Vibrational state control of bimolecular reactions

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 108, NUMBER 8

22 FEBRUARY 1998

Vibrational state control of bimolecular reactions

Christoph Kreher

Institut f u¨ r Physikalische Chemie, Universit a¨ t Z u¨ rich, Winterthurerstr, 190, CH-8057 Z u¨ rich, Switzerland

Jan Leo Rinnenthal and Karl-Heinz Gericke

Institut f u¨ r Physikalische und Theoretische Chemie, Technische Universit a¨ t Braunshweig, Hans-Sommer-

Strasse 10, D-38106 Braunschweig, Germany

͑

Received 31 July 1997; accepted 10 November 1997͒

The inﬂuence of rotation and vibration on the reactivity and the dynamics of the reaction

XϩHCN(␯ ,␯ ,␯ ,J)→HXϩCN(v,J) with XϭH, Cl has been studied. The HCN molecule is

1

2

3

prepared in a speciﬁc rovibrational level by IR/VIS overtone excitation in the wavelength region

Ϫ1

6

500–18 000 cm . The H atoms are generated by laser photolysis of CH SH at 266 nm, the Cl

3

atoms are formed in the photodissociation of Cl at 355 nm. The CN products are probed quantum

2

state speciﬁcally by laser-induced ﬂuorescence ͑LIF͒. For low rotational states of HCN, the

reactivity of Cl and H is independent of the initial rotational state. However, an enhancement in

reactivity of the ClϩHCN reaction is observed when the time of rotation becomes comparable to the

passing time of the Cl atom. The reaction of Cl as well as of the H atom with HCN shows strong

mode speciﬁc behavior, implying a simple direct reaction mechanism, which is also supported from

Rice–Ramsperger–Kassel–Marcus ͑RRKM͒ calculations. An increase in CH stretch vibration

increases both the reaction rate and the CN product vibration. Channeling energy in CN stretch

vibration has only a minor effect on the reactivity and the CN product vibration even decreases.

Trajectory calculations of the HϩHCN system agree with the experimental results. The dependence

of reaction rates on reactant approach geometry is investigated by preparing aligned reactants using

linear polarized light. The CN signal is markedly inﬂuenced by the prepared alignments ͑steric

effect͒. The experimental results suggest that the reaction of hydrogen and chlorine atoms with

vibrationally excited HCN proceeds mainly via a collinear transition state, but the cone of

͓

S0021-9606͑98͒00507-8͔

I. INTRODUCTION

HϩHCN͑␯ ,␯ ,␯ ,J͒→H ϩCN.

͑2͒

1

2

3

2

Controlling the course of a chemical reaction is an im-

portant goal in molecular dynamics. A simple approach is

The ClϩHCN→HClϩCN reaction is 94 kJ/mol

1

10

11

endothermic, has a total barrier of 113 kJ/mol, and has

the control of motion of one reactant, which is directed along

the reaction coordinate of the bimolecular reaction. This mo-

tion along the reaction coordinate corresponds to the motion

of the nuclei which carries the system from the reactants to

the products. There are several experiments of how reactant

vibration affects reactivity and product energy release of the

11,12

13,14

been studied experimentally

as well as theoretically.

13

Ab initio calculations by Harding

show that the

ClϩHCN→HClϩCN reaction proceeds through a linear

transition state. They predict a simple, direct collinear ab-

straction mechanism without complex formation ͑ClHCN͒.

12

Sims and Smith have reported experimental studies of the

1

desired bimolecular reaction. In particular, the preparation

of HOD in two different distinct vibrational states of pure

reverse reaction ͑1͒, CNϩHCl→products, by exciting either

CN or HCl vibration. While there is a negligible enhance-

ment of the reaction rate when exciting CN by one quantum

of vibration, the rate increases by more than two orders of

magnitude when HCl is excited into the ﬁrst vibrational

state. They concluded that CN behaves like a spectator with-

out participation in the reaction.

1

–4

OH or OD stretches leads to different photodissociation

and reaction channels.¹

,5–7

Crim and co-workers investi-

8

gated the photodissociation of HNCO, where vibrational ex-

citation of the second overtone of the NH stretch leads to a

break of the NH bond at energies below the threshold for the

high energy NHϩCO channel. At higher energies both chan-

nels compete. Rosenwaks and co-workers⁹have demon-

strated a rotational state selectivity in bond ﬁssion of C HD,

where the production of H and D atoms depends on the ro-

tational state of the 5␯ mode.

The reaction of HϩHCN→H ϩCN is endothermic by

2

10

15

9

0 kJ/mol with a total barrier of 112Ϯ3 kJ/mol. Ab initio

2

16

calculations by Bair and Dunning predict that the H-atom

reaction also proceeds via a linear transition state, which is

1

17

consistent with the experimental results of Lambert et al.

The present investigation extends the approach of con-

trolling chemical reactions to the endothermic reactions of

hydrogen and chlorine with HCN:

18

and Johnston et al. who observed rotationally unexcited

CN from the reaction of HCN with translationally hot H

atoms. Experimental studies of the reverse H ϩCN reaction

2

ClϩHCN͑␯ ,␯ ,␯ ,J͒→HClϩCN,

͑1͒

report that the reaction rate is unaffected by vibrationally

1

2

3

0021-9606/98/108(8)/3154/14/$15.00

3154

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1

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3155

TABLE I. Band origins ␯₀(cm^Ϫ¹), wavelengths ͑nm͒, absolute intensities A (cm mol^Ϫ¹), and excitation

conditions for different overtone bands of HCN.

Overtone

␯₀/cm^Ϫ¹

␭/nm

A/cm mol^Ϫ¹

Pulse energy dye

15 mJ DCM^f

40 mJ LDS 765

90 mJ Pyridin 1

100 mJ DCM

6519.61^a

12 635.89

12 657.88

14 653.66

14 670.45

15 551.94

16 640.31

16 674.21

1533.4

791.18

789.81

682.24

681.46

642.83

600.79

599.57

569.63

544.01

8.499(54)ϫ10

4a

(

002)←(000)

004)←(000)

302)←(000)

402)←(000)

104)←(000)

005)←(000)

502)←(000)

204)←(000)

105)←(000)

006)←(000)

a

c

e

a

b

157͑1͒ , 154͑2͒

a

b

9.11͑25͒ , 9.7͑2͒

a

8.33͑10͒

9.42͑9͒^a

17.5͑4͒^a

c

0.40͑4͒

50 mJ DCM/Rhodamin 6G

50 mJ DCM/Rhodamin 6 G

120 mJ R6G

1.7͑1͒^c

d

c

a

17 550.42

18 377.01

3.51͑17͒ , 13.9͑4͒

2.61͑13͒ , 2.4͑2͒

c

a

90 mJ Fluorescein

a

Reference 30.

Reference 32.

Reference 34.

Reference 35.

Reference 36.

b

c

d

e

f

Frequency mixing with 1.064 ␮m.

excited CN.¹⁹On the other hand, vibrational excitation of H₂

should increase the reaction rate according to theoretical

studies. Both the experimental and theoretical results sug-

gest, comparable to the Cl atom reaction, that in the

HϩHCN reaction the CN bond is unaffected during the re-

active encounter.

geometry. This was performed by preparing aligned reac-

tants using linearly polarized laser light. Such experiments

give detailed insight into the stereochemistry of the desired

bimolecular reaction.

2

0

II. EXPERIMENT

There have been several experiments on the reactions

with high vibrationally excited HCN.²

1–24

Crim et al.

23,24

ex-

The experimental apparatus has been described in detail

previously.²¹Brieﬂy, the HCN is synthesized by heating a

mixture of KCN and stearic acid under vacuum to ϳ100 °C.

