Dynamics of OH and OD radical reactions with HI and GeH4 as studied by infrared chemiluminescence of the H2O and HDO products

Dynamics of OH and OD radical reactions with HI and GeH 4 as studied by infrared

chemiluminescence of the H 2 O and HDO products

N. I. Butkovskaya and D. W. Setser

Citation: The Journal of Chemical Physics 106, 5028 (1997); doi: 10.1063/1.473550

View online: http://dx.doi.org/10.1063/1.473550

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Dynamics of OH and OD radical reactions with HI and GeH₄as studied

by infrared chemiluminescence of the H₂O and HDO products

N. I. Butkovskaya^a)and D. W. Setser

Department of Chemistry, Kansas State University, Manhattan, Kansas 66506

͑Received 13 September 1996; accepted 10 December 1996͒

The infrared chemiluminescence of vibrationally excited H₂O and HDO from the highly exothermic

reactions of OH and OD radicals with HI and GeH₄was observed in the 2200–5500 cm^Ϫ1range.

The experiments utilized a fast-ﬂow reactor with 0.3–1 Torr of Ar carrier gas at 300 K; the OH͑OD͒

radicals were produced via the H͑D͒ϩNO₂reaction and the H or D atoms were generated by a

discharge in a H₂͑D₂͒/Ar mixture. The H₂O and HOD vibrational distributions were determined by

computer simulation of the emission spectra in the 2200–3900 cm^Ϫ1range. The total vibrational

energy released to H O and HOD molecules is, respectively, f ϭ 0.36 and 0.41 from HI and

͗

͘

2

v

f

ϭ 0.46 and 0.51 from GeH . These values are signiﬁcantly smaller than for the reactions of OH

͗

͘

v

4

and OD with HBr, f ϭ 0.61 and 0.65. The populations of the O–H stretching vibration of HOD

͗

͘

v

and the collisionally coupled ␯ and ␯ stretching modes of H₂O decrease with increasing

1

3

vibrational energy. In contrast, the vibrational distribution from the HBr reaction is inverted. The

bending mode distributions in all stretching states of H₂O and HOD extend to the thermodynamic

limit of each reaction. A surprisal analysis was made for H₂O͑HOD͒ distributions from the title

reactions and compared with that for OH͑OD͒ϩHBr. The surprisal analysis tends to conﬁrm that the

dynamics for the HI and GeH₄reactions differ from the HBr reaction. The HI reaction may proceed

mainly via addition-migration, while the GeH₄reaction may involve both direct abstraction and

addition-migration. A rate constant for the OHϩGeH₄→H₂OϩGeH₃reaction was evaluated by

comparing the H₂O emission intensities with that of the OHϩHBr→H₂OϩBr reaction,

k_GeH/k_HBrϭ 6.5 Ϯ 0.9. Secondary kinetic-isotope effects, k_OH/k_ODϭ 1.4 Ϯ 0.1, 1.0Ϯ0.2, and

4

1.3Ϯ0.2, were determined for reactions of OH and OD with GeH₄, HI, and HBr, respectively, by

͓S0021-9606͑97͒00411-X͔

work¹⁵we have used the infrared emission technique to ana-

I. INTRODUCTION

lyze the vibrational excitation of isotopic water molecules

formed in the reactions of OH͑OD͒ radical with HBr and

DBr,

Hydroxyl radical reactions are important from both prac-

tical and fundamental points of view. Practical applications

include combustion and atmospheric chemistry and involve

reactions with a wide range of organic and inorganic mol-

ecules and radicals. On the theoretical side, the abstraction

reactions giving H₂O provide the opportunity to study the

formation of a triatomic product molecule in speciﬁc quan-

tum states. In particular, the reactions of OH with hydrogen

halides have been extensively studied to provide a kinetic

database for atmospheric chemistry^1,2and hydrocarbon

combustion.³Reaction rates also have been studied for deu-

terium halides^4–7and vibrationally excited hydroxyl

radicals.^6,7In contrast to the kinetics, very little is known

about the dynamics of these important reactions, and only

the ﬁrst efforts are being made to determine the energy dis-

posal and to explain the unusual temperature dependence of

the rate constants.^8–10The infrared chemiluminescence tech-

nique has been successfully used to study the dynamics of

the H atom abstraction reactions by O, F, and Cl atoms, and

comparison of the vibrational-rotational energy distributions

of the products with quasiclassical calculated results led to

an understanding of the reaction dynamics.^11–14In recent

OH͑OD͒ϩHBr→H₂O͑HOD͒ϩBr.

1͒ and ͑1D͒

͑

Chemiluminescent spectra in the 2400–3900 cm^Ϫ1range

were recorded by a Fourier transform spectrometer and ana-

lyzed using computer simulation. The spectra were obtained

from a fast-ﬂow reactor with 0.5–2.0 Torr of Ar for a short

reaction time ͑0.2–0.8 ms͒. The degree of vibrational cou-

pling among levels was determined, and it was shown that

the distributions for

ϩ

v₁v₃

and

of H₂O and

and

v₃

v₂

ϩ

v₁v₂

for HOD could be assigned. The fraction of vibra-

tional energy was 0.61 in H₂O and 0.65 in HOD, and the

vibrational distributions showed an inverted population in

both the stretching and bending modes, as would be expected

for a direct abstraction mechanism. These experimental re-

sults can be compared to a quasiclassical trajectory

calculation⁸and a quantum scattering calculation of Clary

et al.⁹on an approximate potential, which was constructed so

as to provide a negative temperature dependence for the rate

constant of reaction ͑1͒.

In the present work we have studied the reactions of

OH͑OD͒ radicals with HI and GeH₄. Both reactions have

larger rate constants than reaction ͑1͒ and presumably they

a͒

Permanent address: Institute of Chemical Physics, Russian Academy of

Sciences, 117334 Moscow, Russian Federation.

5028

J. Chem. Phys. 106 (12), 22 March 1997

0021-9606/97/106(12)/5028/15/$10.00

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5029

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

TABLE

I.

Thermodynamical

and

kinetic

data

for

the

tions for centrifugal effects, which were introduced in the

present study, are described in Sec. III. The vibrational dis-

tributions are presented in Sec. IV B. In spite of the available

energy being higher than for OHϩHBr, the vibrational dis-

tributions from both HI and GeH₄were noninverted in the

stretching mode. Information theoretical analysis, which is

given in detail in Sec. V A, showed that the surprisal plots

for OHϩGeH₄and ODϩGeH₄reactions are linear, but the

slopes are lower than those for the OHϩHBr and ODϩHBr

reactions. The surprisal plots for OHϩHI and ODϩHI reac-

tions also are linear, but the slopes are close to zero. The

detailed discussion of the reaction mechanisms, along with a

comparison with results from reactions with F, Cl, and O

atoms, is given in Sec. V B.

In addition to providing vibrational distributions, the in-

frared chemiluminescence can be used to obtain relative rate

constants for H₂O and HOD formation by comparison with a

standard reaction. In this work the rate constant for the reac-

tion of OH radical with germane was obtained by compari-

son to HBr. The secondary kinetic-isotope effects for the

GeH₄and HI reactions with OH and OD were obtained by

comparison of the H₂O and HOD emission intensities.

OH͑OD͒ϩHR→H₂O͑HOD͒ϩR ͑RvBr, GeH₃, I͒ reactions.

D₀(HϪR)^aϪ⌬H₀E_a

͗E_av͘

b

k ͑298 K͒

Reaction

kcal mol^Ϫ1

cm³molecule^Ϫ1s^Ϫ1

OHϩHBr

ODϩHBr

OHϩHI

ODϩHI

OHϩGeH₄

ODϩGeH₄

86.64Ϯ0.05

70.42Ϯ0.06

82Ϯ2^d

31.4

30.8

47.7

47.1

36

0

33.7

33.1

49.8

49.2

1.1ϫ10^{Ϫ11 b}

k_H/k_Dϭ1.3Ϯ0.2^c

2.7ϫ10^{Ϫ11 b}

k_H/k_Dϭ1.0Ϯ0.2^c

͑7Ϯ1͒ϫ10^{Ϫ11 c}

k_H/k_Dϭ1.4Ϯ0.1^c

•••^e38.4

36

•••

37.8

^aReference 17͑a͒.

^bReference 1.

^cThis work.

^dSee also Refs. 17͑b͒ and 17͑c͒ for a discussion about Ge–H bond energy.

^eE_aϭ0 can be assigned with the reference to the E_aϭ0.095 kcal mol^Ϫ1for

OHϩSiH₄→H₂OϩSiH₃reaction ͑Ref. 44͒.

also proceed without formal potential energy barriers. The

rate constant for HI is 2.7ϫ10^Ϫ11molecule cm^Ϫ3, which is

2.5 times larger than for HBr.¹The chemistry of GeH₄may

be important in the plasma-enhanced chemical vapor depo-

sition processes,¹⁶but neither dynamical nor kinetic data cur-

rently exist for the OHϩGeH₄reaction.

The infrared chemiluminescent spectra of H₂O and HOD

were measured from the reactions of OH and OD radicals

with HI and GeH₄in the same reactor that was used for

reaction ͑1͒,

II. EXPERIMENTAL METHODS

The experimental methods were given in the preceding

paper¹⁵that described our study of the HBr reaction. The

infrared chemiluminescence spectra from vibrationally ex-

cited H₂O and HOD molecules generated by the reactions of

OH and OD radicals with hydrogen containing molecules

were recorded by a Fourier transform infrared spectrometer

͑BIORAD FTS-60͒, which observed the emission from a

fast-ﬂow chemical reactor operated at 300 K. The spectral

resolution was 1 cm^Ϫ1. The spectrometer chamber and the

tube connecting the observation window ͑NaCl͒ with the

spectrometer inlet lens ͑CaF₂͒ were continuously ﬂushed

with dry air to remove water vapor that would absorb the

chemiluminescent radiation. The response of the liquid N₂

cooled InSb detector was calibrated with a standard black-

body source.

The OH or OD radicals were produced 30 cm upstream

of the observation window ͑NaCl͒ via the H͑D͒ϩNO₂reac-

tion; the H͑D͒ atoms were generated by a discharge through

a H₂͑D₂͒/Ar mixture. The degree of the dissociation of

H₂͑D₂͒ was measured as 50%.¹⁹Molecular reactants were

introduced 3.5 cm upstream of the observation window.

Typical concentrations of GeH₄and HI in the ﬂow reactor

were about 2ϫ10¹³molecule cm^Ϫ3. The total pressure was

varied from 0.3 to 1.2 Torr using Ar as the carrier gas. The

typical reaction time ͑at 0.5 Torr͒ was 0.25 ms.

OH͑OD͒ϩHI→H₂O͑HOD͒ϩI,

OH͑OD͒ϩGeH₄→H₂O͑HOD͒ϩGeH₃,

These reactions were selected because the exoergicity is

larger than in the OHϩHBr reaction and because both reac-

tants have been studied with O, F, and Cl atoms.^11–14The

energy available to the products can be obtained from the

enthalpy changes for reactions ͑1͒–͑3͒ using Eq. ͑4͒,

2͒ and ͑2D͒

3͒ and ͑3D͒

͑

E

ϭϪ⌬H⁰ϩnRTϩE ,

͘

͑4͒

͗

av

a

0

where E_ais the activation energy and nϭ3.5 for reactions

͑1͒ and ͑2͒ and nϭ4 for reaction ͑3͒. The thermodynamical

and kinetic data for these reactions are listed in Table I. One

of the interesting features of this group of reactions is the

zero activation energy. The reduced rate constants, relative to

the collision rate constant, arise as a consequence of the ori-

2

entation requirements for the OH͑X ⌸͒ radical. The Ϫ⌬H₀

values, obtained from the H–R bond energies,¹⁷are 31.4,

47.7, and 36.0 kcal mol^Ϫ1for the OH reactions. The avail-

able energies are sufﬁcient to excite four and three stretching

quanta of the water molecule in reactions ͑2͒ and ͑3͒, respec-

tively. The large rate constants of reactions ͑2͒ and ͑3͒ made

it possible to observe chemiluminescence in the 2200–3900

plus the 4500–5500 cm^Ϫ1range; the latter was used to com-

pare emission intensities from the ͑⌬␯₃ϭϪ1ϩ⌬␯₂ϭϪ1͒

combination transition to the ⌬␯₃ϭϪ1 transition.

