN͑002͒ level ͑18.6 kcal mole ͒.

Comparing the last column in Table II with the initial distri-

bution in Table I and assuming that HCN͑101͒ is relaxed to

6

give HCN͑001͒, as indicated in the experiments of Smith and

54,51

co-workers,

the partitioning of the unobserved HCN vi-

brational levels into the ‘‘energy bins’’ indicated in Table III

was estimated, and summarized in Table III. The HCN mol-

ecules that were not accounted for ͑32%͒ were assumed to be

formed in pure bending states less energetic than HCN͑001͒.

It is of course more likely the above procedure is too crude

and some relaxation bypassed the intermediate HCN͑001͒

and ͑002͒ vibrational levels, and hence, not all of the vibra-

tionally excited HCN population was counted as HCN͑001͒

or ͑002͒. A comparison of the estimated experimental vibra-

tional energy distribution with the distribution found in the

RBA-4D quantum calculations³³is also given in Table III.

Even though the experimental estimate is extremely crude

and can be viewed as a lower limit, there is reasonable agree-

ment with the distribution predicted by the RBA-4D calcu-

lations.

TABLE I. Results for initial vibrational level distribution for HCN(v 0v )

1

3

from the reaction CNϩH₂at Tϭ293 and 324 K. The results have been

corrected for the appropriate Boltzmann factors due to the different J states

probed for each vibrational level. The uncertainties are one standard devia-

tion ͑Ϯ1␴͒ in the data presented in Figs. 6 and 7.

f (v ,0,v )

v

1 3

v

1

3

HCN(v ,0,v )

Tϭ294 K

Tϭ324 K

1

3

͑

000͒

001͒

002͒

100͒

101͒

0.014Ϯ0.014

0.058Ϯ0.025

0.13Ϯ0.038

0.019Ϯ0.012

0.077Ϯ.025

0.007

0.0073Ϯ.009

0.030Ϯ0.017

0.12Ϯ0.022

0.015Ϯ0.014

0.065Ϯ0.013

-

a

͑200͒

^aOnly one measurement.

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

TABLE II. Summary of the analysis of maximum in the f (v 0v ) vs time plots for Tϭ293 and 324 K.

v

1

3

Vibrational relaxation is crudely accounted for by using an appropriate exponential rate constant from Table IV

to extrapolate the observed f (v 0v ) peak back to the origin of time. Values from all the data were averaged

v

1

3

and the uncertainty is Ϯ1␴.

Time for

maximum

͑␮s͒

Extrapolated

tϭ0

f_v(v)_m_a_x

Maximum

krelax

(10^Ϫ¹³cm mol s^Ϫ¹

͒

3

Ϫ1

T

HCN(v 0v )

f (v ,0,v )

1

3

v

1

3

294

͑001͒

0.45Ϯ0.06

0.24Ϯ0.04

0.053Ϯ0.003

0.19Ϯ0.039

110Ϯ 14

15Ϯ5.5

95Ϯ 12

1.4

3.6

0.37

4.3

0.74

0.29

0.059

0.26

͑002͒

͑100͒

͑101͒

21.3Ϯ 15

324

͑001͒

0.36Ϯ.11

0.24Ϯ0.04

0.046Ϯ0.014

0.15Ϯ0.03

117Ϯ 21

19.5Ϯ5.8

131Ϯ 40

28.3Ϯ6.9

1.1

3.0

0.40

3.7

0.53

0.26

0.054

0.19

͑002͒

͑100͒

͑101͒

Recent molecular beam experiments have illuminated

many interesting features of the reaction dynamics of the

classical trajectory calculations. It is not clear why this

should be so, but it too may be related to zero-point energy

effects. There is agreement between theory and experiment

that the HCN͑000͒ ground state is not populated directly in

the reaction to any signiﬁcant extent.