Translationally excited chlorine atoms were generated from

amined the reaction dynamics of two vibrational states of

HCN, the ͑004͒ state in which four quanta of CH stretch are

excited and the ͑302͒ state in which three quanta of CN

stretch and two quanta of CH stretch are excited. Their con-

clusions are that the H atom reaction forms CN primarily by

a direct abstraction reaction and the Cl atom reaction forms

CN by an addition–elimination mechanism in addition to the

direct abstraction. We have previously reported the reactivity

of several different vibrational states of HCN with Cl and

Cl in a pulsed laser photolysis with 20–40 mJ of 355 nm

2

light ͑Quanta Ray DCR1A͒. The photolysis leads to 98% of

2

the chlorine atoms in the P₃ground spin–orbit state with

/2

25

an anisotropy of ␤ϭϪ1Ϯ0.1. Only minor amounts of Cl

atoms are generated in the upper P₁state and, thus, no

2

/2

reliable estimation of the role of different Cl spin–orbit

states can be obtained. The mean collision energy of the

ClϩHCN system is E_c_o_l_lϭ25 kJ/mol. The precursor of H at-

oms is methanethiol, dissociated at 266 nm light generated

from the fourth harmonic of a Nd:YAG laser ͑15 mJ͒. The

photodissociation yields exclusively H atoms with a mean

translational energy of 80 kJ/mol. The anisotropy at 266 nm

2

1

H. HCN was excited to the overtone levels ͑002͒, ͑004͒,

1

Ϫ1

͑

302͒, ͑105͒, and (11 5) with energies up to 18 000 cm .

We excluded the pure spectator model for both the reaction

of ClϩHCN and of HϩHCN, because some memory of the

reactant initial state is retained in the product.

The present paper now represents a continuation of that

study in terms of its mode speciﬁc behavior with new in-

sights in the reaction dynamics. While in all former studies a

long living intermediate complex could not be excluded the

present experiment in conjunction with trajectory studies in-

dicates a rather direct reaction where only a few vibrational

motions within the intermediate take place before it breaks

apart.

26

is not known, but results at 248 nm (␤ϭϪ1) and 274 nm

(␤ϭϪ0.86Ϯ0.05)²⁷suggest that the value is close to Ϫ1.

The reactants ͑CH SH/Cl and HCN͒ were mixed in the re-

3

2

action chamber by separate nozzles. The partial pressures

were P͑Cl ͒ϭ8 Pa and P(CH SH)ϭP͑HCN͒ϭ16 Pa.

2

3

A Nd:YAG laser pumped dye laser ͑Continuum YG 680,

TDL 60, IRP͒ with a pulse width of typically 7 ns at a band-

Ϫ1

We have been able to excite several more HCN overtone

bands and report the state-to-state dynamics of the prepared

HCN(␯ ,␯ ,␯ ,J) with hydrogen and chlorine atoms. In

width ͑FWHM͒ of 0.07–0.09 cm excites the vibrational

states of HCN. All wavelengths in the near infrared and vis-

ible ͑IR/VIS͒ region were obtained using different laser dyes

͑Table I͒. Probing the (002)←(000) overtone band of HCN

in the infrared region near 1.53 ␮m was performed via dif-

ference frequency mixing of a dye laser and a 1.064 ␮m

Nd:YAG laser beam.

1

2

3

particular, we prepared the HCN molecule in the ͑002͒,

͑

004͒, ͑302͒, ͑402͒, ͑104͒, ͑005͒, ͑502͒, ͑204͒, ͑105͒, and

006͒ states. In addition, we analyzed the effect of reactant

rotational excitation on the reaction rate as well as on the

rotational distribution of the CN product. We also investi-

gated the dependence of reaction rates on reactant approach

Nascent CN products were detected applying the laser-

induced

ﬂuorescence

͑LIF͒

technique

via

the

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3156

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

2

ϩ

2

ϩ

B ⌺ ←X ⌺ (⌬vϭ0) band. The required radiation

around 388 nm was supplied by a dye laser ͑Lambda Physik

FL2002, QUI͒ pumped by a XeCl excimer laser ͑Lambda

Physik EMG 101 MSC͒. All LIF spectra were detected with

2

–5 mJ of laser light under saturated conditions. A photo-

multiplier ͑THORN-EMI 9781B͒ monitored the LIF signal

perpendicular to the probe beam through f/1 optics and an

interference ﬁlter (389Ϯ10 nm). All lasers were operated at

a repetition rate of 10 Hz. The time delay between the pho-

tolysis laser, which is in time with the IR/VIS excitation

laser, and the LIF-probe laser was set between 50 and 150

ns.

The overlap of the laser beams was optimized by the CN

signal. The spectral range of the dyes was sufﬁcient to excite

different (␯ ,␯ ,␯ ) vibrational modes. Thus the CN prod-

1

2

3

uct intensities originating from different HCN(␯ ,␯ ,␯ ) re-

1

2

3

actants can be easily compared. No ‘‘beam walk’’ effects

were observed.

III. RESULTS AND DISCUSSION

A. Vibrational state control of the reaction rate

FIG. 1. Comparison of an action and a simulation spectrum for the

ClϩHCN reaction. The HCN excitation laser is tuned over the (004)

←(000) and (302)←(000) bands. The observed intensities of transitions

originating from the ͑302͒ vibrational state are lower than those of the

simulation.

In order to study the inﬂuence of the initial vibrational

state of HCN on the reaction rate with chlorine atoms, the

yield of CN ͑␯ϭ0, Jϭ8͒ products was monitored while the

HCN excitation laser light was tuned to separated rotational

transitions in the different vibrational bands. The CN was

detected at a ﬁxed wavelength via the R(8) line. Using the

selectivity was found in the reaction of HCNϩH→H ϩCN.

constants of k(004)/k(302)Ͼ4.²¹

2

absorption cross section²

8–36

for vibrational overtone excita-

We previously reported a lower limit of the ratio of rate

tion A and the power density of the HCN excitation laser I,

we convert the CN signals S to relative rates k. In case of a

small time delay the ratio of rate constants k /k between

This result agrees with theoretical results obtained by

Bair and Dunning.¹⁶They found that the endothermic reac-

tion has a collinear saddle point with a CH distance of 1.55

Å, compared to the equilibrium bond distance of 1.06 Å in

the HCN molecule ͑late barrier͒. The CN distance is essen-

tially constant being 1.16 Å in HCN, 1.18 Å ͑calc͒ at the

saddle point, and 1.17 Å in free CN. This implies that the

reaction will only be substantially accelerated if the CH

stretch is vibrationally excited. Similar theoretical results

were found for the ClϩHCN reaction by Harding.¹³At the

collinear saddle point, the CH bond distance is 1.58 Å and

the CN bond distance is 1.17 Å. Again, the CH bond is

greatly extended at the barrier and excitation of the CH

stretch will efﬁciently promote the reaction rate.

1

2

two vibrational states of HCN is given by

^k1

^S1

^I2

^P2

^A2

ϭ

•

,

͑3͒

k₂S₂I₁P₁A₁

where P ϭP (␯,J) is the CN product state population in the

i

(

␯,J)-rovibrational state. In case that the excitation energies

between the desired vibrational states are close together, it is

relatively easy to obtain the ratio of rate constants by mea-

suring an action spectrum of HCN. Figure 1 shows the CN

signal ͑lower part͒ from the reaction HCNϩCl→HClϩCN

as a function of the excitation wavelength and a simulation

͑

upper part͒ using the known HCN Franck–Condon and

As in the HCN͑004͒/HCN͑302͒ case we measure the ra-

tio of rate constants of the pairs (104)/(402) near 682 nm

and (204)/(502) near 600 nm. Surprisingly the ͑104͒ and

͑402͒ states of HCN react at a similar rate with chlorine

atoms: a ratio of k(104)/k(402)ϭ1.05Ϯ0.05 is observed.

This ﬁnding can be explained by the 3:2 anharmonic reso-

32

H o¨ nl–London factors. The main peaks in the wavelength

region near 792 nm are due to rotational transitions from the

vibrational ground state to the ͑004͒ vibrational state. Several

less intense rotational lines are transitions to a ͑302͒ vibra-

tional state of HCN, containing two quanta of CH stretch and

three quanta of CN stretch. By comparing the intensities in

the action spectra with the corresponding intensities from the

simulation, we ﬁnd a ratio of rate constants between

HCN͑004͒ and HCN͑302͒ of k(004)/k(302)ϭ2.8Ϯ0.6.²¹

The reaction rate of Cl with HCN is enhanced when the

energy is located in the reaction coordinate ͑the CH stretch͒

instead of locating the same amount of energy in three

quanta of CN and two quanta of CH stretch. A similar mode

nance ͑Fermi resonance͒ between the ␯₁and ␯₃

modes.³

2,34–37

The ͑104͒ and ͑402͒ states undergo quite

32,34

strong anharmonic interaction.