The secondary reaction of germyl radical

OHϩGeH₃→H₂OϩGeH₂

→H₂ϩGeH₂O

͑5a͒

͑5b͒

The experimental chemiluminescent spectra were ana-

lyzed using computer simulation methods previously

developed.^15,18Some improvements concerning line posi-

tions of the combination and hot bands and intensity correc-

must be considered, because the formation of water in chan-

nel ͑5a͒ could effect the H₂O spectra from the primary reac-

tion ͑3͒. The ratio of water concentrations produced in the

secondary and primary steps at short reaction times may be

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5030

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

expressed as ͓H₂O͔_sec/͓H₂O͔_priϭk_5a͓OH͔⌬t/2. For typical

conditions of 0.5 Torr, ͓OH͔ϭ2ϫ10¹³molecule cm³and

⌬tϭ0.25 ms, comparable ͓H₂O͔ and ͓H₂O͔ may be

(K_aϪK_cϽ2),

Jϭ9

(K_aϪK_cϽϪ5)

and

Jϭ10

(K_aϪK_cϽϪ6) are responsible for the bulk of the observed

emission intensity.¹Fortunately, many H₂O bands in the

0–17 000 cm^Ϫ1spectral range have been thoroughly exam-

sec

pri

achieved only if k_5aϾ1ϫ10^Ϫ10cm³molecule^Ϫ1s^Ϫ1. More-

over, when reaction ͑3͒ takes place with an excess of NO₂

ined, and most of the rovibrational energy levels for

,

v₁

₃р4, ₂р2, and Jр8 states are known. This includes

over the

H atom concentration, reaction ͑6͒, with

v

k₆ϭ͑1.06Ϯ0.18͒ϫ10^Ϫ11cm³molecule^Ϫ1s^Ϫ1͑Ref. 20͒ effec-

͑010͒,²²͑020͒, ͑100͒, and ͑001͒,²³͑030͒, ͑110͒, and ͑100͒,²⁴

͑040͒, ͑101͒, ͑120͒, ͑021͒, ͑200͒, and ͑002͒,^25–28͑050͒,

͑130͒, ͑031͒, ͑210͒, ͑111͒, and ͑012͒,^29–32͑211͒, ͑131͒,

͑310͒, ͑112͒, ͑013͒,^32,33͑041͒, ͑220͒, ͑121͒, ͑022͒, ͑300͒,

͑201͒, ͑102͒, and ͑003͒,^32,34͑141͒, ͑320͒, ͑221͒, ͑301͒, ͑202͒,

͑122͒, ͑023͒, ͑400͒, ͑103͒, ͑004͒, ͑231͒, ͑212͒, ͑311͒, ͑410͒,

and ͑113͒ ͑Ref. 35͒ absorption bands. Missing levels were

calculated using expressions for rotational energy from Ref.

26, neglecting J- and K-dependent terms for Fermi and

Darling–Dennison interactions. Where possible, rotational

constants for vibrational states from Refs. 22–35 were used;

other cases were obtained by linear extrapolation of the ro-

tational constants of lower states. The energy levels for states

tively removes the GeH₃radicals,

NO₂ϩGeH₃→products.

͑6͒

A suggested mechanism for reaction ͑6͒ is formation of a

GeH₃NO₂complex, followed by isomerization to GeH₃ONO

and decomposition to GeH₃OϩNO or GeH₂ϩHONO. The

reaction with NO

NOϩGeH₃→GeH₃NO

͑7͒

with k₇ϭ͑1.02Ϯ0.2͒ϫ10^Ϫ12cm³molecule^Ϫ1s^Ϫ1͑Ref. 20͒ is

an order of magnitude slower and can be neglected, because

͓NO₂͔Ͼ͓OH͔ϭ͓NO͔. To examine whether reaction ͑5a͒

plays any role in our system, water emission spectra were

recorded for ͓NO₂͔ϭ1ϫ10¹⁴and ͓GeH₄͔ϭ1.6ϫ10¹³

molecule cm^Ϫ3with OH concentrations of 3.0, 1.2, 0.65, and

0.23ϫ10¹³molecule cm^Ϫ3. All four spectra were identical,

within the experimental error limits, conﬁrming the insigniﬁ-

cance of the secondary reaction ͑5a͒. For most experiments,

we used ͓OH͔Ϸ2ϫ10¹³molecule cm^Ϫ3with excess NO₂in

order to have a better signal to noise ratio.

with ₂ϭ5 and 6 ͑with poor convergency for Jу6͒ were

v

calculated using a polynomial extrapolation of the rotational

levels of ₂ϭ0, 1, 2, 3, and 4 states. As a rule, values for

v

band centers were taken from the HITRAN database. Some

experimental values for high ₂states ͓e.g., ͑151͒ and ͑042͔͒

v

were taken from Ref. 36, the others were obtained from

variational calculations.^37,38

The close energy of symmetric and antisymmetric

stretching vibration levels leads to fast collisional equilibra-

tion between these energy levels, and only the equilibrium

population, ␯_1,3, can be observed in our experiments. Hence,

the simulated spectra for H₂O were calculated as a superpo-

Commercial tank grade Ar was passed through three mo-

lecular sieve traps cooled by acetone/dry ice mixture and

liquid N₂to reduce H₂O and CO₂impurities. The HBr and

HI ͑Matheson͒ were puriﬁed by two freeze–pump–thaw

cycles before the gases were loaded into gas storage reser-

voirs as 10% mixtures with Ar. Tank grade H₂͑D₂͒ and ger-

mane ͑Solkatronic Chemicals Inc.͒ were used without puri-

ﬁcation. The GeH₄was metered to the reactor from a

reservoir containing a 10% mixture with Ar. Germane is a

highly ﬂammable material and should be handled with cau-

tion.

sition of the ‘‘equilibrated’’ ͑

with a negligible 298 K Boltzmann weight, gives the follow-

,

͒ bands. Omitting terms

v_1,3v₂

ing (

₂) groups:

v_1,3v

1, ͒ϭ0.384 0, ,1͒ϩ0.616 1, ₂,0͒, ₂ϭ0–6;

͑

v₂v₂

͑

v

2, ͒ϭ0.15 0, ,2͒ϩ0.38 1, ,1͒ϩ0.47 2, ₂,0͒,

v₂v₂v₂

͑

͑ v

₂ϭ0–6;

v

III. SIMULATION METHODS

3, ͒ϭ0.054 0, ,3͒ϩ0.119 1, ,2͒ϩ0.400 2, ₂,1͒

v₂v₂v₂

͑

͑ v

A. Modeling of H₂O spectra

As in our previous works,^15,18computer simulation of

the H₂O spectra was used to assign the vibrational distribu-

tions. The procedure begins with the relative line intensities

for the ͑001͒ and ͑100͒ fundamental bands as measured in

absorption.²¹The corresponding emission bands were calcu-

lated as in Ref. 18͑a͒ with a Boltzmann rotational population.

Only the modiﬁcations and details necessary for clarity of

reading the present paper are given below. Line positions for

ϩ0.427 3, ₂,0͒, ₂ϭ0–4;

͑

v

4, ͒ϭ0.043 1, ,3͒ϩ0.440 2, ,2͒ϩ0.434 3, ₂,1͒,

v₂v₂v₂

͑

͑ v

₂ϭ0–2.

͑8͒

v

The harmonic oscillator approximation with a cubed fre-

quency adjustment³⁹was used to calculate the intensity of

the ⌬ ϭϪ1 and ⌬ ϭϪ1 bands from the (

v₃v₁

, ₂) states

v_1,3v

of Eq. ͑8͒. In this work, a correction to the line intensities of

all the

(

v₂

,

)→(

,

₃Ϫ1) and

( , , )

v₁v₂v₃

v₁v₂

, ₃) higher bands involved in the H₂O spectra

v

the ⌬ ₃ϭϪ1 combination bands was made with the help of

→( Ϫ1,

v

v₁

F factors, which reﬂect a deviation of the transition intensity

from the rigid-rotor approximation.^40,41The F factors were

calculated according to the theory of the ﬁrst-order intensity

perturbations for the vibration-rotation lines of asymmetric

rotors developed by Braslawsky and Ben-Aryen for funda-

mental bands.⁴⁰The theory was extended to give correction

factors for combination and hot bands; the relevant formulas

were obtained as a difference of the rovibrational energy

levels of the corresponding transitions. Since the energy

available for the OHϩHI reaction is sufﬁcient to excite up to

four H₂O stretching quanta, the bands with

ϩ

₃ϭ4,

₃ϭ1,

v₁

v

р2;

ϩ

ϭ3, р4; ϩ ϭ2, р6; and

v₂v₁v₃v₂

ϩ

v₂

v₁v₃

₂р6 energy levels must be considered. Transitions between

v

the rotational levels with Jр7 ͑all K_a, K_c͒, Jϭ8

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5031

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

TABLE II. Band strength coefﬁcients for the equilibrated H₂O and HOD emission bands.

H₂O

HDO

3

Band centers

͓␯₀(i)/␯ ͑1͔͒

_1,3[␯₀(i)/␯₀(2)]³

v

0

Band

center

͓␯₀(i)/

a

3

a

Band

␯

␣

Band

␯ ͑1͔͒

␣

3

1

3

1

3

1

0

͑1,

v₂

͑2,

v₂

͑3,

v₂

͑4,

v₂

͒

3756

3689

3587

3505

3657

3545

3398

3621

1

0.427

0.719

0.908

1.576

͑

_1,2,1͒

_1,2,2͒

_1,2,3͒

_1,2,4͒

3707

3543

3381

3204

1

v

0.947

0.871

0.813

0.911

0.802

0.971

1.894

2.613

3.252

1.822

2.406

3.884

0.873

0.759

0.646

1.75

2.28

2.58

^aBand strength coefﬁcient, ␣, is deﬁned as S⁰(

/

₃)ϭ␣S⁰(001); see text for example.

v

v₁v₂

␯

are presented in the Appendix. The band centers of the

_1,3ϭ1, 2, 3, and 4 emission spectra are separated by ϳ90

͑3000–3900 cm^Ϫ1͒, which is supposed to be the ‘‘active’’

mode⁸for the OD reactions under study, is not overlapped

with emission from any other normal mode, and the ␯₃levels

are not collisionally coupled to any other set of levels.

v

cm^Ϫ1, which allows the

distribution of each

level to

v_1,3

v₂

be assigned with conﬁdence. Selection of a vibrational popu-

lation to ﬁt a given experimental spectrum was made using a

least-squares procedure with normalization of the calculated

spectrum to the peak with maximum intensity in the experi-

mental spectrum.

Hence, the nascent ␯ distribution can be uniquely obtained

3

by examining the ⌬␯₃ϭϪ1 HDO spectra from reactions ͑2D͒

and ͑3D͒. Furthermore, simulation of the ⌬␯₁ϭϪ1 HOD

spectra ͑2300–3000 cm^Ϫ1range͒ gives the population in the

Integrated intensity measurements were employed in the

following sections for the evaluation of rate constants. Some

equations are given below to explain the relations between

the observed intensities from H₂O for different reactions.

