Energy-dependent cross sections and nonadiabatic reaction dynamics in F(2P3/2,2P1/2) + n - H2→HF(v,J) + H

Energy-dependent cross sections and nonadiabatic reaction dynamics in F ( 2 P 3/2 , 2

P 1/2 )+n– H 2 HF (v,J)+ H

Sergey A. Nizkorodov, Warren W. Harper, William B. Chapman, Bradley W. Blackmon, and David J. Nesbitt

Citation: The Journal of Chemical Physics 111, 8404 (1999); doi: 10.1063/1.480182

View online: http://dx.doi.org/10.1063/1.480182

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 111, NUMBER 18

8 NOVEMBER 1999

Energy-dependent cross sections and nonadiabatic reaction dynamics

2

in F„ P_3/2,²P_1/2…؉n–H₂˜HF„v,J…؉H

Sergey A. Nizkorodov, Warren W. Harper, William B. Chapman, Bradley W. Blackmon,

and David J. Nesbitt^a)

JILA, University of Colorado and National Institute of Standards and Technology,

and Department of Chemistry and Biochemistry, University of Colorado, Boulder,

Colorado 80309-0440

͑Received 1 June 1999; accepted 13 August 1999͒

High-sensitivity direct IR laser absorption methods are exploited to investigate quantum

state-resolved reactive scattering dynamics of Fϩn-H (jϭ0,1)→HF( ,J)ϩH in low-density

v

2

crossed supersonic jets under single collision conditions. Nascent rotational state distributions and

relative cross sections for reactive scattering into the energetically highest HF ( ϭ3,J) vibrational

v

manifold are obtained as

a function of center-of-mass collision energies from E_com

ϭ2.4 kcal/mole down to 0.3 kcal/mole. This energy range extends substantially below the

theoretically predicted transition state barrier ͓E_barrierϷ1.9 kcal/mole; K. Stark and H. Werner, J.

Chem. Phys. 104, 6515 ͑1996͔͒ for the lowest adiabatic F(²P_3/2)ϩH₂potential energy surface,

2

*

therefore preferentially enhancing nonadiabatic channels due to spin–orbit excited F ( P_1/2

)

(⌬E_spin–orbitϭ1.15 kcal/mole) in the discharge source. The HF ( ϭ3,J) cross sections decrease

v

gradually from 2.4 kcal/mole down to the lowest energies investigated (E_comϷ0.3 kcal/mole), in

contrast with exact adiabatic quantum calculations that predict a rapid decrease below E_com

Ϸ1.9 kcal/mole and vanishing reaction probability by E_comϷ0.7 kcal/mol. Further evidence for a

2

*

nonadiabatic F ( P_1/2) reaction channel is provided by nascent rotational state distributions in HF

( ϭ3,J), which are Ͼ2–3-fold hotter than predicted by purely adiabatic calculations. Most

v

dramatically, the nascent product distributions reveal multiple HF ( ϭ3,J) rovibrational states that

v

would be energetically inaccessible from ground state F(²P_3/2) atom reactions. These quantum state

resolved reactive scattering studies provide the ﬁrst evidence for ﬁnite nonadiabatic dynamics

involving multiple potential energy surfaces in this well-studied ‘‘benchmark’’ FϩH₂reaction

collision energies ͑Fig. 1͒.^6–8Thus, a detailed study of reac-

I. INTRODUCTION

tive cross sections versus center-of-mass collision energy can

begin to elucidate the importance of nonadiabatic ͑i.e., mul-

tisurface͒ versus adiabatic ͑i.e., single surface͒ contributions

to the reaction dynamics.