Assuming that most of

the (402)←(000) transition intensity is due to the mixing,

from the intensity ratio we obtain the mixing amplitudes 0.73

and 0.69 for the ͑104͒ and ͑402͒ states, respectively.³⁴Thus

the vibrational wave functions and thereby the reactivity of

HCN in these vibrational states are very similar. To a certain

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J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3157

TABLE II. Ratio of rate constants of the reaction ClϩHCN(␯ ,␯ ,␯ ).

1

2

3

HCN. This is not surprising, because the CH bond is the one

which has to break. The reaction rate of ClϩHCN(006) is

already close to the gas kinetic limit which was roughly es-

timated by comparing the intensity of the signal with the

sensitivity of the apparatus known from various dissociation

Ratio of rate constants

Dye mixing

^k⁰04 ^/^k104

1.25Ϯ0.4

5.1 Ϯ0.5

1.05Ϯ0.2

0.4 Ϯ0.1

2.0 Ϯ0.3

LDS765/Pyridin 1

DCM/Pyridin 1

R6G/DCM

Fluorescein 27/R6G

k₀₀₅/k₁₀₄

k₀₀₅/k₁₀₅

k₂₀₄/k₁₀₅

k₀₀₆/k₁₀₅

38

experiments.

An additional excitation of the CN stretch does not

change this behavior. The reaction of chlorine atoms with

HCN is ﬁve times faster when HCN is excited to the ͑105͒

state instead of the ͑104͒ state. The reaction of HCN mol-

ecules excited to nearly isoenergetic states that correspond to

different nuclear motions provides further evidence that the

unreacting bond is a spectator in the reaction. Channeling

vibrational energy into a coordinate perpendicular to the re-

action coordinate by exciting the CN stretch will have only a

minor inﬂuence on the reactivity. The observed mode selec-

tivity ͑isoenergetic states with different nuclear motions have

unequal reaction rates͒ demonstrates that the reaction must

be fast where the time left is not sufﬁcient for energy redis-

tribution. Thus we expect the H/ClϩHCN reaction to be a

direct abstraction reaction leaving the unreacted CN bond

largely with its initial vibrational excitation.

extent this is also the case for the (204)/(502) pair, where

the ͑204͒ level of HCN is in Fermi resonance with the ͑502͒

level. However, the anharmonic mixing is weaker, and the

mixing amplitudes are calculated to be 0.9 and 0.44 for the

͑204͒ and for the ͑502͒ states, respectively. Consequently,

we have measured different rate constants between the reac-

tions HCN͑204͒ϩCl and HCN͑502͒ϩCl. Since we could not

determine the CN state distributions from both reactions we

assume in Eq. ͑3͒ P₂₀₄ϷP₅₀₂and a ratio of rate constants of

k(204)/k(502)ϭ1.2Ϯ0.1 is determined. Again, the ͑204͒

state of HCN promotes the ClϩHCN reaction more efﬁ-

ciently than that state having the main part of its energy in

the CN stretch. The weakest mixing occurs for the ͑004͒ and

A small inﬂuence of the CN stretch can be seen in Fig. 2

͑302͒ states of HCN and therefore, the corresponding rates

by comparing the relative rates of the HCN͑␯ ,0,4͒ϩCl reac-

1

with chlorine differ most.

tion with ␯ ϭ0, 1, and 2. The observed increase of reactivity

1

To compare the reaction rates between vibrational states

of HCN which are not energetically close together, we tuned

the excitation laser alternately on a known rotational transi-

tion of the two vibrational bands. The required wavelength

region of the dye laser was obtained by mixing different dyes

together. The results are listed in Table II. In order to deter-

mine the ratio of rate constants between the states ͑204͒ and

reﬂects the properties of the normal-mode model of HCN,

which accurately describes the highly excited stretching vi-

brations in HCN.³⁹A single excitation of one of the two

stretch modes of HCN corresponds to nuclear motions in

both the CH and the CN bonds. Consequently, an excitation

of the CN stretch causes a weak vibration in the CH bond

and thus an increase of reactivity.

͑

105͒ according to Eq. ͑3͒ we assume that P₂₀₄/P₁₀₅

Similar mode speciﬁc reaction dynamics were observed

in the reaction of water molecules with Cl

and H atoms. They found that the local mode stretching state

by Crim et al.⁴

0,41

ϷP₁₀₄/P₀₀₅. This assumption seems to be valid from the

observed CN product state distributions generated in other

HCN(␯ ,␯ ,␯ ,J) reactions.

Figure 2 shows all the relative rates as a function of

internal vibrational energy. The relative rate measurements

clearly demonstrate the mode selectivity in promoting reac-

Ϫ

͉

03

͘

promotes the HϩH O as well as the ClϩH O reaction

1

2

3

2

Ϫ

much more efﬁciently than the state

its energy in bending excitation. Furthermore, the HϩH O

reaction is slower when H O is excited to the

tional state, which has its excitation energy distributed over

͉

02

͘

͉

2

͘

having part of

2

Ϫ

͉

12

͘

vibra-

2

tions by vibrational excitation. The CH stretch mode ␯ pro-

3

motes the ClϩHCN reaction much more efﬁciently than the

both OH stretches and only two quanta are available along

Ϫ

CN stretch mode ␯ . The ͑005͒ state reacts four times faster,

the reaction coordinate, even though the energy of the ͉12

͘

1

Ϫ

the ͑006͒ state even eight times faster than the ͑004͒ state of

͘

level is slightly higher than that of ͉03 . These results were

explained by a simple spectator model in which excitation in

the nonreacting OH bond is inefﬁcient in promoting the re-

action.

B. The role of reactant rotational excitation on the

reactivity

Because the line intensities in action spectra depend on

both the absorption cross section and the reaction probabil-

ity, one can measure the reaction rate not only in dependence

on the vibrational state, but also on the rotational state of

HCN. We have studied the inﬂuence of highly rotationally

excited HCN on the reaction rate of the reaction

HCN͑␯ ϭ4,J͒ϩCl→HClϩCN

͑4͒

3

by measuring an action spectrum of the (␯ ϭ0, J)→(␯

FIG. 2. Reactivity for the ClϩHCN reaction as a function of the excitation

energy of HCN.

3

ϭ4, JЈϭJϪ1) in the wavelength region 793.5–799 nm.

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1

3158

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

tional levels. The difference of rotational energies between

Ϫ1

JЈϭ16 and of the JЈϭ28, E (28)ϪE (16)ϭ720 cm , is

rot

much less than the vibrational energy of one CH stretch

Ϫ1

quantum (E_v_i_bϭ3311 cm ).

The increase of reactivity is rather a consequence of a

geometrical constraint of the ClϩHCN reaction. In Sec. III D

we will present measurements of the reaction rate for two

different alignments of the reactants. The observed steric ef-

fect was explained by a favored reaction geometry where the

Cl atom reacts with the H atom end of HCN. When the

rotation of HCN is low compared to the passing time of the

Cl atom, the reaction can occur only if the Cl atom ap-

proaches on the H atom end of HCN. However, at fast rota-

tions of HCN, when the time of rotation is faster than the

passing time, the Cl atom has enough time to ﬁnd the ideal

approach geometry.

FIG. 3. Action spectrum ͑lower part͒ and simulation ͑upper part͒ for the

ClϩHCN(004) reaction. The intensities of rotational lines belonging to high

rotational states with JЈϾ21, marked by arrows, are higher in the action

spectrum than in the simulation.