₃ϭ0 level, except for the dark ͑000͒ and ͑010͒ states. How-

v

ever, the latter population can be estimated by either assum-

ing a similarity to the ␯ /␯ distribution in the ₃ϭ1 state or

v

1

2

The absorption band sum intensities²¹of H₂O are S_v⁰͑␯ ͒

by extrapolation of the ␯ distribution of the ␯₃ϭ0 level. A

2

3

ϭ7.20ϫ10^Ϫ18and S_v⁰͑␯ ͒ϭ4.96ϫ10^Ϫ19cm^Ϫ1/molecule

disadvantage of the HOD molecule is that populations in the

1

cm^Ϫ2, giving a ratio of 0.069. Since the frequency difference

is not large, we assume the ratio to be valid for the emission

bands as well. Using this ratio, Eq. ͑8͒, and the corrected

harmonic oscillator approximation, we obtained estimates for

␯ and ␯ modes cannot be assigned separately, because the

1

2

small energy difference between the

and 2␯ levels leads

v₁

to rapid collisional equilibrium within the ␯ , ␯ ͑ ₂у2͒ sets

2

v

2

1

of levels. Accordingly, the obtained distributions are deﬁned

by the ␯ equilibrium state denoted by the equivalent num-

1,2

the band strength coefﬁcients of the equilibrated ␯ bands

1,3

ber of bending quanta. For example, the ͑4, ͒ level is com-

v₃

that are presented in Table II. For example, the ͑2, ͒ emis-

v₂

posed of three states; a (0,4, )ϩa (1,2, )ϩa (2,0, ₃),

v₃v₃

v

1

2

3

sion consists of two ⌬ ϭϪ1 bands from ͑0, ₂,2͒ and

v₃

v

where the 300 K Boltzmann weights are a₁ϭ0.333,

͑1, ,1͒ states and two ⌬ ϭϪ1 bands from ͑1, ₂1͒ and

v₂

v

a₂ϭ0.253, and a₃ϭ0.414 for ₃ϭ1; a₁ϭ0.364, a₂ϭ0.260

v

͑2, ₂,0͒ states. The Boltzmann weights are determined by

v

Eq. ͑8͒, and vibrational band strength are equal to 1.89S⁰_v͑␯ ͒

and a ϭ0.376 for ₃ϭ2, etc. The band strength coefﬁcients,

v

3

and 1.00S⁰͑␯ ͒, respectively, for the two ⌬ ₃ϭϪ1 bands and

which are used below to determine the secondary kinetic-

isotope effect for reactions ͑1D͒–͑3D͒, are given in Table II.

v

3

1.00S⁰_v͑␯ ͒ and 1.82S⁰_v͑␯ ͒, respectively, for the two

1

⌬

₁ϭϪ1 bands. Taking into account the S⁰_v(␯₁)/S_v⁰(␯₃) ra-

v

IV. RESULTS

tio, the resulting emission strength for ͑2, ͒ is calculated

v₂

as 0.15[1.89•S_v⁰(␯₃)] ϩ 0.38[1.0•S⁰_v(␯₃) ϩ 0.07•S_v⁰(␯₃)]

ϩ 0.47[1.82•0.07 •S_v⁰(␯₃)]ϭ 0.72S_v⁰(␯₃), as presented in

Table II.

A. Experimental chemiluminescent spectra:

2200–3900 cm^؊1range

The H₂O emission spectra from reactions ͑1͒–͑3͒ in the

range of 2950–3900 cm^Ϫ1, corrected for the detector re-

sponse function, are shown in Fig. 1. This range includes the

⌬␯₁ϭϪ1 ͑symmetric stretch͒ and ⌬␯₃ϭϪ1 ͑antisymmetric

stretch͒ bands of H₂O. The spectra were collected at 0.5 Torr

and a reaction time of 0.25 ms with ͓OH͔ in the range of

͑1–2͒ϫ10¹³molecule cm^Ϫ3. Each spectrum represents the

average of 512 scans of the spectrometer. The superimposed

dotted curves represent the calculated spectra with vibra-

tional distributions to be given in the next section.

B. Modeling of HOD spectra

The spectroscopic database for HOD is much more lim-

ited than for H₂O, hence, the positions of the emission bands

from high levels were approximated by red-shifting the ori-

gins of the fundamental bands, as we described in Ref. 15.

The magnitude of the shift was calculated as a difference of

band centers, which were taken from the HITRAN database

and Ref. 42. Band centers for transitions that were not pre-

viously reported were calculated using the conventional ex-

pression for the vibrational energy levels with anharmonic

and Fermi-resonance constants provided in Ref. 42.

The possibility of vibrational relaxation ͑beyond the

coupling of ␯ and ␯ of H₂O and ␯ and ␯ of HOD͒ has

1

3

1

2

been discussed earlier.^15,18The rate constants from Ref. 43

show that the quenching of H₂O͑␯_1,3ϭ1͒ by Ar is not impor-

tant for р0.7 Torr and our residence time. Due to the large

One very important advantage of the HOD spectra, rela-

tive to the H₂O spectra, is that emission from the ␯ mode

3

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5032

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

FIG. 2. Infrared emission spectra in the 2200–3900 cm^Ϫ1range produced

by the reactions of OD with HBr, GeH₄and HI at 0.5 Torr. The spectra,

which have been corrected for the detector response function, are plotted

with normalization to the maximum peak intensity. ͑a͒ ODϩHBr reaction

with ͓OD͔ϭ1.9, ͓HBr͔ϭ0.8; ͑b͒ ODϩGeH₄reaction with ͓OD͔ϭ1.6,

͓GeH₄͔ϭ1.3; ͑c͒ ODϩHI reaction with ͓OD͔ϭ1.2, ͓HI͔ϭ1.7 ͑the concen-

trations are in units of 10¹³molecule cm^Ϫ3͒. The dashed lines represent the

best-ﬁt simulated spectra.

FIG. 1. Infrared emission spectra in the 2940–3900 cm^Ϫ1range produced

by the reactions of OH with HBr, GeH₄and HI at 0.5 Torr. The spectra,

which have been corrected for the detector response function, are plotted

with normalization to the maximum peak intensity. ͑a͒ OHϩHBr reaction

with ͓OH͔ϭ1.2, ͓HBr͔ϭ1.6; ͑b͒ OHϩGeH₄reaction with ͓OH͔ϭ1.9,

͓GeH₄͔ϭ1.5; ͑c͒ OHϩHI reaction with ͓OH͔ϭ1.7, ͓HI͔ϭ2.5 ͑the concen-

trations are in units of 10¹³molecule cm^Ϫ3͒. The dashed lines show the

best-ﬁt simulated spectra.

3000–3900 cm^Ϫ1range consists of ⌬␯₃ϭϪ1 ͑O–H stretch͒

bands of HOD. The emission intensity in the 2200–3000

cm^Ϫ1range is visibly higher for the HI and GeH₄reactions

than for the HBr reaction. Since the O–D spectator bond in

HOD is not expected to be excited in this type of H atom

abstraction reaction, this immediately gives evidence for a

signal from reaction ͑2͒, we could show that identical H₂O

spectra were obtained at 0.34, 0.46, and 0.71 Torr of Ar for

⌬tϭ0.35 ms with the same reactant ﬂows, conﬁrming the

insigniﬁcance of quenching by Ar in this pressure range. The

distributions from these spectra are shown later in Table IV.

Similar conclusions¹⁵previously were reached about the dis-

tributions assigned to reaction ͑1͒. Since the _1,3distribution

v

higher bending excitation and/or a higher population in ₃ϭ0

v

from HBr is inverted, vibrational relaxation would be espe-

cially noticeable. Other probable quenching agents are OH

radicals, NO, NO₂, and reactant molecules. For each reac-

tion, we tested experimentally the range of reactant concen-

trations, ͓RH͔, for which ͑i͒ the integrated spectral intensity

was linear vs ͓HR͔ and ͑ii͒ the relative intensity of the

prominent peaks in the spectra remained constant. For a re-

action time of 0.35 ms ͑Pϭ0.7 Torr͒, these concentrations

are ͓HBr͔ϭ͓HI͔Ϸ2.8ϫ10¹³, ͓GeH₄͔Ϸ1.5ϫ10¹³molecule

cm^Ϫ3. Using the OHϩHBr reaction as a test case, the range

of ͓OH͔ was determined that satisﬁed the same criteria, and

the ͓OH͔ was Ͻ2.5ϫ10¹³molecule cm^Ϫ3. No effects of re-

from reactions ͑2͒ and ͑3͒ compared to reaction ͑1͒. The

greater intensity from lower wavenumbers in both bands that

is clearly evident in Figs. 2͑a͒, 2͑b͒, and 2͑c͒ from the HI and

GeH₄reactions corresponds to an overall increase of vibra-

tional excitation from reactions ͑2͒ and ͑3͒, relative to the

HBr reactions. The HOD spectra demonstrate more distinct

differences among the three reactions than the H₂O spectra,

because excitation in the new H₂O bond leads to both ␯₃and

␯ excitation and, furthermore, these levels are collisionally

1

mixed in H₂O. The detailed vibrational distributions derived

from these spectra are presented in the next section.

laxation was observed up to ͓NO₂͔ϭ3ϫ10¹⁴molecule cm^Ϫ3

.

B. Vibrational distributions for H₂O and HOD

The HOD emission spectra from reactions ͑1D͒–͑3D͒ in

the range of 2200–3900 cm^Ϫ1, corrected for the detector

response function, are shown in Fig. 2. The spectra were

measured at 0.5 Torr for ⌬tϭ0.25 ms, reagent concentra-

tions of about 1ϫ10¹³molecule cm^Ϫ3and ͓OD͔ of about

͑1–2͒ϫ10¹³molecule cm^Ϫ3. The weak emission in the

2200–3000 cm^Ϫ1range consists of ⌬␯₁ϭ1 ͑O–D stretch͒

and ⌬␯₂ϭϪ2 ͑bend͒ bands. The strong emission in the

The best simulated H₂O and HOD spectra for the 0.5

Torr data are shown in Figs. 1 and 2 by the dotted curves and

the corresponding distributions are presented in Tables III

and IV. Only populations in the

у1 and

v_1,3

levels can be

v₂

obtained from simulation of the H₂O spectra. The total popu-

lation in a given _1,3level, P_1,3, was obtained by summation

v

over the speciﬁc

populations. The P_1,3values are pre-

v₂

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

TABLE III. Vibrational distributions of H₂O from reactions ͑1͒, ͑2͒, and

͑3͒.

with a certain

number; these are given in the bottom line

v₂

of each distribution in Table III. The rather abrupt decrease

in the ₂ϭ4 population that seems to exist for all three reac-

v

v₂

tions probably is a defect of the simulation procedure.