The FϩH₂reaction system has represented an important

focus of chemical dynamics research for several decades.^1–4

This reaction has several features that make it both particu-

larly interesting and chemically challenging. First of all, it is

The body of existing experimental and theoretical

knowledge about the FϩH₂system is extensive. From the

experimental side, the temperature-dependent reaction rate

constants,^9–12Arrhenius activation energies,⁴cross

sections,^13–18and product partitioning of rotational/

vibrational energy^19–24are available from a number of

sources. In particular, early ‘‘arrested relaxation’’ experi-

ments in the Polanyi group^2,19played a major role in our

understanding of the FϩH₂reaction, as well in developing

extremely useful models of atomϩdiatom reaction dynamics,

in general. Crossed molecular beam studies in the Lee group

by Neumark et al.^13,14,25have provided an enormously rich

source of experimental information about relative cross sec-

tions and vibrationally resolved HF product angular distribu-

tions at selected center-of-mass collision energies. More re-

cently, Faubel, Toennies, and co-workers have succeeded in

measuring improved differential cross sections for the FϩD₂

isotopic variant of the reaction,^26–32as well as for inelastic

scattering of F atoms by both H₂and D₂,^15,33with substan-

tially enhanced energy and angular resolution. Based on a

highly exothermic ⌬Eϭ32.001(14) kcal/mol , which leads

to subsequent energy dispersal into many vibrational and ro-

tational states of the HF products. Indeed, this reaction leads

͓

͔

to a highly vibrationally inverted HF( р3) product distri-

v

bution, which has long been exploited as an efﬁcient pump-

ing mechanism for HF chemical lasers.⁵Additionally, the

reaction proceeds over a low activation barrier (E_act

Ϸ1.6 kcal/mole)⁴and is therefore quite rapid under room

temperature conditions. Most importantly, the presence of

unpaired electrons in the F atom reagent results in multiple,

closely spaced potential energy surfaces on which the reac-

tion can proceed, asymptotically correlating with different

projections of the total electron spinϩorbital angular mo-

mentum along the intermolecular axis. This proves espe-

cially relevant in the present work, since in the Born–

Oppenheimer approximation, only reactions that remain on

the lowest adiabatic surface should be accessible at these

a͒

Electronic mail: djn@jila.colorado.edu

0021-9606/99/111(18)/8404/13/$15.00

8404

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nonadiabatic reaction dynamics

8405

line tunable HF chemical lasers and optothermal detection to

probe HF( ,J) products from FϩH reactions. This offers

v

2

the ability to obtain differential cross section information

with full rovibrational quantum state resolution.

The list of theoretical studies on the FϩH₂system is

perhaps even more impressive; the interested reader is re-

ferred to Refs. 1, 3, and 4 for an extensive historical discus-

sion on the topic. One of the theoretical milestones of the last

decade has been the calculation of a fully ab initio potential

energy surface ͑PES͒ for FϩH₂by Stark and Werner

͑SW͒,^39,40claimed to be accurate to better than Ϯ0.2 kcal/

mole for all relevant nuclear conﬁgurations. This should be

contrasted with previous potential energy surfaces that were

for the most part either purely empirical or contained empiri-

cal corrections optimized to reproduce existing experimental

results.^41–47Classical and quantum-mechanical calculations

performed on the SW PES were found to reproduce qualita-

tively ͑i͒ vibrationally resolved reaction differential cross

sections,^48–52͑ii͒ thermal rate constants,^49,53͑iii͒ kinetic iso-

tope effects,⁵³͑iv͒ rovibrationally resolved differential cross

section results,^17,51as well as ͑v͒ nascent HF product state

distributions.³⁸Most importantly, a detailed photoelectron

structure arising from transition state spectroscopy of FH₂^Ϫ

was also correctly predicted,^54,55which was not possible with

any other PES. Indeed, though some experimental results

exist ͑such as the differential cross sections for inelastic

FϩH₂/D₂scattering͒ for which semiempirical potential en-

ergy surfaces appear to perform as well or even better,³³the

Stark and Werner PES is widely considered to be the best

currently available.