In order to estimate the typical passing time T , we

p

assume a maximum distance of intermolecular forces be-

tween Cl and HCN of dϭ4 Å ͑gas kinetic diameter͒. With a

thermal relative velocity of

Figure 3 shows the CN ﬂuorescence signal ͑lower part͒ as a

function of the excitation wavelength. Because the signals of

the high rotational transitions are very weak, the action spec-

trum could only be measured at higher pressures and delay

times. At a total pressure in the reaction cell of 900 mTorr

and a time delay of 300 ns, the HCN molecules have about 3

to 4 collisions prior to the CN detection. Thus partial rota-

tional relaxation might have occurred. By comparing the line

intensities of each rotational transition with those from the

simulation ͑upper part in Fig. 3͒, we obtain the information

on the relative reactivity of an individual rotational state of

HCN. The dependence of the reactivity on the rotational

quantum number JЈ is shown in Fig. 4. While the reaction

rate for JЈϽ16 is not affected by rotation, we found an in-

crease of the reactivity for higher rotational levels. HCN

^␯rel

ϭ

ͱ

²^Ecoll /␮ϭ685 m/s

͑5͒

we obtain a mean passing time of T ϭd/␯ ϭ0.6 ps. The

p

rel

time of rotation, T ϭ2␲/␻, is given by the rotational energy

r

1

ប

2

E ϭ I•␻ ϭ

•␻ .

͑6͒

r

2

2 4␲c B

0

The energy of a rotational state with the quantum number J

is given by

2

E ϭ2␲បc B•JЈ͑JЈϩ1͒Ϸ2␲បc B•JЈ .

͑7͒

r

0

From Eqs. ͑6͒ and ͑7͒ we ﬁnally obtain the time of rotation

T ϭ͑2•c •B•JЈ͒^Ϫ¹ϭ11.6 ps/JЈ.

͑8͒

r

0

molecules in the ͑␯ ϭ4, JЈϭ28͒ state react about three

3

For HCN in the JЈϭ8 level we obtain T ϭ1.5 ps, which is

r

times faster than those HCN molecules in the ͑␯ ϭ4, JЈ

3

slower than the passing time T . Thus the chlorine atom

p

Ͻ16͒ states. Thus high rotational excitation of the HCN mol-

ecules can efﬁciently promote the reaction rate with chlorine

atoms.

We assume that this effect is not due to the increase of

the total internal energy in HCN when exciting high rota-

passes the HCN molecule, which apparently is not moving.

For higher rotational levels with JЈϾ19 the situation

changes: For example, the time of rotation for HCN in the

JЈϭ28 rotational level is T ϭ0.4 ps, which is shorter than

r

the typical passing time.

On the other hand, in the region 0ϽJЈϽ26 the reactivity

of the reaction HCN(␯ ϭ5, JЈ)ϩCl→HClϩCN is indepen-

3

dent from JЈ. We believe that the reaction rate cannot be

further enhanced by rotational excitation because the reac-

tion of HCN in the highly vibrationally excited state with

␯₃

ϭ5 is already very fast ͓In Sec. III A we obtained

k(005)/k(004)Ϸ4.͔ Neither did we observe an effect in the

reaction of fast H atoms with HCN(␯ ϭ4). Because of the

3

high relative velocity of about 12 900 m/s we obtain an ex-

tremely short passing time, T ϭ25 fs. Thus for all observed

p

rotational levels we have T ӶT .

p

r

For an attractive potential the speed of the approaching

reactants will be accelerated. Therefore the passing time

might be slightly less than one calculated from thermal ve-

locities. Nevertheless, the order of magnitude of the passing

time will remain unchanged.

FIG. 4. Relative rate of the ClϩHCN(␯ ϭ4,JЈ) reaction as a function of

the rotational quantum number JЈ. The reactivity increases with increasing

rotational excitation of HCN.

3

We have already mentioned that the action spectrum

shown in Fig. 3 was not measured under nascent conditions

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1

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3159

TABLE III. CN product state distributions from different ClϩHCN reactions. The vibrational distributions have an uncertainty of about Ϯ0.03 for vϭ0, 1,

0

and vϭ2. E_a_vis the available energy equal to E_c_o_l_lϩE_i_n_tϪ⌬ H . E is the internal vibrational and rotational energy of HCN equal to E_i_n_tϭE_v_i_bϩBJЈ(JЈ

r

int

ϩ1), JЈϭ9. E_r_o_tand E_v_i_bare the rotational and vibrational energies of the CN product.

E_i_n_t^b

E_a_v^b

vϭ0

vϭ1

vϭ2

vϭ3

E_r_o_t^b

E_v_i_b^b

Experiment

E_c_o_l_l^b^,^c

T_r_o_t/K

ClϩHCN(002)

ClϩHCN(004)

ClϩHCN(302)

ClϩHCN(402)

ClϩHCN(104)

ClϩHCN(005)

ClϩHCN(105)

ClϩHCN(006)

36

25

79

152

177

186

211

221

21

94

83

0.86

0.51

0.52

0.45

0.68

0.71

0.41

0.65

0.34

1700Ϯ45

910Ϯ50

900Ϯ60

820Ϯ60

730Ϯ50

710Ϯ50

730Ϯ23

740Ϯ30

0.13

0.34

0.43

0.25

0.23

0.38

0.25

0.34

940Ϯ50

840Ϯ40

820Ϯ50

760Ϯ50

750Ϯ50

710Ϯ50

750Ϯ50

700Ϯ70

610Ϯ30

Ͻ0.01

0.15

0.14

0.12

0.07

0.06

0.15

0.10

0.23

•••

530Ϯ50

•••

13.3

7.2

6.5

6.0

5.8

6.0

5.6

3.7

15.6

15.3

16.3

9.7

a

740Ϯ40

820Ϯ160

660Ϯ130

620Ϯ50

700Ϯ50

720Ϯ50

640Ϯ60

690Ϯ60

Ͻ0.02

0.06

83

108

117

142

152

8.4

21.4

11.0

26.0

Ͻ0.02

0.09

660Ϯ60

a

Reference 21.

Energies in kJ/mol.

E_c_o_l_lis the average of a distribution of collisional energies. From Ref. 21.

b

c

tionally excited CN products are obtained when Cl reacts

with HCN where 6 CH stretch quanta are excited ͑Fig. 5,

lower part͒. Second, we ﬁnd a mode-speciﬁc dependence of

the CN vibrational excitation. In contrast to the reactions of

HCN where only the CH stretch mode is excited, an addi-

tional excitation of one CN stretch quantum surprisingly

leads to a decrease of CN vibrational excitation. A ﬁt of the

spectrum when highly excited HCN͑104͒ is used as reactant

yields that 71% of the CN radicals are generated in vϭ0,

23% in vϭ1, and 6% in vϭ2. Although the excitation en-

ergy of the ͑104͒ state is higher than that of the ͑004͒ state,

we obtained a signiﬁcant change in the former tendency of

increasing CN vibration with increasing CH stretch excita-

tion. The CN vibrational excitation decreases again, although

one quantum of CN stretch has been excited in addition to

four CH stretch quanta. The same situation was found when

HCN was prepared in a state having ﬁve quanta of CH

stretch and one quanta of CH stretch excitation ͑Fig. 5, upper

part͒. The reaction leads to CN where only 35% of all mol-

ecules are in vibrationally excited states (vϾ0), compared

to 59% when

(

P•␶ϭ0.27 Torr ␮s). Thus the initial preparation of HCN in

a speciﬁc rotational state was scrambled by nonreactive col-

lisions in the time scale of the measurements. R-R energy

transfer is the primary relaxation pathway for rotationally

excited molecules in our experiment. There are no data for

rotational relaxation of HCN out of the ͑004͒ levels, but

42

measurements for the ͑003͒ levels allow an estimation of

the rotational relaxation. Wu et al.⁴²found that the relaxation

rate of rotational levels with 5ϽJЈϽ15 are at least k

R-R

Ϫ1

ϭ150 Torr ␮s . Thus the relaxation time is 0.27•150

Ϸ40 times faster than our time delay. The relaxation of ro-

tational levels with JЈϾ25 proceeds slower with a relaxation

rate of k_R_-_RϽ10 Torr ␮s . This means that complete ro-

tational relaxation will have occurred only in low lying rota-

tional levels. On the other hand, most of the HCN molecules

in high rotational levels did remain in the initially prepared

rotational state or in states close to it. Consequently, the

effect of rotational relaxation in high rotational levels was

small.