Table IV presents the H₂O vibrational distributions de-

rived from the spectra of reaction ͑3͒ obtained at Ar pres-

sures of 0.34, 0.48, 0.70, 1.0, and 1.2 Torr. These spectra

were analyzed in order to identify the onset of vibrational

relaxation. To within the reliability of the assignment of the

distributions, the stretching populations, P_1,3, do not change

with pressure in the 0.34–0.70 Torr range. A gradual growth

st

a

b

c

0

1

2

3

4

5

у6 P_1,3P_1,3P_1,3

P

v_1,3

1,3

OHϩHBr

••• ••• •••

0

1

2

3

•••

••• 22

48.9 38

41.4 32

14

42

36

8

53.1

35.5

10.9

0.5

8.9 13.2 10.4 8.4 4.5 3.5

16.9 17.7 3.9 2.9

6.5 3.1

9.6

7.5

b,d

P₂

30.4 33.1 15.4 12.1 5.2 4.0 •••

41.4 26.2 15.8 8.9 4.6 2.1 1.0

P^s₂^t

of the population in the _1,3ϭ1 level is evident from the

v

spectra at 1.0 and 1.2 Torr. These distributions conﬁrm that

vibrational relaxation by Ar is insigniﬁcant at р0.7 Torr and

⌬tр0.35 ms.

The vibrational distribution given in Table V for the OD

ϩHBr reaction is the same as presented in Ref. 15. This

distribution, which serves as the reference for direct abstrac-

tion, was conﬁrmed again from new spectra obtained in the

OHϩHI

••• ••• •••

11.7 11.3 11.7 12.2 6.9 2.8 1.6 58.3 27

11.1 8.3 2.0 3.2 0.6 0.2

4.4 4.4 3.9 2.1

1.2 0.4

0

1

2

3

4

•••

••• 54

42

34

15

9

35.3

34.2

20.6

8.3

25.4 12

14.8

1.4

7

0.6

0.8 1.7

b,d

P₂

24.9 22.3 18.7 18.9 9.3 3.9 2.0

31.9 22.9 16.2 11.1 7.2 4.6 5.9

P^s₂^t

present work. The HOD͑ ͒ distributions for reactions ͑2͒

v₃

e

OHϩGeH₄

••• ••• •••

11.5 13.6 12.7 14.6 4.4 2.8 0.7 60.2 34

and ͑3͒ in Table V are similar to the H O͑ ͒ distributions

v_1,3

2

0

1

2

3

•••

••• 44

33

47.0

36.0

14.6

2.3

in that they extend to the thermodynamic limits and decrease

40

21

6

with increase of ₃. The populations in ₃ϭ0 states were

v

10.7 9.6 4.1 4.1

6.3 4.8

31.4 17

8.4

5

b,d

P₂

24.5 25.7 18.5 21.0 5.7 3.6 0.9

38.5 25.0 16.0 9.8 5.6 3.0 2.2

TABLE IV. Vibrational distributions of H₂O from modeling the chemilu-

P^s₂^t

minescence spectra from OHϩGeH₄at different reactor pressures.^a

^aPopulation in _1,3ϭ0 is not considered.

v

^bPopulation in

ϭ0 is assumed to be equal to the population in ₃ϭ0 for

v

v₂

v_1,3

P

͑Torr͒

the similar reaction with OD.

0

1

2

3

4

5

у6

P_1,3

v_1,3

^cP_1,3͑0͒ from linear surprisal plots ͑model I prior͒.

^dBending distribution in

ϭ0 is assumed to be the same as in _1,3ϭ1.

v

v_1,3

0.34

1

2

3

11.4 13.7 12.5 14.5

4.2

1.0

2.8

60.1

29.8

10.1

^eStatistical distributions calculated for model I prior.

11.0 10.3

5.3 4.4

4.0

0.4

4.5

sented in the last four columns of Table III, normalized to

100% for different assignments of the P_1,3͑0͒ population; ͑a͒

P_1,3͑0͒ was not considered; ͑b͒ P_1,3͑0͒ was assumed to be

similar to the P₃͑0͒ that was experimentally determined from

the HOD distributions; ͑c͒ P_1,3͑0͒ was obtained from linear

surprisal plots. These experimental distributions are com-

pared to the calculated statistical distribution, P^s₃^t. Although

the vibrational distributions for reaction ͑1͒ were deduced

from new data, they are the same as given in Ref. 15 and

they are included here for convenient reference. The experi-

P₂

27.7 28.4 16.9 19.0

11.4 13.0 13.8 13.5

4.2

4.7

1.0

1.1

2.8

2.5

0.46

0.71

1.0

1

2

3

60.0

30.0

10.0

11.1

4.4

9.5

4.8

4.4

0.8

5.0

P₂

26.9 27.3 19.0 18.5

13.3 11.5 11.0 11.1

4.7

6.3

1.1

3.4

2.5

4.9

1

2

3

61.5

29.0

10.3

12.2

3.2

7.5

5.9

2.8

1.2

6.5

mental distributions decline with increasing

for both re-

v_1,3

extends to the ther-

P₂

29.0 24.9 15.0 17.6

16.9 16.0 12.6 11.5

6.3

2.3

3.4

2.8

4.9

3.1

actions ͑2͒ and ͑3͒, but the range of

v₂

level. The OHϩHI reaction

mochemical limit for each

v_1,3

1

2

3

65.0

25.9

9.0

has a more extended stretching distribution in agreement

with larger available energy, but the population of the

ground stretching state exceeds that from the GeH₄reaction,

according to both ͑b͒ and ͑c͒ assignments of P_1,3͑0͒. It is also

11.5

3.1

8.4

4.6

2.3

1.4

3.7

P₂

31.5 29.0 16.3 15.2

20.8 20.3 15.9 12.0

2.3

1.8

2.8

3.1

noteworthy that the population in the highest _1,3ϭ3 level

v

1.2

1

2

3

70.8

21.4

7.8

from reaction ͑3͒, which is within 0.79 of the energy limit, is

8.9

2.9

6.3

3.9

4.7

1.0

1.5

signiﬁcantly higher than the population in _1,3ϭ4 from reac-

v

tion ͑2͒, which has an energy equal to 0.7 of the thermo-

chemical limit. The maximum population for both reactions

P₂

32.6 30.5 21.6 13.5

1.8

is in the

ϭ1, ₂ϭ3 state. The global H₂O bending distri-

v_1,3

v

bution, P , was obtained by summation over all

states

^aPopulation in _1,3ϭ0 is not considered.

v

v_1,3

2

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5034

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

TABLE V. Vibrational distributions of HDO from reactions ͑1D͒, ͑2D͒, and ͑3D͒.

v₂

a

b

0

1

2

3

4

5

6

7

у8

P₃

P^s₃^t

v₃

ODϩHBr

3.5

0

1

2

3

2.6^c

6.7

12.5

2.9

2.3^c

5.9

9.7

2.8

3.7

6.3

7.1

0.1

6.1

4.9

2.0

4.1

2.3

0.9

1.7

0.3

0.8

•••

21.7

33.0

37.3

5.8

21.7

33.0

37.3

5.8

76.2

20.5

3.2

2.6

0.8

0.1

a

P_1,2

24.7

22.3

20.7

15.8

17.2

21.4

15.9

13.7

8.4

12.9

6.9

7.0

2.6

4.7

1.1

1.8

•••

0.4

st

P

1,2

ODϩHI

6.0

0

1

2

3

4

6.1^c

4.2

3.1

0.6

0.4

5.0^c

3.9

0.6

0.1

8.2

3.5

1.0

0.4

4.8

1.8

3.4

4.6

4.4

2.5

5.1

3.2

4.4

0.7

9.6

53.8

28.2

16.9

1.6

59

25

15

1.4

0.4

62.9

25.8

8.9

2.2

0.3

6.5

3.0

0.5

a

P_1,2

14.4

13.1

13.5

10.3

13.1

15.8

10.0

11.9

11.5

13.4

15.5

9.6

8.3

9.1

5.1

6.0

9.6

10.8

st

P

1,2

d

ODϩGeH₄

0

1

2

3

6.9^c

5.7

6.9

1.9

5.3^c

5.2

5.3

1.8

8.4

6.2

2.8

8.5

2.8

2.1

4.4

1.1

3.4

5.5

2.2

2.6

3.1

1.4

2.8

1.2

44.2

29.1

23.1

3.7

41

31

24

4

72.0

22.7

4.9

0.5

a

P_1,2

21.4

18.9

17.6

13.7

17.4

19.7

13.4

13.6

8.9

13.5

10.3

8.4

5.7

6.5

4.2

3.3

1.2

2.4

st

P

1,2

^aP₃͑0͒ from the simulation.

^bP₃͑0͒ from the linear surprisal plots ͑model I prior͒.

^cPopulation in dark ͑000͒ and ͑010͒ states obtained using the analogy to the populations in ͑000͒, ͑010͒, and

͑020͒ for statistical distribution ͑model I prior͒.

^dP^s₃^tand P are the statistical distributions calculated for model I prior.

st

1,2

obtained from modelling the ⌬␯₁ϭϪ1 plus ⌬␯₂ϭϪ2 emis-

sion, as shown in Fig. 2. Estimation of the population in

͑000͒ and ͑010͒ states was made by analogy with the relative

population of ͑000͒, ͑010͒, and ͑020͒/͑100͒ states in the sta-

tistical distribution. The statistical calculation gives 6.4, 5.3,

and 4.3ϩ4.3 as the relative populations for the ͑000͒, ͑010͒,

and ͑020͒ϩ͑100͒ levels, respectively, for the HI reaction and

11.0, 8.5, and 6.6ϩ6.6 for the GeH₄reactions. After know-

ing the population in ͑020͒ϩ͑100͒ level, the populations in

the ͑000͒ and ͑010͒ levels were estimated as 0.74 and 0.61 of

this value for HI, and 0.83 and 0.64 for GeH₄reactions. This

grated H₂O emission intensity from both reactions for con-

stant ͓OH͔. Comparison of the integrated total intensities in

the 3000–3900 cm^Ϫ1region was made for a range of reac-

tant concentration less than 3ϫ10¹³molecule cm^Ϫ3. Below

this reagent concentration, a linear dependence of the inten-

sity of the H₂O chemiluminescence on reagent concentration

was observed, as expected for a reaction following the

second-order differential rate law with constant ͓OH͔. Fur-

thermore, the shape of the spectra was unchanged, which

insured that the vibrational distributions were constant. Fig-

ure 3 shows the dependencies of the H₂O emission intensities

from the OHϩHBr and OHϩGeH₄reactions measured at 0.7

Torr. On average, the H₂O emission from GeH₄was 5.8

times stronger than that from HBr. The observed ratio should

be corrected to account for the populations of the nonemit-

gave a total of 53.8% and 44.2% for the population in ₃ϭ0

v

for reactions ͑2D͒ and ͑3D͒, respectively. The contrast be-

tween the inverted P₃distribution from the ODϩHBr reac-

tion and the declining distributions from HI and GeH₄should

be noted. Since they were obtained using exactly the same

methods, the difference should be reliable. The total popula-

ting _1,3ϭ0 level, which is 21% for HBr and 33% for GeH₄,

v

and for the distributions among the _1,3ϭ1, 2 and 3 states.

v

tions in a given

state, which were obtained by summa-

v_1,2

tion over the ₃number, are given in the bottom row as P_1,2

From the distributions, incorporating band strength coefﬁ-

cients from Table II, it follows that the intensity of the nor-

malized spectrum corresponds to 0.38S⁰_n͑␯ ͒ and 0.44S_n⁰͑␯ ͒

.

v

The populations in the ␯ levels extend to the energy limit

1,2

3

and the distributions are fairly close to the statistical popula-

tions.

for H₂O from GeH₄and HBr, respectively. Accordingly, the

ratio of the rate constants is k₃/k₁ϭ6.5Ϯ0.9. Taking

k₁ϭ1.1ϫ10^Ϫ11cm³molecule^Ϫ1s^Ϫ1, which is the recom-

C. Rate constant for the OH؉GeH₄reaction

1.7

mended value,¹we obtain k₃ϭ͑7.1Ϯ ͒ϫ10^Ϫ11cm³

1.0

The rate constant of reaction ͑3͒ was determined relative

to the rate constant of reaction ͑1͒ by measuring the inte-

molecule^Ϫ1s^Ϫ1. The lower error limit corresponds to the

standard deviations of the slopes in Fig. 3; the upper one

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

includes the uncertainty in the P_1,3͑0͒ for reaction ͑3͒ ͑Table

III͒. The GeH₄reaction appears to be one of the fastest

known reaction of hydroxyl radicals with a stable molecule.