CNϩH reaction. In particular, double differential cross sec-

2

tions measurements on this reaction revealed that the newly

formed DCN molecules have a high degree of internal

2

9

excitation. Unfortunately, the excited DCN molecules

could not be assigned to individual vibrational levels; how-

ever, the product distribution was consistent with consider-

As is evidenced by the experimental and theoretical ob-

servations ͑Fig. 8͒, the HCN͑101͒ vibrational level is directly

populated the CNϩH reaction, and the CN vibration should

2

48

able bend-CD stretch excitation. Interestingly, the energy

not be considered a pure spectator bond in the reaction dy-

namics. Features of the potential energy surface must couple

the C–N and H–C vibrations. The role the CN vibration

plays in the reaction dynamics has been explored in a recent

study by Takayanagi and Schatz.⁵⁵Using the RBA-4D dy-

namical theory, they calculated the initial HCN product vi-

brational level distribution for two PESs: the THS surface³¹

and the model LEPS-type PES constructed by Sun and

Bowman.²³One difference between these two PESs is that

the THS surface incorporates an accurate representation of

of the bendless combination stretching manifold,

DCN(v 0v ), also falls near the peak in the internal energy-

1

3

resolvable differential cross section. The relatively large ex-

citation into the HCN͑101͒ level found in the present work,

Table I, would suggest some fraction of the product DCN

molecules was also formed in the DCN(v 0v ) levels.

1

3

The experimentally determined initial vibrational level

distribution of HCN(v 0v ) is compared to the results from

1

3

32

the recent quasiclassical trajectory calculations and the

RBA-4D quantum dynamical calculations³³in Fig. 8. Also₃,

the results of the RBA-4D quantum dynamical calculations³

are summarized further in Table III. Both calculations were

carried out on the global THS surface, and provide an illu-

minating comparison with experiment between a quasiclas-

sical trajectory and quantum dynamical calculation. As is

evident from Fig. 8, there is remarkable agreement between

the theoretical predictions and the experimental measure-

ments. The only major shortcoming appears to be the fall-off

in the HCN͑002͒ distribution in the classical trajectory cal-

culation. This fall-off has been directly traced to the effects

of the violation of zero-point energy constraints that can oc-

cur when the product molecule is formed with vibrational

energy that is a large fraction of the reaction exothermicity.³²

The most striking observation about the HCN product distri-

bution is the signiﬁcant population in the HCN͑101͒ vibra-

tional level. This immediately raises the question as to the

spectator nature of the CN bond in the reaction. Although the

scatter in the experiment measurements is large, it appears

the population in the HCN͑001͒ level is overestimated in

both theoretical calculations. Experimentally, it is clear that

there is a population inversion between HCN͑002͒ and

HCN͑001͒; see the inset in Fig. 1͑b͒. Population in the pure

CN stretching manifold appears to be overestimated in the

56

the HCN intramolecular force ﬁeld while on the Sun and

TABLE III. Comparison of an estimated vibrational energy distribution

based on the partitioning of vibrational energy inferred from the maximum

in the f (v 0v ) vs t plots with the RBA-4D quantum calculations ͑Ref. 33͒

v

1

3

͗ ͘

for similar quantities. The states labeled by the 02v₃brackets are ﬁcti-

tious, and represent an average vibrational energy lying between the corre-

sponding HCN(00v ) bendless levels.

3

Evib^a

b

f

(v10v3)

f (v10v3)

v

RBA-4D

v

HCN(v 0v )

͑kcal mole^Ϫ¹͒

Experimental

1

3

͑

000͒

0.0

4.75

5.99

9.46

14.1

15.4

18.6

22.5

0.011

0.32

0.017

0.044

0.25

0.071

0.125

0.16

0.004

0.048

0.017

0.093

0.38

0.16

0.169

0.131

͗020͘

͑

͗

͑

100͒

001͒

021͘

101͒

002͒

͗022͘

Evib

͘

/Eavail^c

͗

͘

E_v_i_b/E_a_v_a_i_l

͗

0.48

0.563

a

Calculated from Ref. 48.

b

c

Ref. 33.