Ϫ1

C. Inﬂuence of the initial HCN excitation on the CN

product state distribution

The complete CN product state distribution is obtained

2

ϩ

by probing the rovibrational transitions of the B ⌺

2

ϩ

←

X ⌺ system. Simulations of the CN spectrum were used

to ﬁt all observed rotational lines. We have already reported

the product state distribution of CN in the reaction of chlo-

rine atoms with HCN͑002͒, HCN͑004͒, HCN͑302͒, and

2

1

HCN͑105͒. In this paper we will continue the investigation

by analyzing the reactions of Cl atoms with HCN͑104͒,

HCN͑402͒, HCN͑005͒, and HCN͑006͒. The characteristic

quantities of all CN product state distributions are listed in

Table III. The main result is that the amount of vibrational

excitation in the CN product depends strongly on the initially

prepared vibrational state of HCN. First, we ﬁnd that the CN

vibration increases linearly with increasing pure CH-stretch

excitation. The reaction of Cl with HCN(␯ ϭ2) leads to less

3

vibrationally excited CN products with population ratios of

P(vϭ0):P(vϭ1):P(vϭ2)ϭ86%:13%:Ͻ1%, while the

FIG. 5. Laser-induced ﬂuorescence spectra of CN generated in the reactions

of chlorine atoms with HCN in the ͑105͒ state ͑upper part͒ and in the ͑006͒

state ͑lower part͒. The reactions lead to different CN product state distribu-

tions.

reaction of Cl with HCN(␯ ϭ4) leads to CN products with

3

52% in vϭ0, 34% in vϭ1, and 14% in vϭ2. Highly vibra-

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3160

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

can assume that the reaction only occurs if the CH bond is

lengthened, i.e., at the upper left corner of the probability

density diagram of Figs. 7͑a͒ and 7͑b͒, where the probability

is highest ͑classical turning points͒, because the high-energy

eigenstates are strongly anharmonic. Since the CN bond is

compressed at the turning point, at the end of the reaction the

CN molecule will be vibrationally excited. The observed

variation of the product state distribution when exciting an

additional quantum of CN stretch reﬂects the properties of

the vibrational wave functions of HCN, too. Figures 7͑c͒ and

7

͑d͒ show the wave functions for HCN in the states ͑104͒

and ͑105͒. Because the vibrational quantum number ␯₁is

now equal to one, the two states have a regular structure with

an additional node along the second stretch coordinate. In

contrast to the case discussed above, the end peak with the

largest CH bond distance has now a CN bond distance close

to the equilibrium distance of the free CN molecule. If the

reaction proceeds via a direct stripping mechanism, then the

CN product should not be vibrationally excited which is ex-

actly what was observed in our experiments. This assump-

tion agrees with the qualitative spectator model from Sec.

III A, because the CN product vibrational excitation directly

reﬂects the nodal pattern of the vibrational wave function in

the excited HCN molecule. However, it should be mentioned

that this simple model neglects any inﬂuence of the ap-

proaching Cl atom on the Cl–H–CN coordinates of the

potential-energy surface.

FIG. 6. Vibrational and rotational energy of the CN product as a function of

the HCN excitation energy. The chlorine atoms in the ClϩHCN(002) reac-

tion are generated from the photolysis of Cl₂at 308 nm. The vibrational

energy of CN from the reaction of Cl with HCN(00␯ ), ␯ ϭ2–6, can be

3

ﬁtted by a straight line.

HCN is excited to the ͑005͒ state. The additional excitation

of one quantum of CN stretch does not increase the vibration

of the CN product.

On the other hand, the state distributions of CN are simi-

lar when HCN is excited to the isoenergetic states ͑004͒ and

͑302͒. The CN vibrational energy in the reactions

HCN͑004͒ϩCl and HCN͑302͒ϩCl are 15.5 and 16.3 kJ/mol,

respectively ͑Table III͒. Further on, we ﬁnd a similar vibra-

tional energy release in the CN product when HCN is excited

to the isoenergetic ͑104͒ and ͑402͒ states ͑8.4 and 9.7 kJ/mol,

respectively͒. We believe that the 3:2 anharmonic resonance

is responsible for an increased complexity of our state selec-

tive data. The two states ͑104͒ and ͑402͒ that undergo the

strongest anharmonic interaction lead to CN products with

vibrational energies differing only by 15%. For the last reso-

nant pairs (205)ϩ(502) we could not measure nascent CN

spectra in order to compare the CN state distribution.

The vibrational excitation of the CN molecule seems to

be a consequence of the initial vibration of HCN. This as-

sumption is also conﬁrmed by the results of the HϩHCN

reaction ͑2͒.²¹Figure 8 illustrates this by comparing the state

distributions of the CN fragment from both the chlorine and

the hydrogen reaction. Both reactions produce CN with a

very similar vibrational distribution, suggesting that the vi-

brational state distribution is not determined by mass effects.

With respect to our interpretation it is important to point

out that the eigenstates of HCN, depicted in Fig. 7, are only

correct for the free molecule. They are more complicated

when the Cl atom approaches the HCN molecule. Thus exact

explanations can only be made with quantum mechanical

calculations of the complete four-atom system ClϩHCN.

The main result concerning the rotational distribution of

CN is that each distribution can be well characterized by

rotational temperatures. In general, the CN products from the

reaction of Cl with vibrationally excited HCN are rotation-

ally cold ͑Table III͒. The only exception is the reaction

ClϩHCN͑002͒→HClϩCN which produces CN products

with the characteristic temperature parameters of T(vϭ0)

The mode speciﬁc dependence of the CN vibrational ex-

citation is illustrated in Fig. 6 where the internal CN energies

͑vibration and rotation͒ are depicted as a function of the

HCN excitation energy. First of all, it is surprising that the

CN vibration increases with increasing CH stretch excitation.

As we can see in Fig. 6 the vibrational energy increases

almost linearly with the excitation energy of the HCN͑00␯₃͒

states with ␯ ϭ2, 4, 5, and 6. We believe that the observed

3

increase of the product vibrational energy is due to the

normal-mode model of the initially prepared vibrational

states of HCN. As we have described in Sec. III A, after

exciting the pure CH stretch mode of HCN, not only the CH

bond, but also the CN bond is in motion. If the reaction is

direct ͑e.g., stripping reaction͒ and the initial motion in the

CN bond is transferred into the CN product, an excitation of

the CH stretch causes a weak vibrational excitation of the

CN product. A qualitative quantum mechanical explanation

could be as follows. Figure 7 shows various wave functions

for HCN as functions of the internal bond distances ͑adapted

from Ref. 43͒. The dashed line indicates the bond length of

21

ϭ1700 K and T(vϭ1)ϭ945 K. The rotational energy of

the CN products slightly decreases with increasing HCN ex-

citation ͑see Fig. 6͒. The lowest rotational excitation of CN

from the reaction with Cl is obtained for HCN͑006͒, where

the CN product receives only 4% of the energy available to

the reaction (E ϭ5.6 kJ/mol). Even less rotational excita-

rot

tion of CN is obtained from the reaction of hydrogen atoms

with HCN͑002͒ and HCN͑004͒²¹͑Fig. 8͒. At a collision en-

ergy of 80 kJ/mol, only 4.5 kJ/mol ͑002͒ and 3.8 kJ/mol

͑004͒ remain in the CN product rotation.

the free CN radical. In the case of the (00␯ ) states of HCN,

3

the CN distance decreases with increasing CH distance. One

Since the temperatures of the experimental CN rotational

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J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3161

FIG. 7. ⌿²contour plots of the wave function of some HCN overtones, adapted from Ref. 43. The wave functions are easily identiﬁed by counting the nodal

planes; ͑a͒ 002; ͑b͒ 005; ͑c͒ 104; and ͑d͒ 105. The dashed line indicates the bond length of the free CN radical.