The value for k₃agrees with the expected trend in rate

constants^1,44for OHϩCH₄, kϭ͑7.0Ϯ0.2͒ϫ10^Ϫ15and

OHϩSiH₄, kϭ͑1.2Ϯ0.2͒ϫ10^Ϫ11cm³molecule^Ϫ1s^Ϫ1, re-

ﬂecting the weakening of the H bond. A similar trend of

reactivity is observed for oxygen atoms; kϭ5.0ϫ10^Ϫ18

,

4.8ϫ10^Ϫ13

,

and kϭ3.2ϫ10^Ϫ12cm³molecule^Ϫ1s^Ϫ1for

OϩCH₄,⁴⁵SiH₄,⁴⁵and GeH₄͑Ref. 46͒ reactions, respec-

tively.

Reactions of both OH ͑or OD͒ and H atoms with GeH₄

also gave a relatively weak emission in the 1900–2200 cm^Ϫ1

range ͑see Fig. 4͒ with a maximum intensity at ϳ2110 cm^Ϫ1

.

This intensity attained 10% of the peak intensity of the H₂O

or HOD emission for high ﬂows of GeH₄. This peak matches

the Q-branch of the ␯ fundamental vibration ͑degenerate

3

Ge–H stretch, 2114 cm^Ϫ1͒ of the GeH₄molecule, as con-

cluded from comparison to the vibration-rotation absorption

spectrum.⁴⁷The frequencies of the GeH₃radical lie in a dif-

ferent range ͓␯₁ϭ1839, ␯₂ϭ928, ␯₃ϭ1813, ␯₄ϭ850 ͑Ref.

48͔͒ We suggest that the observed emission is a result of the

nearly resonant VϪV energy exchange process,

FIG. 3. Dependence of the integrated H₂O emission intensity from the

OHϩGeH₄and HBr reactions on reactant concentration for Pϭ0.7 Torr,

⌬tϭ0.35 ms, and ͓OH͔ϭ2.9ϫ10¹³molecule cm^Ϫ3

.

H₂O͑␯ ͒ϩGeH₄→H₂O͑␯ ͒ϩGeH₄͑␯ ͒Ϯ50 cm^Ϫ1

.

͑9͒

vibrational stretching distributions from Tables III and V,

and taking into account the correspondence between the sum

1,3

2

3

The ␯ ͑GeH₄͒ band strength in absorption,⁴⁹⌫ϭ14 300

3

intensities of the ₃fundamental bands of H₂O and HOD, we

v

cm²mol^Ϫ1, converted to the cgs esu system used in the HI-

obtain k_OH/k_ODϭ1.3Ϯ0.2, 1.0Ϯ0.2, and 1.4Ϯ0.1 for the re-

actions with HBr, HI, and GeH₄, respectively. The other

directly relevant secondary kinetic-isotope effect available

for comparison is k_OH/k_ODϭ1.55Ϯ0.15 for the reactions with

HCl,⁶which is close to our value for HBr. The secondary

kinetic-isotope effects are generally negligible for other H

atom abstraction reactions by OH/OD radicals ͓for example,

the CH₃OOH ͑1.02Ϯ0.10͒ ͑Ref. 50͒ and n-butane ͑0.97

Ϯ0.12͒ ͑Ref. 51͒ reactions͔.

TRAN, is equal to S⁰͓␯ ͑GeH₄͔͒Ϸ⌫␯₀/Aϭ5.17ϫ10^Ϫ17

␯

3

cm^Ϫ1/molecule cm², where ␯₀ϭ2113.6 cm^Ϫ1, Aϭ6.03ϫ10²³

molecule mol^Ϫ1. This S_v⁰value is 7.2 times larger than the ␯

3

.

band sum intensity of H₂O, 7.2ϫ10^Ϫ18cm^Ϫ1/molecule cm^Ϫ2

Taking into account the frequency difference ͓␯ ͑GeH₄͒

3

ϭ2110 cm^Ϫ1and ␯ ͑H₂O͒ϭ3756 cm^Ϫ1͔, the sum intensity

3

ratio for emission becomes equal to ϳ1.4. At 0.5 Torr, ⌬t

ϭ0.25 ms and ͓GeH₄͔ϭ1.5ϫ10¹²molecule cm^Ϫ3, the mea-

*

sured GeH₄to H₂O integrated intensity ratio is approxi-

mately 7ϫ10^Ϫ3, giving ͓GeH₄͔/͓H₂O ͔ Ϸ 0.01. For these

experimental conditions, about 1% of the water molecules

were deactivated by reaction ͑9͒, which corresponds to a rate

*

constant of the order of k₉ϳ3ϫ10^Ϫ11cm³molecule^Ϫ1s^Ϫ1

.

D. Secondary kinetic-isotope effects

The secondary kinetic-isotope effect for reactions ͑1͒–

͑3͒, i.e., the ratio of rate constants for the OHϩHR→H₂OϩR

and ODϩHR→HODϩR reactions, was estimated using the

same procedure as used in the previous section for the esti-

mation of the rate constant of reaction ͑3͒. The integrated

emission intensities of H₂O and HOD in the 3000–3900

cm^Ϫ1range were measured in the same experiment with ex-

change of equivalent H₂and D₂ﬂows with the same excess

͓NO₂͔. The average ratio of H₂O to HOD intensity was

I_{H O}/I_HODϭ 0.48 Ϯ 0.06 for HBr, 0.49Ϯ0.10 for HI, and 0.52

2

Ϯ0.04 for GeH₄in experiments at 0.7 ͑HBr͒ and 0.5 ͑HI and

GeH₄͒ Torr. The error limits are the standard deviations for

three ͑HBr and HI͒ and ﬁve ͑GeH₄͒ measurements with dif-

ferent reactant concentrations. Using the intensity relations

between the equilibrated emission bands from Table II, the

FIG. 4. Infrared chemiluminescence in the 1900–2100 cm^Ϫ1range from

GeH₄. ͑a͒ OHϩGeH₄reaction for the same conditions as for Fig. 1͑b͒ and

͓NO₂͔ϭ6.0; ͑b͒ HϩGeH₄reaction with ͓H͔ϭ3.0, ͓GeH₄͔ϭ1.1 ͑the concen-

trations are in units of 10¹³molecule cm^Ϫ3͒.

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

and 2.07Ϯ0.09 for HOD. As has been already determined,

the sum intensity of the ⌬␯₃ϭϪ1 spectra from HI are equal

to 0.42 S⁰_v͑␯ ͒ for H₂O and 0.67 S⁰_v͑␯ ͒ for HOD. For the

3

same distributions, the calculated sum intensity in the 4500–

5500 cm^Ϫ1range is equal to 0.74 S_v⁰͑␯₂ϩ␯ ͒ for H₂O and to

3

1.02 S⁰_v͑␯₂ϩ␯ ͒ and 0.17 S⁰_v͑2␯ ͒ for HOD. In this calcula-

3

1

tion, the intensity of the combined emission for the bands

with Ͼ1 and ₃Ͼ1 was assumed to follow the frequency

v₂

v

corrected harmonic approximation for the ␯ mode and the

3

simple harmonic approximation for the bending mode, be-

cause anharmonic coefﬁcients x₂₂are relatively small for

both H₂O and HOD. The calculated ratios of intensities are

I₃/I₂₃ϭ1.7Ϯ0.3 for H₂O and 9.0Ϯ1.3 for HOD; the agree-

ment is very good with the measured value for H₂O, but the

HOD value is 4.3 times larger than the experimental result.

Analogous calculations for the GeH₄spectra gave sum

intensities of 0.59 S⁰_v͑␯₂ϩ␯ ͒ for H₂O and 0.99 S_v⁰͑␯₂ϩ␯ ͒

3

and 0.15 S⁰_v(2␯₁) for HOD spectra in the 4500–5500 cm^Ϫ1

range, and ratios of I₃/I₂₃ϭ2.0Ϯ0.3 for H₂O and 11.4Ϯ2.3

for HOD. The measured ratios are I₃/I₂₃ϭ2.0Ϯ0.1 for H₂O

and 3.0Ϯ0.3 for HOD. In this case the agreement also is

excellent between the observed and calculated intensity ratio

for H₂O, but the calculated ratio exceeds the experimental

value by a factor of 3.8. The most likely reason for the dis-

crepancy with HOD is that the sum intensity

FIG. 5. Infrared chemiluminescence in the 4500–5500 cm^Ϫ1range from

combination and overtone emission from the OH and OD reactions with

GeH₄and HI. The experimental conditions are the same as for the experi-

ments described in Figs. 1 and 2.

S⁰_v͑␯₂ϩ␯ ͒ϭ3.67ϫ10^Ϫ23cm^Ϫ1/molecule cm^Ϫ2for HOD is

3

underestimated, and the real value is about 4 times larger. It

seems possible, since the above value was obtained from

only 576 lines identiﬁed in the band, while the ͑001͒ band of

HOD, and ͑001͒ and ͑011͒ bands of H₂O contain 1651, 1546,

and 1306 lines, respectively.²¹

E. Experimental chemiluminescent spectra:

4500–5500 cm^؊1range

Figure 5 shows the H₂O and HOD emission from reac-

tion ͑2͒ in the 4500–5500 cm^Ϫ1range, arising from the com-

Simulation of the H₂O spectra from reactions ͑2͒ and ͑3͒

in the 4500–5500 cm^Ϫ1range was made in a simpliﬁed man-

ner by red shifting the ͑011͒–͑000͒ band, which was calcu-

lated from the HITRAN absorption band, to the band centers

for transition from higher energy levels. The calculated H₂O

͑011͒–͑000͒ emission band is given in Fig. 5͑a͒ for refer-

ence. Using the distribution from Table III for the OHϩHI

reaction, we obtained the spectrum shown as the dotted

curve in Fig. 5͑b͒. For simulation of the HOD spectrum in

this range, the ͑011͒–͑000͒ and ͑200͒–͑000͒ HITRAN ab-

sorption bands were used in a similar way ͓see Fig. 5͑c͔͒.

The calculated spectrum for the ODϩHI reaction using the

distribution from Table V is shown in Fig. 5͑d͒. The contri-

bution of the ␯₁overtone emission intensity in this spectra is

about 6%. Although the model spectra do not reproduce all

the individual strong peaks, they ﬁt the general intensity pat-

tern in a satisfactory way and conﬁrm the vibrational distri-

butions given in Tables III and V.

bined ⌬ ϭϪ1ϩ⌬ ₂ϭϪ1 transition; this emission was

v₃

v

detectable from all three reactions. These spectra can be used

to check the intensity relations between the combination and

fundamental bands and to conﬁrm the vibrational distribu-

tions in Tables III and V. The HITRAN database gives val-

ues of S⁰_vϭ7.20ϫ10^Ϫ18and 8.04ϫ10^Ϫ19cm^Ϫ1/molecule

cm^Ϫ2for H₂O and S_v⁰ϭ1.42ϫ10^Ϫ21and 3.67ϫ10^Ϫ23

cm^Ϫ1/molecule cm^Ϫ2for HOD for the intensities of the

͑001͒ and ͑011͒ absorption bands, respectively.²¹The ratio of

the emission intensities, which are proportional to the cube

of the transition frequency, can be estimated using the band

center frequencies, 3756 and 5331 cm^Ϫ1for H₂O and 3707

and 5090 cm^Ϫ1for HOD, respectively, which gives

S⁰_v(␯₂ϩ␯₃)/S_v⁰(␯₃)ϭ0.32 for H₂O and 0.067 for HOD. The

4500–5500 cm^Ϫ1range also includes ͑110͒–͑000͒ emission

from H₂O ͑␯₀ϭ5235 cm^Ϫ1͒ and ͑200͒–͑000͒ emission from

HOD ͑␯₀ϭ5372 cm^Ϫ1͒. The absorption band sum intensity

for the former transition is only 3.72ϫ10^Ϫ20

cm^Ϫ1/molecule cm^Ϫ2͑Ref. 21͒ and can be neglected. How-

ever, the ﬁrst overtone transitions of ␯ from HOD are not

V. DISCUSSION

1

negligible, S_v⁰ϭ1.59ϫ10^Ϫ23cm^Ϫ1/molecule cm^Ϫ2, and they

were taken into consideration.