E_a_v_a_i_lϭ⌬H ϩE

ϩ5/2RTϭ26.3 kcal mole^Ϫ¹

.

0

barrier

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1

J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

4233

FIG. 8. A comparison of the initial HCN(v 0v ) vibra-

1

3

tional level distribution for the CNϩH reaction mea-

2

sured in this work with quasiclassical trajectory ͑Ref.

3

͑

3

2͒ and RBA-4D quantum dynamical calculations,

Ref. 33͒ both carried out using the THS surface ͑Ref.

1͒.

Bowman surface this is not the case and all off-diagonal

quadratic force constants were omitted. As a result, the cal-

culations showed no excitation of the HCN͑101͒ mode when

the Sun and Bowman PES was used, but a large excitation

was found for the THS surface. As pointed-out by ter Horst

tance of reactive conﬁgurations having bent geometries even

on PESs with highly constrained linear transition states.⁵

7,58

The reaction dynamics of CNϩH is expected to be

2

similar to the dynamics of the FϩH reaction. Both are exo-

2

thermic with linear transition states, or nearly so, located in

the entrance valley, and both belong to the HϩLL kinematic

classiﬁcation of reaction systems ͑where H stands for heavy

3

1

et al., an important point to keep in mind is that the normal

modes of HCN are not pure local modes, and the ␷ normal

3

mode can have signiﬁcant C–N character. Furthermore, in

the region of the PES in which the reaction exothermicity is

being released, there is strong mixing between the newly

developing vibrations in the HCN and the motions in the

reactants that correlate to these vibrations. In fact, if the iso-

and L for light masses͒. The FϩH reaction still has many

2

59

interesting features to be investigated experimentally₆, and

0

just recently, accurate quantum dynamics calculations have

been reported using an high quality ab initio PES.⁶¹For

roughly 300 K reactants, the exothermicity of the FϩH re-

2

lated CN vibration adiabatically correlates to the ␷ normal

action is partitioned⁶²into the product degrees of freedom in

1

mode of HCN, then the frequency of this vibration can actu-

ally change quite rapidly over a narrow region on the PES

where the reaction exothermicity is being released ͑see Fig.

a very similar fashion as the CNϩH reaction, i.e., E

2

trans

ϭ0.26, E ϭ0.083, and E_v_i_bϭ0.664. For energy partition-

rot

ing, the major difference appears to be the presence of an

10 of Ref. 33͒.

energy barrier for the CNϩH reaction, and as a result, more

2

One of the intriguing aspects about the dynamics of

of the reaction exothermicity is channeled into product trans-

polyatomic reaction systems is the large number of degrees

of freedom compared to atomϩdiatomic molecule systems.

The interaction between these internal degrees of freedom

will lead to a rich partitioning of the reaction exothermicity

into the product degrees of freedom. Both full dimensional

quasiclassical trajectory calculations³²and experimental ob-

servations of this work show that the bending motion of

HCN is highly excited even though the transition state is

linear. The RBA-4D quantum dynamical calculations of

Takayanagi and Schatz³³also show this to be the case even

though the H–H–C nuclei were constrained to be linear in

the quantum calculations. This constraint implies that there is

no bending motion at the transition state involving these

three nuclei in the quantum dynamical calculations. Other

mechanisms for bending excitation must be operative and

dominating. Again, in the regions on the PES where the re-

action exothermicity is just being released, anharmonic and

coriolis effects can cause strong coupling between the reac-

tant motions and evolving product vibrations. Previous stud-

ies on atomϩdiatom dynamics have pointed out the impor-

lation in CNϩH than in FϩH . This effect can be rational-

ized by the requirement that the extra translational energy

2

needed to surmount the barrier in the CNϩH reaction re-

2

14

mains predominantly as product translational energy.