D. Inﬂuence of the collision energy on the CN product

state distribution

distributions for the H/ClϩHCN reactions are low, we as-

sume that both reactions produce CN mainly by direct

mechanisms with a collinear transition state. This result

agrees well with theoretical results by Clary.⁴⁴

In order to study the inﬂuence of the collision energy on

the product state distribution a shorter photolysis wavelength

The cause for the rotational excitation of the CN product

was used. When Cl is photodissociated at 308 nm instead of

2

from the reaction HϩHCN→H ϩCN are manifold. Rota-

2

3

55 nm, the collision energy of the system Cl/HCN increases

tional excitations may result from the zero-point energy of

the bending mode of HCN, from their cone of acceptance for

the H atom ͑large orbital angular momentum͒ or from the

initial rotation of the HCN molecule. To examine the role of

the initial HCN rotation on the CN product rotation we pre-

pared the HCN molecule in different rotational levels of the

21

by 11 kJ/mol from 25 to 36 kJ/mol. However, this increase

in collision energy has no signiﬁcant effect on the CN prod-

uct state distribution ͑see Table III͒. This is also conﬁrmed

by the study of Crim and co-workers who used thermal Cl

atoms (E_c_o_l_lϭ4 kJ/mol) to study the reaction with HCN͑004͒

leading to the same CN product state distribution as in the

present experiment. Therefore the ClϩHCN(004) reaction

generates CN products with the same amount of vibrational

energy over a wide range of collisional energies. Therefore

the translational energy of the reactants is not responsible for

the vibrational excitation of the CN product as an impulsive

model would suggest. It is rather due to the initial vibrational

excitation of the HCN molecule ͑Sec. III C͒.

͑004͒ vibrational state. The rotational distribution of CN(v

ϭ0) was obtained by probing the P branch of the (vЈ

ϭ0←vϭ0) transition in the wavelength region of 388.5–

387.5 nm. We prepared the HCN molecule in rotational

states with rotational quantum numbers of JЈϭ2, 9, and 16.

All rotational distributions are well characterized by Boltz-

mann distributions and the respective temperatures for

CN(vϭ0) are 490 KϮ7%, 530 KϮ5%, and 620 KϮ4%.

The rotational excitation of the CN product increases with

increasing rotational excitation of the HCN product. There-

fore we observe a positive correlation between reactant and

product rotation.

Likewise, no signiﬁcant effect of the collision energy on

the observed vibrational distribution of CN was found for the

hydrogen reaction ͑2͒. The reactions of HCN(␯ ϭ4) with

3

thermal H atoms (E_c_o_l_lϭ4 kJ/mol͒ and photolytic H atoms

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3162

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

FIG. 8. Vibrational state distribution and rotational temperatures of CN

produced in the reactions of H and Cl atoms with vibrationally excited

HCN(00␯ ).

3

(

E_c_o_l_lϭ80 kJ/mol) lead to very similar vibrational distribu-

tions of the CN product: The CN vibrational energies are

2.7 and 14.9 kJ/mol, respectively. Again, the vibrational

1

excitation of CN cannot be a consequence of using fast H

atoms with high translational energy. Therefore one would

predict a low product vibrational excitation of the CN frag-

ment when fast hydrogen atoms react with HCN in the vi-

brational ground state. This assumption was conﬁrmed by

Lambert et al. and Johnston et al. who observed a CN

state distribution which is characterized by a relatively high

rotational and low vibrational energy release, similar to the

ClϩHCN(002) reaction ͑Table III͒.

FIG. 9. Schematic view of the two approach geometries after preparation of

៝

ʈ

exc phot

the reactants with linearly polarized light. ͑a͒ E ЌE

and ͑b͒ E

E

.

exc

phot

of Cl at 355 nm as well as the hydrogen atoms from the

4

5

46

2

photolysis of methanethiol at 266 nm show an angular dis-

tribution, which is described by an anisotropy parameter of

␤

ϭϪ1 ͑see Sec. II͒. Thus the photolysis is a prompt disso-

ciation following excitation via a transition dipole moment ␮

which lies perpendicular to the molecular bond. Thus the

angular distributions of the hydrogen and chlorine atoms

E. Stereospeciﬁc reaction dynamics

2

nearly have a sin ␽ distribution and the most probable ﬂight

In order to study the steric effect in the reactions of

path lies in the xy plane ͑Fig. 9͒.

HϩHCN͑␯ ϭ2,4͒→H ϩCN

and

ClϩHCN͑␯ ϭ2,4͒

3

2

3

1

The transition dipole moment of the HCN ⌺Ϫ ⌺ tran-

sition lies along the intermolecular axis of the molecule.

Thus the linearly polarized laser beam selects HCN mol-

ecules whose intermolecular axes have an initial distribution

→

HClϩCN, the reactants were optically aligned using lin-

early polarized laser light. All relative rate measurements

were performed for two different reactant approach geom-

etries by rotating the polarization vector E of the HCN

៝

exc

2

៝

of cos ␪, where ␪ is the angle between ␮ and E ͑Fig. 9͒.

excitation laser beam with respect to the vector E

of the

exc

phot

Because the HCN molecule rotates prior to collision, the

degree of alignment depends strongly on the rotational state

of HCN. The exact quantitative expressions for this align-

photolysis laser beam.

The fragments of the photodissociation show an aniso-

tropic distribution of recoil velocities, which has an expres-

sion of the form

48

ment are described by Zare.

In a forthcoming paper⁴⁹equations are developed which

allow a relatively easy conversion of experimental results to

the angle of attack. A qualitative understanding of the inﬂu-

ence of polarized light on the preferred reaction geometry

P͑␽͒ϭ͓1ϩ␤•P ͑cos ␽͔͒/4␲.

͑9͒

2

P(␽) is the probability to realize a certain angle ␽, which is

៝

the angle between the polarization vector E and the direction

can be extracted from Fig. 9 which shows the approach ge-

of the velocity of the photofragment. P (cos ␽) is the second

2

៝

ometry of the reactants if the polarization vector E of the

Legendre polynomial, and the so-called ‘‘␤ parameter’’ pro-

exc

47

HCN excitation laser beam is perpendicular ͓Fig. 9͑a͔͒ or

vides a quantitative measure of the recoil anisotropy. The

2

៝

parameter range varies from ϩ2 for a pure cos ␽ distribu-

parallel ͓Fig. 9͑b͔͒ to the polarization vector Ephot of the

2

៝

tion to Ϫ1 for a pure sin ␽ distribution. For ␤ϭ0, the dis-

photolysis laser beam. In the ﬁrst case (E ЌE_p_h_o_t), the fa-

exc

tribution is isotropic. The chlorine atoms from the photolysis

vored approach geometry for the photolysis fragments is

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J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3163

transition state. However, a further increase of ␯ excitation

3

leads to an alignment effect which is close to Sϭ1.0. Thus

the reaction of Cl with HCN͑004͒ favors an approach geom-

etry, where the angle of acceptance has increased and the Cl

atom may also attack the HCN molecule broadside. This

observation can be explained by the cone-of-acceptance

model for the reaction ClϩHCN.⁴⁹For low vibrational exci-

tation of HCN, only a narrow range of Cl atom approach

angles can lead to a reaction. An increase of vibrational ex-

citation widens the cone of acceptance, so that the chlorine

atoms can strike the HCN at larger angles. The restriction to

a collinear reaction geometry is less if the CH bond in HCN

is vibrationally excited. As a consequence the reaction prob-

ability increases, while the alignment effect S decreases. Fur-

thermore, the cone of acceptance is larger for the bulky Cl

FIG. 10. Relative reactivity of the HϩHCN(␯ ϭ4,J)→H ϩCN system

3

2

measured in alternating order of the two approach geometries. The HCN

molecule is excited to the vibrational state via the R(1) and the R(8) rota-

tional transitions. Solid circles mark the relative rates with the polarization

vectors aligned perpendicular to each other, while open circles mark the

rates with the polarization vectors aligned parallel to each other.

atoms than for the H atoms. Similar results were found by

Loesch et al.⁵

0,51

in the reaction of Li/KϩHF. They found a

decrease of the alignment effect, when the bulky K atom

reacts instead of Li. This gives evidence that the size of the

reacting atom may have an inﬂuence on the PES in the re-

gion of the transition state and hence, on the cone of accep-

tance. But this assumption has to be conﬁrmed by quantum

mechanical or quasiclassical trajectory studies ͑QTC͒. We

will present a more general and quantitative description of

the different approach geometry and the cone-of-acceptance

model in a separate paper.⁴⁹

both end-on and side-on with respect to the HCN molecule.

៝

In the second case (E

ʈ

E_p_h_o_t), the fragments preferentially

exc

approach the broadside of HCN ͑side-on͒. The rotation of the

polarization plane of the excitation laser beam was simply

achieved by a ␭/2 plate which was mounted in front of the

entrance window of the reaction chamber.