A. Reaction mechanisms

2

Let us at ﬁrst consider the emission spectra from the HI

reactions, which are shown in Fig. 5. The average ratio of the

integrated intensities of the antisymmetric stretch emission,

Reactions of OH͑X ⌸͒ radicals with HBr and HI pro-

ceed to give a single product, H₂O, without a potential en-

ergy barrier.¹However, complications exist in the entrance

2

I₃, and combined antisymmetric stretchϩbend emission, I₂₃

,

channel since AЈ and AЉ components of the potential sur-

2

obtained from ﬁve spectra are I₃/I₂₃ϭ1.75Ϯ0.45 for H₂O

face correlate to OH͑X ⌸͒. A similar complication exists on

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

the product side, since Br or I atoms can be formed in the

for excited rotational states of OH.^8,9This quantum calcula-

tion predicted a B^1/2dependence of the rate constant, where

B is the rotational constant of the OH molecule. Substituting

the B values of OH for OD gives a factor of 1.4 decrease of

the reaction rate in agreement with k_OH/k_ODϭ1.3Ϯ0.2 found

in the present work for reactions ͑1͒/͑1D͒. A lowering of the

OH reaction probability with rotational excitation also was

obtained by Nyman and Clary for the OHϩCH₄→H₂OϩCH₃

reaction using the rotating bond approximation,⁵⁶and the

isotope effect of k_OH/k_ODϭ1.4Ϯ0.1 for GeH₄may be asso-

ciated with a dependence of the reaction probability on rota-

tional state. On the other hand, the quasiclassical

calculations⁸for OH͑OD͒ with HBr did not give a consistent

isotope effect and the variational transition-state theory cal-

culations give a small inverse secondary kinetic-isotope ef-

fect. So, the origin of the secondary kinetic-isotope effect is

uncertain. The quantum and quasiclassical calculations for

potentials of the LEPS type give inverted H₂O and HOD

vibrational distributions for reaction ͑1͒. The extensive qua-

siclassical trajectory study⁸of the OH͑OD͒ϩHBr reaction

showed that the traditional viewpoint for H–L–H dynamics

for triatomic systems was applicable to the vibrational en-

ergy disposal to H₂O ͑HOD͒, providing that new dynamical

²P_1/2state, as well as the ground state. The lower energy ²AЈ

potential correlates to the ground state product. The possibil-

2

ity of formation of Br ͑ P_1/2͒ atoms was discussed before,¹⁵

*

and it was concluded to be unimportant. A search for

2

I͑²P_1/2→ P_3/2͒ emission was made in the HI experiments. A

single weak peak was detected in the vicinity of 7600 cm^Ϫ1

from reactions ͑2͒ and ͑2D͒. The peak height correlated with

the intensity of the H₂O and HOD emission and, hence,

2

could be attributed to emission from the I͑²P_1/2→ P_3/2͒ tran-

sition with ⌬Eϭ21.7 kcal mol^Ϫ1. The radiative transition

probability for this transition is 4.1 times weaker than the

S⁰_v͑␯ ͒ of HOD.⁵²The measured intensity ratio for the I and

*

3

HOD emission was of the order of ͑3–8͒ϫ10^Ϫ4from which

*

an upper limit of 0.03% may be set for the formation of I

relative to the ground state iodine atoms. Evidently, forma-

2

*

tion of the I ͑ P_1/2͒, either in the primary reaction or as a

result of V–E energy transfer, can be neglected for reactions

2

͑2͒ and ͑2D͒. We conclude that reaction occurs on the AЈ

potential.

A zero activation barrier for the reaction of OH with

GeH₄is implied by the large rate constant for H₂O formation

and from comparison with the OHϩCH₄͑Ref. 1͒ and SiH₄

͑Ref. 44͒ family of reactions with E_aϭ3.8 kcal mol^Ϫ1and

0.095 kcal mol^Ϫ1, respectively. In addition to H abstraction,

other product channels for the OHϩgermane primary reac-

tion could be GeH₃OHϩH ͑substitution͒ and GeH₃OϩH₂

͑addition/H₂elimination͒. Since enthalpy of formation and

bond energy data are available for only a few germanium

compounds, we estimated the H₃Ge–OH bond energy from

the reaction enthalpy of H₂GeO→H₂GeϩO͑³P͒, which is

aspects associated with excitation of the bending mode ͑␯ ͒

2

were added. The HI and GeH₄reactions initially were chosen

for study because we expected to display direct abstraction

dynamics for reactions with larger exoergicity. However, the

reactions of OH radical with HI and GeH₄give vibrational

distributions that decline with increasing energy in both the

stretch and the bend modes, indicating reaction dynamics

that differ from reaction ͑1͒. This conclusion rests heavily

108 kcal mol^{Ϫ1 53}

.

This bond is intermediate between ␲ and

semipolar bonding, and the two limiting estimates for the

bond strength are D₀͑H₃Ge–OH͒Ϸ77 and 54 kcal mol^Ϫ1

upon our ability to assign populations in the ₃ϭ0 and

v

_1,3ϭ0 levels. Since reactions ͑2͒ and ͑3͒ have been directly

v

compared to reaction ͑1͒, this conclusion seems valid. There-

fore, the reaction mechanism for HI and GeH₄must be more

complex than direct abstraction with H–L–H dynamics on a

LEPS type potential surface.⁴The surprisal analysis pre-

sented in the next section gives a more quantitative measure

of the difference between the energy disposal for HBr vs HI

and GeH₄reactions.

.

The former is the difference of GevO bond strength and a

value of 31 kcal mol^Ϫ1for the ␲-bond energy in

H₂GevCH₂;⁵³the latter is half of the Ge:O bond energy.

Both estimations give positive reaction enthalpies,

⌬H₀Ϸ͑5–28͒ and Ϸ͑3–26͒ kcal mol^Ϫ1for the substitution

and addition/H₂elimination channels, respectively. Even be-

ing in error by several kcal mol^Ϫ1, the thermochemistry rules

out alternative reaction pathways. However, two microscopic

channels for H₂O formation in reaction ͑3͒, direct abstraction

and addition-migration, may exist.

B. Surprisal analysis of H₂O and HOD vibrational

distributions

The rate constants ͑per H atom͒ increase in the HBr,

GeH₄, HI series and they are 1.1, 1.8, and 2.7ϫ10^Ϫ11

cm³molecule^Ϫ1s^Ϫ1, respectively. This trend resembles the

increase of reaction cross sections with the weight of

halogen^54,55for the OHϩX₂͑XϭF, Cl, Br, I͒ series of reac-

tions. This was explained by the decrease of the ionization

potential from F₂to I₂, and the subsequent ability of the

halogen molecule to form a radical-halogen bond.⁵⁴The 300

K rate constant for the direct abstraction OHϩHBr reaction

has been matched by quasiclassical⁸and quantum scattering⁹

calculations with Clary’s potential. A negative temperature

dependence of the OHϩHBr reaction was found in ultra-low

temperature experiments between 23 and 295 K.¹⁰A partial

explanation is provided by the reduced reaction probability

The information-theoretical approach to analysis of the

H₂O and HOD vibrational distributions was described in our

previous report of the OH͑OD͒ϩHBr͑DBr͒ reactions.¹⁵The

priors for reactions ͑2͒, ͑2D͒ are the same as ͑1͒, ͑1D͒. How-

ever, the OH͑OD͒ϩGeH₄reaction needs a different formu-

lation for calculation of the prior vibrational distributions,

since the other reaction product is a polyatomic radical,

which can accumulate energy in its internal degrees of free-

dom. Three models were used in which GeH₃was treated as

an atom ͑I͒, a rotating symmetric top ͑II͒, and a symmetric

top with 6 vibrations ͑III͒ grouped as follows: 2110͑3͒, 931,

819͑2͒ for calculation of the prior distribution.

The surprisal plot for the experimental HOD stretch dis-

tribution from ODϩHI is presented in Fig. 6͑a͒. The variable

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

The three plots for GeH₄in Figs. 6͑a͒ and 6͑b͒ corre-

spond to different models of the prior for GeH₃͑circles, I;

upward triangles, II; and downward triangles, III͒. The sur-

prisal plots for HOD ͑P_v3͒ are remarkably linear with slopes

␭_v3ϭϪ3.5, Ϫ5.4, and Ϫ10.8, respectively. The renormalized

₃ϭ0 populations, obtained from the intersection of these

v

linear plots with the ordinate, are 0.41, 0.34, and 0.24, re-

spectively. The former value agrees with the measured popu-

lation, ϳ44%, while models II and III seem to give values

that are too low. This suggests that GeH₃does not participate

in the dynamics or, at least, does not receive much internal

energy. The slopes of the surprisal plots for H₂O ͑P_1,3͒ are

␭

_v1,3ϭϪ1.5 ͑model I͒, Ϫ3.7 ͑model II͒, and Ϫ9.8 ͑model

III͒, and the corresponding renormalized populations of the

_1,3ϭ0 state are 0.33, 0.25, and 0.15. As for HOD, the clos-

v

est value to the P ( ₁₃ϭ0)ϭ0.44 population selected in

v

13

Table III for H₂O is obtained from model I as a prior.

Let us consider more deeply the assignment of P_1,3͑0͒ in

reactions producing H₂O. The initial release of energy is to

the local mode of the new bond and the old O–H bond is

mainly expected to play a spectator role. Since a local H₂O

stretch mode is an equal mixture of symmetric and antisym-

metric normal modes, the P₃͑0͒ population observed for the

O–H mode of HOD also corresponds to the P_1,3͑0͒ for H₂O.

If the old O–H bond is a perfect spectator with a local dis-

FIG. 6. Surprisal plots for vibrational stretching distributions ͑a͒ HOD from

the ODϩGeH₄and HI reactions; ͑b͒ H₂O from the OHϩGeH₄and HI re-

actions.

tribution of 100% in ϭ0, the whole P_1,3distribution would

v

coincide with the P₃distribution of HOD. If, on the other

hand, the old bond receives some energy, the resulting P_1,3

distribution can be obtained as a product of two local distri-

is the fraction of the available energy in a certain O–H

stretching level of HOD, so that f_v3ϭ1 corresponds to the

thermochemical limit. The surprisal for reaction ͑2D͒ has a

very small slope, ␭_v3Ϸ0, although the points are scattered.

butions. In this case, the statistics for

and

are differ-

v_1,3

v₃

ent, and P_1,3͑0͒ is only the fraction of P₃͑0͒ that corresponds

to P₁͑0͒. Suppose that the old bond receives a statistical

fraction of the reaction energy. For the OHϩHBr reaction

The population in ₃ϭ0 of 0.59 obtained from the zero slope

v

surprisal actually agrees with the P₃ϭ0.54 value from the

spectral simulation. The surprisal parameter for reaction ͑2D͒

is very different from reaction ͑1D͒, which is also linear but

with ␭_v3ϭϪ6.1. The analogous surprisal plot for OHϩHI

reaction is shown in Fig. 6͑b͒; the variable f_v1,3denotes the

fraction of the reaction available energy in a given

with E_avϭ33.5 kcal mol^Ϫ1

,

the statistical probability

old

new

local

P

͑0͒ϭ0.74 and, if P ͑0͒ϭP₃͑HOD͒ϭ0.22, the com-

local

bined P_1,3͑0͒ϭ0.16. This is very close to the P_1,3͑0͒ϭ0.14

value obtained from the surprisal plot.