In previous work,³

5,36

the initial vibrational state distri-

butions for HCN(v 0v ) in the bendless stretching mani-

1

3

folds were determined for the abstraction of H atoms by CN

from simple alkanes, i.e., CNϩC H and CNϩCH . The

2

6

4

family of reactions, CNϩRH→HCNϩR, where R is C H ,

2

5

CH , or H, has some interesting features; namely, the reac-

3

tion exothermicity is approximately constant while the bar-

rier to reaction increases as the complexity of R decreases.

As a consequence of the trend in activation barrier, the tran-

sition state becomes more constrained to be linear, and

moves towards the product channel. Interestingly, the parti-

tioning of the reaction exothermicity into the bendless

stretching manifolds, HCN(00v ), HCN(v 00), and

3

1

HCN(v 0v ), increased with the barrier height and the more

1

3

constrained linear transition state. For all three members of

this family of reactions, the production of HCN products

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

with a high fraction in the bending vibrations has been

stressed, but it should be kept in mind that a near equally

large or larger fraction of the HCN products have the ␷₃

vibrational mode excited as well. This is of course the ex-

pectation because the nuclear motions in this mode are most

reaction coordinatelike.

and Professor G. Schatz for many stimulating discussions.

The authors also wish to thank Professor D. Setser for the

generous gift of a bottle of cyanogen. This work was sup-

ported by the U.S. Department of Energy, Ofﬁce of Basic

Energy Sciences, Division of Chemical Sciences, under Con-

tract No. W-31-109-ENG-38.

V. SUMMARY AND CONCLUSION

APPENDIX: VIBRATIONAL RELAXATION OF

The initial vibrational level distribution of HCN(v 0v )

HCN„v10v3…

1

3

from the reaction CNϩH₂was determined using time-

resolved absorption spectroscopy on single rovibrational

states of HCN. These measurements were carried out at a

pressure of 4 Torr and temperatures of 293 and 324 K. The

initial HCN vibrational level distribution was determined us-

ing an extrapolation of the fractional vibrational population

proﬁles, f (v 0v ), to time equal to zero. In order to de-

It is important to measure the parameters describing the

time dependence of the HCN(v 0v ) levels in order to de-

termine if there are any vibrational relaxation processes rapid

enough to invalidate the extrapolation procedure used to ex-

1

3

tract the HCN initial vibrational level distribution from the

concentration proﬁles. As in previous work,³

5,36

each time

v

1

3

dependent ͓HCN(v 0v )͔ proﬁle was ﬁt to a series of expo-

nential terms of the basic form:

1

3

scribe the time dependence of the total HCN population,

both the diffusion of HCN͑000͒ and the time dependence of

CN were carefully considered.

͓HCN͑v 0v ͔͒ϭA

exp͑Ϫk_f_a_l_l_ft͒ϩA_f_a_l_l_s

1

3

fall f

The initial HCN(v 0v ) vibration distribution deter-

1

3

ϫexp͑Ϫk_f_a_l_l_st͒ϪA_r_i_s_eexp͑Ϫk_r_i_s_et͒,

mined in this work is given in Table I, and compared to both

32

the quasiclassical trajectory and RBA-4D quantum dy-

namical calculations³³in Fig. 8. There is good agreement

between theory and experiment, in particular with the quan-

tum dynamical calculations. An analysis, based on the maxi-

mum values observed for the f (v 0v ) curves, was used to

͑A1͒

where the positive pre-exponential factors describe the tem-

poral decay (k_f_a_l_l_fϾk_f_a_l_l_s) and the negative pre-exponential

factor describe the temporal rise of the ͓HCN(v 0v )͔. The

1

3

v

1

3

parameters in Eq. ͑A1͒ were determined by a nonlinear least

provide clues about the distribution of the unobserved HCN

vibrational levels, i.e., levels with bending excitation. About

0% of the available reaction exothermicity went into prod-

uct vibration. Again, this was in excellent agreement with the

vibrational level distribution provided by the RBA-4D quan-

tum dynamical calculations; see Table III.