To determine the effect of molecular alignment on the

reactivity we tuned the probe laser to the R(8) rotational line

of CN(vϭ0) and measured the laser-induced ﬂuorescence

intensity for the perpendicular and the parallel case. Mean

CN signals of one reaction geometry were obtained by sum-

ming up over 400 single measurements. This was repeated

several times with altering approach geometry. The result for

the HϩHCN(␯ ϭ4,J)→H ϩCN reaction is shown in Fig.

F. RRKM calculation

We calculated the vibrational population of CN with a

simple extension of the Rice–Ramsperger–Kassel–Marcus

͑RRKM͒ theory where one assumes that the CN stretch vi-

bration of the transition state migrates adiabatically into vi-

bration of the CN radical. Using this assumption one yields

for the vibrational population of the CN product

3

2

1

0. The HCN molecule was excited to the vibrational state

k͑v͒

via the R(1) and the R(8) rotational transitions. The time

delay between the excitation/photolysis laser and the probe

laser was 230 ns, at a total pressure in the reaction cell of 500

mTorr. Figure 10 clearly shows that the signal intensity is

higher for the perpendicular case than for the parallel case.

The signals are used to calculate the alignment effects de-

ﬁned by

P͑v͒ϭ

,

k͑E͒

where k(E) is the RRKM rate and k(v) is the RRKM rate

with a vibrational quantum number of v in the transition

state. The proposed reaction pathways and geometries of the

transition states are shown in Fig. 11. The used constants for

HHCN and ClHCN are listed in Table IV.

The results of the RRKM calculation are listed in Table

V. As can be seen, both the ClϩHCN and the HϩHCN

reaction should generate less vibrationally excited CN prod-

ucts than are observed in the experiment. Therefore RRKM

theory is not appropriate to describe the H/ClϩHCN

SϭI /I

ʈ

.

͑10͒

Ќ

We obtain a small but signiﬁcant alignment effect of S

ϭ1.07Ϯ0.03 for the R(1) and 1.09Ϯ0.03 for the R(8) ro-

tational line of HCN. A value of SϾ1 indicates a preference

of the approach geometry, where the atoms preferentially

attack the HCN molecule end-on. Thus the production of CN

is enhanced for collinear collisions of the reactants. A similar

result is obtained for the reaction of H atoms with HCN(␯₂

ϭ2), having an alignment effect of Sϭ1.12.

In the same way we measured the steric effect for the

chlorine reaction ͑1͒. HCN was excited via the R(8) rota-

tional line to the ͑002͒ and ͑004͒ vibrational levels. Interest-

ingly, we ﬁnd a mode-speciﬁc dependence of the alignment

effect S. If HCN is excited to the ͑002͒ state we measured a

signiﬁcant preference for the perpendicular case, indicating

→

HCl/H ϩCN reaction. So we conclude that there is not

enough time for energy randomization. Both reactions seem

to proceed rather direct.

2

G. Trajectory study

To study the details of how reactant vibrational excita-

tion inﬂuences reactivity and product state energy partition-

ing, we performed quasiclassical trajectory calculations

͑QTC͒ for the forward reaction ͑2͒. Several quantum theo-

retical results have been reported concerning the mode-

5

2,53

that the reaction HCN͑␯ ϭ2͒ϩCl proceeds via a collinear

speciﬁc reaction rates in HϩHCN͑␯ ,␯ ,␯ ͒→H ϩCN.

3

1

2

3

2

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1

3164

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

FIG. 12. Reaction probability for HϩHCN͑␯ ,0,␯ ͒→H ϩCN as a function

1

2

of the collisional energy ͑in kJ/mol͒. The reaction probability is equal to the

number of trajectories leading to the products divided by the total number of

trajectories.

The surface shows a late barrier with bond distances at the

saddle point HЈHCN of r ϭ0.85 Å, r_C_Hϭ1.42 Å, and

H H

Ј

r_C_Nϭ1.165 Å. The bond distances of the products H and

2

CN are 0.742 and 1.164 Å, respectively. Classical trajecto-

ries were obtained using the classical perturbation theory ap-

proach for determining good action-angle variables.⁵

This procedure leads us to specify the initial semiclassical

states of HCN accurately.

7–60

The total reaction probabilities for HϩHCN͑001, 002,

03, 004, 101, 302͒ are plotted in Fig. 11. The results indi-

FIG. 11. Reaction geometries and pathways ͑Refs. 16 and 23͒ used in the

RRKM calculations. Distances are given in Å.

0

cate that the reaction threshold is lowered efﬁciently by vi-

brational excitation of HCN. This result is consistent with

the fact that reaction ͑1͒ has a late barrier. More speciﬁcally,

the threshold is lowered more effectively by exciting the CH

stretch than by exciting the CN stretch. While the reaction of

HCN in the ͑001͒ state occurs at collision energies

Ͼ44 kJ/mol, no reaction at any collision energy was found if

Our trajectories were calculated for a collinear reaction ge-

ometry of the four atoms. We used a LEPS-like potential-

energy surface ͑PES͒ of the form

V͑r

,r_C_H_Ј,r_C_H,r_C_N͒ϭV_L_E_P_S͑r

,r_C_H_Ј,r_C_H

͒

Ј

H H

Ј

H H

only the CN stretch up to ␯ р3 is excited. The same result

was found when HCN is in the vibrational ground state

ϩV ͑r_C_N͒,

which was developed by Brooks.⁵⁴

Here V_L_E_P_Sis a three-body LEPS-type surface and V_Mis

a modiﬁed Morse potential to describe the CN interaction.

͑11͒

1

M

͑000͒. Thus the endothermic reaction with a late barrier can-

not be promoted either by translational excitation nor by CN

stretch excitation. This is in good agreement to experimental

results and theoretical results obtained by Takayanagi and

5

5,56

Other PES

of Sun and Clary do not reproduce the HCN

vibrational normal modes with such high accuracy. Using the

parameters shown in Table VI the reaction enthalpy of our

potential surface is 91 kJ/mol and the classical barrier of the

forward reaction is 113 kJ/mol which both are in good agree-

ment with theoretical results. The CH and CN bond distance

in the free HCN molecule are 1.00 and 1.17 Å, respectively.

52

Schatz, who found a very small cross section for the

HCN͑000͒ϩH

Ͼ110 kJ/mol.

reaction

at

translational

energies

If HCN is excited to different but isoenergetic vibra-

tional states ͓such as ͑004͒ and ͑302͔͒, the threshold is al-

ways lower for the vibrational state where mainly the CH

mode is excited. In Fig. 12 it can also be seen that pure CH

excitation increases the reaction probability more efﬁciently

than CN excitation. At collision energies lower than 22 kJ/

mol the reactivity for HCN͑004͒ is larger than for

HCN͑302͒. However, at higher collision energies the reac-

tive rate changes are reversed. This is due to the restriction

we have made in the QCT study, namely that the reaction

can only proceed via a collinear collision geometry. How-

ever, as we have seen from the experiment ͑Sec. III E͒, re-

action geometries with a wide cone of acceptance can occur.

This might also explain why the calculated vibrational CN

distributions are higher than the one we measured in the

TABLE IV. Constants of the transition states ͑Refs. 16 and 23͒.

A

B

C

D

E

F

Ϫ1

␻₁

␻₂

␻₃

/cm

3350

1950

1000

641

3058

1761

1451

1046

3130

963

2275

2110

771

3505

2375

952

906

282

3236

2104

1260

991

773

435

2966

1821

186

88

^␻4

213

␻₅

␻₆

844

Ϫ1

␻_i/cm

1303i

1009i

762i

53.1

372i

17.1 113

Ϫ1

Energy/kJ mol

44.77 Ϫ79.91

127.61

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J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

3165

TABLE V. Results of the RRKM calculations for RϩHCN(0,0,␯ )→RHϩCN(v) using the quantities given in

3

Table IV. For a better comparison the experimental results are also listed.

E_c_o_l_l

kJ/mol͔

vϭ0

͓%͔

vϭ1

͓%͔

vϭ2

͓%͔

vϭ3

͓%͔

vϭ4

͓%͔

vϭ5

͓%͔

͓

HϩHCN͑002͒RRKM

HϩHCN͑002͒Exp.