For the OHϩHI reaction with E_avϭ49.8 kcal mol^Ϫ1, we

old

have P ͑0͒ϭ0.62 from the statistical calculations. If this is

ϭ

ϩ

state. The surprisal plot for H₂O ͑P_1,3͒ from HI

v_1,3v₁v₃

local

new

local

combined with the P₃distribution from HOD taken as P

,

may be considered as linear with a slope close to zero, al-

though the best ﬁt corresponds to ␭_v1,3ϭ0.9. The plus sign of

the surprisal slope means that the higher vibrational states

have a smaller population than the prior distribution. The

the resulting P_1,3͑0͒ is 0.36. This P_1,3͑0͒ value, as well as the

combined P_1,3distribution as a whole, is rather close to the

c

P_1,2distribution from Table III with P_1,3͑0͒ϭ0.42 from the

linear surprisal plot. For the OHϩGeH₄reaction with

␭

value, which is a global measure of the energy release

v1,3

E_avϭ38.4 kcal mol^Ϫ1

,

the statistical population is

to

levels, may be compared with ␭_v1,3ϭϪ4.5 for the

v_1,3

OHϩHBr reaction and the surprisal analysis identiﬁes a dif-

old

P

͑0͒ϭ0.70, and the combined ground stretching state

local

fraction is P_1,3͑0͒ϭ0.29, which again in a good agreement

with the linear surprisal result of 0.33 from model I. These

ﬁndings support the concept of a partial energy release to the

old O–H bond in reactions ͑1͒–͑3͒, and, consequently, the

ference in the dynamics of these reactions. The P ( ₂) dis-

v

2

tribution of H₂O given in Table III can be compared to

P^si͑ ͒. A very slight overpopulation in the ₂ϭ2–4 levels

v₂

v

2

seems to exist, relative to the statistical limit. The overall

c

distributions labeled P_1,2in Table III seem to be more reli-

f

value for the HI reaction is 0.41 ͑HOD͒ and 0.36 ͑H O͒

͗

͘

v

2

b

able than those labeled P_1,2

.

vs 0.65 ͑HOD͒ and 0.61 ͑H₂O͒ for the HBr reaction. The

energy disposal pattern clearly shows that the dynamics for

the HBr and HI reactions are quite different. The most likely

explanation is that the OH radical initially attacks the I atom

end of HЈI, then the HЈ atom migrates to the oxygen atom

and H₂O is ejected; the HI reaction is not a direct process in

contradistinction to the HBr reaction.

C. Vibrational energy disposal and comparison with

X؉HBr, HI, and GeH₄(X

؍

F, Cl, and O) reactions

The vibrational distributions of the HF, HCl, and OH

products from the reactions of F, Cl, and O͑³P͒ atoms with

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5039

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

TABLE VI. Comparison of energy disposal for the OH͑OD͒ϩHR

→H₂O͑HOD͒ϩR and XϩHR→HXϩR ͑RvBr, I, GeH₃; XvF, Cl, O͒

reactions.^a

tional mode connected most directly to the reaction coordi-

nate. The values of the mean total vibrational energy, E

the mean fraction of the available energy released as HOD

,

͘

͗

v

vibrational energy, , and the fraction of energy in the

O–H stretch mode relative to the total vibrational energy,

f

͗

͘

͗E_av

͘

v

kcal mol^Ϫ1

f

͘

v

E_v_s/E_v

Ϫ␭

b

c

Reaction

͗

␯n

E

/ E , are given in Table V for reactions ͑1D͒–͑3D͒.

͗

͘ ͗

͘

v

3v

OHϩHBr

ODϩHBr

OHϩHI

ODϩHI

OHϩGeH₄

ODϩGeH₄

FϩHBr

ClϩHBr

OϩHBr

FϩHI

ClϩHI

OϩHI

FϩGeH₄

ClϩGeH₄

OϩGeH₄

33.7

33.1

49.8

49.2

38.4

37.8

51.0

18.2

22.0

67.2

34.4

35.4

62.6

30.0

0.61

0.65

0.36

0.41

0.46

0.51

0.60

0.38

0.51

0.55

0.64

0.56

0.50

0.24

0.46^e

0.30

0.61

0.46

0.31

0.41

0.48

4.5

6.1

Ϫ0.9

0.2

1.5–3.7

3.5–5.4

5.7

The ODϩHI reaction has

E

ϭ20.0 kcal mol^Ϫ1, which

͘

v

͗

when compared with the available energy of 49.2

kcal mol^Ϫ1, gives

f

ϭ0.41; the energy released speciﬁ-

͗

͘

v

cally to the O–H mode is

sponding to E / E ϭ0.31. These values are smaller than

the corresponding values for the ODϩHBr reaction,

E

ϭ6.2 kcal mol^Ϫ1, corre-

͘

3v

͗

͘ ͗

͘

3v

v

3.0

f

ϭ0.65 and E / E ϭ0.61. The ODϩGeH reaction

͗

͘

͗

͘ ͗

͘

v

3v

4

is an intermediate case; the E is 19.4 kcal mol^Ϫ1and the

4.4

6.2

•••^d

5.5

2.7

3.4

͗

͘

v

available energy is 37.8 kcal mol^Ϫ1, which gives f ϭ0.51.

͗

͘

v

The energy in the O–H vibration is ͗E_3vϭ9.3 kcal mol^Ϫ1

,

͘

corresponding to E / E ϭ0.48. The greater release of

energy to

v₁v₂

tively͔ rather than to

The fraction of the total vibrational energy released to

H₂O is nearly the same as for HOD, but the speciﬁc energy

release to the new bond is masked by mixing with the local

mode of the old O–H bond. The OHϩHI reaction with a

͗

͘ ͗

͘

3v

v

ϩ

͓0.69 and 0.52 for ͑2D͒ and ͑3D͒, respec-

should be noted.

v₃

^aReference 15 for OH͑OD͒ϩHBr and Refs. 11, 12, 58 for the atomic reac-

tions.

^bsϭ2 ͑␯ mode͒ for OH and sϭ3 ͑␯ mode͒ for OD reactions.

2

3

^cnϭ1,3 ͑␯ mode͒ for OH and nϭ3 ͑␯ mode͒ for OD reactions.

1,3

3

^dNonlinear surprisal if the experimental value is used for P͑0͒; however,

OH͑ ϭ0͒ may have a contribution from formation of I͑²P ͒ atoms.

v

1/2

^eIf the P(1)/P(0) from Ref. 58 is used, the

f

increases to 0.53.

͘

v

distribution extending to _1,3ϭ4, demonstrates a reduction of

v

͗

vibrational energy;

E f ϭ0.36,

ϭ17.9 kcal mol^Ϫ1and

͘ ͗ ͘

v v

͗

compared to E ϭ20.6 kcal mol^Ϫ1and

f ϭ0.61 for the

͘

v

͗

͘

͗

v

GeH₄, HI, and HBr have been studied by infrared

OHϩHBr reaction. This vibrational disposal to H₂O is

57,58

chemiluminescence^11–14and laser-induced ﬂuorescence

slightly less than the statistical limit, f ^stϭ0.38, for reac-

͗

͘

v

methods. The f and Ϫ␭ values are compiled in Table VI.

tion ͑2͒. The energy in just the bending mode of H O, E

,

͘

v2

͗

͘

͗

v

2

All reactions displayed inverted HX( ) distributions. In the

can be assigned for the OH reactions. The

E

is 8.2

v

͗

͘

v2

case of the OϩHI reaction, the P͑0͒ population of OH was

higher than P͑1͒, as obtained by laser-induced ﬂuorescence

experiments.¹⁴If the P͑0͒ point is ignored, the distribution

gives a linear surprisal plot. The F atom reactions all give

kcal mol^Ϫ1for HI reaction, which corresponds to

/ E ϭ0.46. This value slightly exceeds the statistical

E

͗

͘ ͗

͘

v

v2

fraction f / f ^stϭ0.41 and the HI reaction has the high-

͘ ͗

͗

͘

v2

v

est fraction for bending excitation of the three reactions. The

mean vibrational energy for the OHϩGeH₄reaction, using

the P_1,3͑0͒ϭ0.33 deduced from the linear surprisal plot, is

similar results with

f ϭ0.5–0.6, and they are prototypes

͘

v

͗

for the H–L–H class of dynamics. The Cl atom results are

more varied, but care must be taken in the interpretation of

the HBr reaction because of the small available energy. Al-

though the rates are much slower, the results for O͑³P͒ atoms

resemble those from F atoms with ͗f_v͑OH͒͘Ϸ0.5. The linear

vibrational suprisal and the f value for O͑³P͒ϩGeH₄are

equal to

E

ϭ17.7 kcal mol^Ϫ1, and

f ϭ0.46. This is

͗ ͘

v

͗

͘

v

larger than the statistical value for model

I

prior,

f

E

^stϭ0.35. The energy in the bending vibrations is

͗

͘

v

ϭ7.3 kcal mol^Ϫ1, corresponding to E / E ϭ0.41;

͘ ͗

͘

͗

͘

v

v2

the statistical value is

f

/ f ^stϭ0.44 for model I prior.

͗

͘

͗

͘ ͗

͘

v

v2

v

consistent with direct abstraction. The nonstatistical OH

␭-doublet population from GeH₄has been interpreted as evi-

dence for an insertion component.⁵⁸However, the low P͑0͒

yield and the difﬁculty of interpretation of ␭-doublet

distributions⁵⁷in low J levels make this claim less than cer-

tain. The highly inverted vibrational distributions from the

O͑³P͒ϩHBr and HI reactions are reproduced by quasiclassi-

cal trajectory calculations⁵⁹and they can be understood in

terms of a direct abstraction mechanism for a H–L–H mass

An interesting feature is the growing fraction of bending en-

ergy, E / E ϭ0.30, 0.41, and 0.46 for the HBr, GeH ,

͗

͘ ͗

͘

v

v2

4

and HI series. This pattern is consistent with a growing com-

ponent for an addition-migration reaction mechanism.