A great deal is known about the dynamics of the CNϩH₂

reaction, both experimentally and theoretically. The THS

surface appears to be able to reproduce a large body of ex-

63

squares procedure based on Marquardt’s method. Only the

HCN͑000͒ and HCN͑001͒ levels required more than one rise

and one fall term to obtain an adequate ﬁt.

The exponential rate constants for each vibrational level

were determined as a function of the P_H₂keeping the

5

P₍_C_N₎2^Ϸ⁰^.⁰⁷^T^o^r^r^aⁿ^d^t^h^e^t^o^t^a^l^p^r^e^s^s^u^r^e^c^oⁿ^s^t^aⁿ^t^.^T^h^e^s^l^o^p^e^s

of such plots give the second order rate constant for H , and

2

the intercept the combined effect of (CN) and Ar. A sum-

2

mary of these least squares ﬁts for temperatures of 293 and

24 K is presented in Table IV.

perimental observations for the CNϩH reaction: thermal

2

3

rate constant data, HCN vibration product level distribution,

translational energy release, and angular distribution of prod-

The exponential rate constants reported in Table IV are

not state speciﬁc vibrational relaxation rate constants, as in

previous work on the vibrational relaxation of HCN ͑see

Refs. 53, 54, and 64͒, but are merely parametric constants

describing the time evolution of the HCN(v 0v ) manifold.

ucts. Further reﬁnements of the THS surface may lead to

_e_v_e_n_b_e_t_t_e_r_a_g_r_e_e_m_e_n_t_b_e_t_w_e_e_n_t_h_e_o_r_y_a_n_d_e_x_p_e_r_i_m_e_n_t_.₃0 On

the dynamical side, extending the quantum dynamical calcu-

lations to include the in-plane bending degree of freedom

along the H–H–C axis will further our understanding of the

role of intramolecular coupling on the product state distribu-

tions. It also appears that further work is needed in order to

clarify the role of zero-point effects in quasiclassical trajec-

1

3

However, it appears that the HCN͑000͒ and HCN͑001͒ vi-

brational levels are strongly coupled, and that the formation

of the ground state arises predominantly from relaxation

through HCN͑001͒. The exponential rate constant describing

the rise in HCN͑000͒ is very similar to the exponential rate

constant k_f_a_l_l_sfor HCN͑001͒; as well, the largest exponential

3

2

tory calculations. On the experimental side, it would be

important to determine a more complete HCN vibrational

level distribution, in particular the distribution of the bending

fall rate constant for HCN͑000͒ is similar to k

for

rise

53

HCN͑001͒. It might have been anticipated that the stretch-

vibrations over the l sublevels. The quasiclassical trajectory

1

2

1

2

less bending manifold, i.e., HCN(0,v ,0), would populate

calculations showed that the HCN(v ) vibrational level

the HCN ground state more rapidly than HCN͑001͒ because

population was lower for bending levels with odd l. This

effect could be a sensitive feature for the reﬁnement of the

the frequency of ␷ is four times smaller than the ␷ funda-

2

3

mental and three times smaller than the ␷ fundamental. Ap-

1

out-of-plane forces on the CNϩH PES.

2

parently, this is not the case.

An important observation from the results in Table IV is

the identiﬁcation of the exponential rate constants that are of

similar magnitude to k_R₁. Only chemical reaction depends

solely on the P_H₂so that only exponential rate constants with

ACKNOWLEDGMENTS

The authors wish to thank Dr. G. Manke II for help in

the early stages of this work, Dr. A. F. Wagner, Dr. K. Liu,

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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998

Bethardy et al.

4235

TABLE IV. Summary of the linear least squares ﬁt to the exponential rate

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Slope

Intercept

Ϫ14

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HCN

vibration

Exponential

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(10

cm

(10

cm

Temperature

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mol^Ϫ¹

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ϫ10^Ϫ¹⁴cm mol

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1

Article Doi

Initial vibrational level distribution of HCN[X1Σ+(v10v3)] from the CN(X2Σ+)+H2→HCN+H reaction

DOI: 10.1063/1.477028

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