HϩHCN͑003͒RRKM

HϩHCN͑004͒RRKM

HϩHCN͑004͒Exp.

80

98

95

84

69

53

60

52

2

Ͻ5

15

24

33

0

1

6

14

9

0

1

0

2

5

0

0.4

1

0

0.3

HϩHCN͑005͒RRKM

HϩHCN͑006͒RRKM

28

30

12

ClϩHCN͑002͒RRKM

ClϩHCN͑002͒Exp.

ClϩHCN͑003͒RRKM

ClϩHCN͑004͒RRKM

ClϩHCN͑004͒Exp.

ClϩHCN͑005͒RRKM

ClϩHCN͑005͒Exp.

ClϩHCN͑006͒RRKM

ClϩHCN͑006͒Exp.

36

25

100

86

100

96

51

89

41

78

34

0

13

0

Ͻ1

0

4

0

34

11

38

20

34

15

0.4

15

2

0

6

0.1

Ͻ9

23

both CH and CN stretch modes of HCN. Again, the calcu-

^l^a^t^e^d^r^a^t^e^k004 ^/^k302 is in good agreement with the experimen-

^t^a^l^r^e^s^u^l^t⁽^k004 ^/^k302р4).²¹

experiment. At a collision energy of E_c_o_l_lϭ80 kJ/mol the

QCT calculation leads to CN vibrational distributions P(v

ϭ0):P(vϭ1):P(vϭ2):P(vϭ3) of 0.51:0.39:0.10:0.0 for

the HCN͑002͒ reaction and 0.10:0.30:0.23:0.35 for the

HCN͑004͒ reaction.

Thus one can assume that the reaction will proceed via

the collinear transition state if the collision energy is thermal.

Figure 13 shows the result of the trajectory calculation with

a Boltzmann-like collisional energy distribution at 300 K

which was obtained by arbitrarily choosing a collision en-

ergy between 0 and 50 kJ/mol for each trajectory. At the end

of the trajectories, the reaction probability is weighted by

We also calculated the energy release into the vibration

of the H product at a thermal collision energy of 4 kJ/mol.

2

When HCN is in the ͑002͒ vibrational state, about 12%,

6

4%, and 24% of the total available energy are located in CN

vibration, H vibration, and in product translation, respec-

2

tively. If HCN is excited to the ͑004͒ vibrational state, the

energy release was found to be 21%, 61%, and 18%, respec-

tively. Thus about 2/3 of the available energy are located in

the H vibration. This result is consistent with theoretical

2

results showing that vibrational excitation of H can efﬁ-

P(E_c_o_l_l)ϭE_c_o_l_l•exp(ϪE /kT). This leads to a mean colli-

2

coll

ciently promote the reverse reaction H ϩCN→HϩHCN and

sion energy of 4 kJ/mol. Figure 13 compares the QCT results

with our experimental results where thermal hydrogen atoms

were used as collision partners. The translational relaxation

is achieved by adding He into the reaction cell, as described

in Ref. 21. In the upper part of Fig. 13 the CN vibrational

distributions are plotted which belong to the HϩHCN(␯₃

ϭ2) reaction, while in the lower part those which belong to

2

that a signiﬁcant energy transfer into the vibration of the CN

product must occur. The CN internal energy release in-

creases with increasing CH stretch excitation which is also

found in the experiment ͑Sec. III C͒.

the HϩHCN(␯ ϭ4) reaction are plotted. In both cases there

3

IV. CONCLUSIONS

is a very good agreement between the QCT result and the

experiment. The calculated rates of reactivity are k₀₀₃/k₀₀₂

ϭ34Ϯ4, k₀₀₄/k₀₀₃ϭ5.7Ϯ0.6, and k₀₀₄/k₃₀₂ϭ3.7Ϯ0.4. Thus

the reactivity is enhanced by a factor of 194Ϯ43 when HCN

is excited to the ͑004͒ state instead of ͑002͒. Furthermore,

the reactivity is larger when the vibrational energy is located

only in the CH mode, instead of locating the same energy in

We used vibrational overtone excitation to prepare HCN

molecules in a speciﬁc rotational and vibrational state and to

study the inﬂuence of reactant excitation on the endothermic

reactions HϩHCN→H ϩCN and ClϩHCN→HClϩCN. In

2

the reaction of chlorine atoms with HCN, the CH stretch

mode promotes reaction much more efﬁciently than the CN

stretch mode. Thus channeling energy into the reaction co-

ordinate will increase the reactivity while energy located in a

coordinate perpendicular to the reaction coordinate will have

no or only a minor inﬂuence on the reaction rate. These

results are consistent with the qualitative spectator model in

which excitation in the nonreacting CN bond has no effect

on the reactivity. The reactions of chlorine atoms with HCN

in vibrational states having similar energy but corresponding

to very different nuclear motions demonstrate the mode spe-

ciﬁc behavior of the reactivity. The results agree with a

TABLE VI. Parameters used in the potential-energy function ͑LEPS͒. Other

Ϫ1

parameters: p_C_HϭϪ0.136, p_C_NϭϪ0.059, and qϭ0.75a₀

.

͑1

Ϫ1

hartreeϭ219 400 cm , a ϭ0.529 177 Å͒.

0

Ϫ1

0

AB

D_A_B/hartree

␤_A_B/a₀

r

/a₀

⌬_A_B

HЈH

CHЈ

CH

0.17

1.0583

0.9245

1.4065

1.4014

1.9993

2.1864

0.1

-

0.1528

0.2102

0.350 59

CN

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1

3166

J. Chem. Phys., Vol. 108, No. 8, 22 February 1998

Kreher, Rinnenthal, and Gericke

simple, direct reaction mechanism without complex forma-

tion. The reaction must be fast without time left for energy

redistribution.

Furthermore, the product vibrational energy is strongly

inﬂuenced by the initial vibrational state of HCN. The vibra-

tional energy of the CN product distribution in the chlorine

reaction could qualitatively be explained by the nodal pattern

of the vibrational wave function of the HCN molecule.

Hence the CN product vibration is a consequence of the ini-

tial vibrational excitation of the HCN molecule. This is again

in accordance with the spectator model in which the nonre-

acting CN bond does not participate in the reaction and is

conﬁrmed by the observation that neither different collisional

energies of the reactants nor different masses of the reacting

atom ͑H/Cl͒ have a signiﬁcant inﬂuence on the vibrational

distribution of CN.

Reactions from different rotational states of HCN(␯₃

ϭ4) show the inﬂuence of an initial rotation of HCN on the

reaction. The rotational excitation of HCN promotes the

ClϩHCN reaction very efﬁciently, suggesting a geometrical

constraint on the reaction. At low rotations of HCN, the re-

action can occur only if the Cl atom approaches on the H

atom end of HCN, whereas at fast rotations of HCN, the Cl

atom has sufﬁcient time to ﬁnd the ideal approach geometry.

These observations suggest that the relative orientation of the

reactants strongly affects the reaction rate, which is con-

ﬁrmed by our measurements with optically aligned reactants.

In the case of HϩHCN and ClϩHCN the CN is predomi-

nantly formed in a collinear reaction geometry, but for the

latter reaction there is less restriction to a collinear geometry

if the CH bond in HCN is highly vibrationally excited. The

additional experimental measurements have changed our

original picture of the reaction dynamics, namely with regard

to the existence of complex formation²¹͓gained from similar

results of HCN͑004͒ and HCN͑302͒ reactions͔, now favoring

a pure direct abstraction. The conclusion agrees with theo-

retical results of Harding¹³and Bair et al. who predict the

lowest energy route for both reactions to be a direct, collin-

ear abstraction. The detailed information from our measure-

ments offers a possibility for comparison with results ob-

tained from quasiclassical trajectory studies or quantum

mechanical calculations.

FIG. 13. Vibrational state distribution of CN for the reactions

HϩHCN(002) ͑upper part͒ and HϩHCN(004) ͑lower part͒. Comparison of

the results obtained from the experiment and the trajectory study is shown.

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Vibrational state control of bimolecular reactions

DOI: 10.1063/1.475712

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Article abstract of DOI:10.1063/1.475712

Full text of DOI:10.1063/1.475712

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