In summary, the

f

values for reactions ͑1͒–͑3͒ de-

͘

͗

v

crease from a maximum of 0.61–0.65 for HBr, to an inter-

mediate value, 0.46–0.50, for GeH₄, and, to the nearly sta-

tistical limit of 0.42–0.43 for the HI reaction. A direct

comparison of the energy disposal into the newly formed

combination. The similarity of

f

values for OH͑OD͒

bond is provided by E / E from reactions of the OD

͘ ͗

͗

͘

͗

͘

v

v3

v

ϩHBr and FϩHBr reactions has previously been noted,¹⁵

and this is why the OH͑OD͒ϩHBr is taken as the reference

reaction for direct H atom abstraction by OH radicals. In the

paragraphs below, the energy disposal and dynamics are

summarized for OH͑OD͒ϩHI and GeH₄.

radical. The major part of the vibrational energy, 61%, is

concentrated in the new bond by the HBr reaction, indicating

the high speciﬁcity of the vibrational energy release. For

GeH₄some speciﬁcity holds with nearly half of the vibra-

tional energy in the new bond. But for HI, E / E is

͘ ͗

͗

͘

v3

v

We shall ﬁrst consider reactions of OD, because the P₃

distributions describe the energy disposal to the O–H vibra-

equal to the statistical limit of one third. The trend of the

average values is augmented by the surprisal analysis, where

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N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

Ϫ␭ values serve as a measure of deviation from the statis-

distributions of H₂O and HOD were obtained by computer

simulation of spectra in the 2400–3900 cm^Ϫ1range. The

spectroscopic simulation for H₂O incorporates the exact line

positions for the transitions from levels with E_vр18 000

cm^Ϫ1͑51 kcal mol^Ϫ1͒. The H₂O emission from the combina-

v3

tical distribution. The ␭ values are Ϫ6.1, Ϫ3.1, and ϳ0 for

v3

the HBr, GeH₄, and HI reactions, respectively. As the energy

release to the new bond declines, the energy in the bending

mode increases for these three reactions. We are forced to

conclude that in spite of the zero activation energy, the pre-

ferred characteristic reaction pathways differ for OH radicals

with HBr, HI, and GeH₄. Evidently, obtaining a microscopic

understanding of H atom abstraction reactions by OH radi-

cals from various reagents will be more difﬁcult than for F,

Cl or O atom reactions.

tion ␯₂ϩ␯ bands in the 4500–5500 cm^Ϫ1range also was

3

observed; the relative intensity was consistent with the sum

intensity for ͑011͒ band strength given in HITRAN database.

However, a serious disagreement, about a factor of 4, was

found between the predicted intensity of the HOD ͑011͒

band from the HITRAN database relative to the experimental

intensity.

In retrospect different dynamics for the HBr and HI re-

actions is not surprising in view of the ability of molecules

containing iodine to form complexes with OH radicals^54,55

and O atoms.^60–62At low initial translational energy, 3.8

The fraction of the available energy released as H₂O and

HOD vibrational energy decreased from 0.65 to 0.41 for the

HBr, GeH₄, and HI series, despite the increasing exothermic-

ity and rate constants in the series. The stretching vibrational

distribution of H₂O͑HOD͒ was inverted for the HBr reaction

in accord with expectation for a direct abstraction reaction.

The vibrational energy distribution decreased with increasing

E_v, but was still nonstatistical, for the GeH₄reaction, and

the distribution was nearly statistical for the HI reaction. Sur-

prisal analysis of the vibrational distributions indicated a de-

cline in the speciﬁc energy release into the newly formed

O–H bond for the HBr, GeH₄, and HI series of reactions.

Conversely, the release of energy to the bending mode, ␯₂,

increased in the series. The speciﬁc features of the vibra-

tional distributions from the OH/OD reactions with HBr,

GeH₄, and HI permitted the assignment of the mechanisms

as direct abstraction in the former case and addition-

migration in the latter. The reaction with germane may pro-

ceed by both pathways or, less likely, the direct abstraction

mechanism has a potential surface that favors excitation of

the bending mode, rather than the stretch modes, of water.

Based on these three examples, the energy disposal to

H₂O͑HOD͒ from OH radical reactions is much more varied

than for analogous reactions of F, Cl or O atoms.

kcal mol^Ϫ1

,

both IO and HOI products from the

O͑³P͒ϩC₂H₅I reaction emerge from the OIC₂H₅complex, as

has been shown in crossed molecular beam experiments.^61͑a͒

The formation of the HOI product arises from the OIC₂H₅

complex through a ﬁve-centered ring transition state in

which the H atom migrates to the oxygen from the terminal

CH₃group. Vibrationally hot HOI formed via a ﬁve-centered

transition state was also observed as a product from

O͑³P͒ϩC₂H₅I, nϪC₃H₇I, ͑CH₃͒₂CHI, and ͑CH₃͒₃CI

reactions.^60,61HOI was a major product of the OHϩI₂reac-

tion, and it was also detected in the OHϩCH₃I and CH₂I₂

chemical systems by observation of the O–H stretch and

bend modes of HOI via a FTIR technique.⁶²The absence of

the

HOBr

product

from

the

exoergic

O͑³P͒ϩC₂H₄Br₂→HOBrϩC₂H₃Br reaction was explained

by the location of the ﬁve-centered transition state in the exit

valley of the potential energy surface, which is inaccessible

to collisions with a low initial translational energy.^61͑b͒The

nearly statistical vibrational distribution of H₂O from

OHϩHЈI suggests the formation of a HO–I–HЈ complex

with subsequent migration of the HЈ atom via a three-

centered transition state to give H₂O. Migration of a H atom

initially bound to the I atom has been observed in

HϩIF͑ICl͒→HF͑HCl͒ϩI reaction, as a second microscopic

channel in addition to the direct reaction.⁶³

ACKNOWLEDGMENT

This work was supported by the National Science Foun-

dation of the USA, CHE-9505032.

Additional information is needed before a ﬁrm decision

can be made about the dynamics for the GeH₄reaction. Pos-

sibly the mechanism is a mixture of direct abstraction and

addition-elimination pathways. Trajectory calculations⁸for

the OHϩHBr reaction illustrated a difﬁculty for understand-

ing the mechanism that was responsible for releasing ad-

equate amounts of energy into the water bending mode.

Finding a potential energy surface that would give even a

APPENDIX: CALCULATION OF F FACTORS

The intensity of a rotation-vibrational line in absorption

may be expressed^40,41by

Iϭ ␯/␯ ͒S⁰Lg exp ϪE /kT͒F/Q ,

͑A1͒

͑

Љ

0

R

␯

where S⁰is the vibrational band strength, L is the rigid rotor

␯

higher f

in a direct abstraction reaction for OHϩGeH₄

͘

͗

2v

transition intensity, EЉ is the lower state rotational energy, g

is the statistical weight of the lower level, Q_Ris the rota-

tional partition function, and F is the F factor. The ﬁrst-order

general expression for the F factor is

would be a difﬁcult challenge.

VI. CONCLUSIONS

2

Fϭ 1Ϫ U␦ J²ϩW␦E ␬͒

,

͑A2͒

͓

͑

͔

͕

͗

͘

͖

The vibrational excitation of the H₂O and HOD mol-

ecules formed in the reactions of OH͑X ⌸͒ and OD ͑X ⌸͒

radicals with HBr, GeH₄, and HI have been studied via

analysis of the infrared chemiluminescence accompanying

these reactions in a fast-ﬂow reactor at 300 K. Vibrational

where ␦͗J²͘ is the difference of J(Jϩ1) for the upper and

lower levels, and ␦E(␬)ϭEЈ(␬)ϪEЉ(␬). Here ␬ϭ(2BϪA

ϪC)/(AϪC) is the asymmetry parameter and E(␬) is a

term in the energy expression for a rigid asymmetric rotor.

2

J. Chem. Phys., Vol. 106, No. 12, 22 March 1997

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5041

N. I. Butkovskaya and D. W. Setser: Reactions with HI and GeH₄

The constants U and W for the fundamental band of the

⁵D. Husain, J. M. Plane, and N. K. H. Slater, J. Chem. Soc. Faraday Trans.

2 77, 1949 ͑1981͒.

antisymmetric mode are given by the expression⁴⁰

⁶I. W. M. Smith and M. D. Williams, Chem. Soc. Faraday Trans. 2 82,

1043 ͑1986͒.

U ϭ ␣^xxϩ␬␣^yy͒/ 1ϩ␬͒, W ϭ ␣^xxϪ␣^yy͒/ 1ϩ␬͒,

͑

3

⁷B. D. Cannon, J. S. Robertshaw, I. W. M. Smith, and M. D. Williams,

Chem. Phys. Lett. 105, 380 ͑1984͒.

͑A3͒

where and a^x₃^xand a₃^yyare deﬁned by

⁸B. Nisamov, D. W. Setser, H. Wang, G. H. Peslhersbe, and W. L. Hase, J.

Chem. Phys. 105, 9897 ͑1996͒.

a³_xz

1/2

⁹D. C. Clary, G. Nyman, and R. Hernandez, J. Chem. Phys. 101, 3704

͑1994͒.

2B

2A

␣^xxϭϪ␮ / 2␮ ͒

͑A4͒

͑

ͩ ͪ

0

3

1/2

3

␻˜

3

I

¹⁰I. R. Sims, I. W. M. Smith, D. C. Clary, P. Bocherel, and B. R. Rowe, J.

Chem. Phys. 101, 1748 ͑1994͒.

3

xx

and

¹¹B. S. Agrawalla and D. W. Setser, in Gas-Phase Chemiluminescence and

Chemi-Ionization, edited by A. Fontijn ͑Elsevier, Amsterdam, 1985͒, p.

157.

y

13

␨

␻˜

₃2C

␮ ␻˜

1 1

␣₃^yyϭ

ͫ

2

3

1/2

␻

˜

²₁Ϫ␻

˜

͒

¹²B. E. Holmes and D. W. Setser, in Physical Chemistry of Fast Reactions,

edited by I. W. M. Smith ͑Plenum, New York, 1980͒, Vol. 2, p. 83.

¹³B. S. Agrawalla, A. S. Manocha, and D. W. Setser, J. Phys. Chem. 85,

2873 ͑1981͒.

␮

␻˜ ␻˜

1

͒

͑

3

y

␨

␮ ␻˜

2

23

ϩ

ͬ

2

3

1/2

␻˜

²₂Ϫ␻

˜

͒

␻˜ ␻˜

͒

͑

2 3

͑

¹⁴B. S. Agrawalla and D. W. Setser, J. Chem. Phys. 86, 5421 ͑1986͒.

¹⁵N. I. Butkovskaya and D. W. Setser, J. Phys. Chem. 100, 4853 ͑1996͒.

¹⁶A. Lloret, M. Oria, B. Seoudi, and L. Abouaf-Marguin, Chem. Phys. Lett.

179, 329 ͑1991͒.

y

23

1/2

␮ ␨

␻˜

2C ␻

˜

␻˜

͒

͑

2

3

2

3

Ӎ

.

͑A5͒

2

3

²₂Ϫ␻

˜

͒

␮

͒

͑

␻˜

͑

3

17

͑a͒ J. Berkowitz, G. B. Ellison, and D. Gutman, J. Phys. Chem. 98, 2744

Here, z₁^y₃and z₂^y₃are the Coriolis constants, ␻ is the funda-

͑1994͒; ͑b͒ M. J. Almond, A. M. Doncaster, P. N. Noble, and R. Walsh, J.

Am. Chem. Soc. 104, 4717 ͑1982͒; ͑c͒ B. Ruscic, M. Schwarz, and J.

Berkowitz, J. Chem. Phys. 92, 1865 ͑1990͒.

s

mental frequency of the sth mode and m_sϭ

ץ

m/

ץ

q_sis the

dipole derivative relative to the normal coordinate q_s. For

the water molecule the ﬁrst term in brackets in Eq. ͑A5͒ is

much smaller than the second one due to the smaller Coriolis

coupling ͑z₁^y₃ϭϪ0.005518; z₂^y₃ϭϪ0.9996͒ and dipole de-

rivative ͑m₁ϭ0.0239; m₂ϭ0.171͒, and it can be neglected

despite the smaller denominator.

18

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Dynamics of OH and OD radical reactions with HI and GeH4 as studied by infrared chemiluminescence of the H2O and HDO products

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