*

FIG. 1. Potential energy surfaces ͑PES͒ for a colinear reaction between F/F

and H₂, plotted in Jacobi coordinates. Of the three low lying PES, two

͑1 ²A and 1 ²A ) correlate to FϩH and one (2 A ) to F ϩH ͑only 1 ²A

2

*

Ј

Љ

Ј

2

and 2 ²A PES are displayed͒. FϩH reactions ͑solid arrow͒ occur on 1 ²A

Ј

2

PES ͑also shown as a contour plot͒, over an early 1.9 kcal/mole energy

barrier. The 2 ²A surface is strongly repulsive, and thus F ϩH collisions

*

Ј

2

are predicted to be completely nonreactive in the adiabatic ͑i.e., Born Op-

*

penheimer͒ limit. However, some fraction of the F ϩH₂encounters may

result in a nonadiabatic crossing to the 1 ²A surface followed by the reac-

Ј

tion ͑e.g., dashed arrow͒. The main thrust of the present work is to exploit

nascent HF( ,J) quantum state distributions as a function of E_comto experi-

v

mentally identify and characterize these nonadiabatic processes.

Despite this considerable progress, several fundamen-

tally important theoretical and experimental questions re-

main. One issue that has received increasing attention in re-

cent years concerns the interplay between spin–orbit

excitation and nonadiabatic effects in the FϩH₂reaction

dynamics.³Atomic ﬂuorine has two low lying spin–orbit

states, F(²P_3/2) and F(²P_1/2) separated by only ⌬E_spin–orbit

ϭ1.15 kcal/mole,^56,57which will be designated throughout

clever alternative approach, FϩH₂reaction dynamics have

also been studied in the Neumark group by photoelectron

detachment studies of the FH^Ϫ₂anion, thereby directly ac-

cessing the FH₂transition state region.^34–36

In the above beam studies, information on the reaction

dynamics and ﬁnal quantum state distributions is achieved

by kinetic energy analysis of the product fragments, with a

resolution limited by time-of-ﬂight ͑TOF͒ methods. This

level of resolution can readily distinguish product HF vibra-

tional states (⌬E_HFϷ4000 cm^Ϫ1), but is typically insufﬁ-

cient to achieve rotational state resolution (B_HFϷ20 cm^Ϫ1).

*

this paper as F and F , respectively. Though energetically

small, this spin–orbit excitation is dynamically crucial, since

*

the F ϩH₂potential energy surface correlates with a

strongly repulsive quartet state of the products ͑see Fig. 1͒.

In the Born–Oppenheimer approximation, therefore, only the

lower spin–orbit state F atom is predicted to be reactive with

H₂.⁸Thus, the presence or absence of signiﬁcant spin–orbit

excited reaction pathways in such a system directly tests

whether reactive collisions are constrained to a single, adia-

batic potential surface or whether much richer and more

complicated dynamical possibilities exist due to nonadia-

batic interactions on multiple potential surfaces.

Many theoretical studies have predicted appreciable

nonadiabatic effects in the FϩH₂reaction,^58–79though scat-

ter in the estimate of these effects is large. For example,

semiclassical treatments by Komornicki et al.^63,64show that

cross sections for the nonadiabatic F(²P_1/2)ϩH₂channel can

be as high as 50% of those for the adiabatic F(²P_3/2)ϪH₂

channel, especially at higher collision energies. Similarly,

Lepetit et al.⁶⁶have found very signiﬁcant nonadiabatic re-

action probabilities using close-coupling calculations and hy-

A dramatic advance in HF( ,J) quantum state resolution can

v

be achieved by laser-based detection schemes. For example,

shot noise limited direct IR absorption methods have been

exploited in our group by Chapman et al.^37,38to study FϩH₂

reaction dynamics in low-density, crossed supersonic mo-

lecular jets, rigorously yielding nascent HF( ,J) product

v

state distributions under collision-free conditions. The spec-

tral resolution of these crossed jet direct absorption methods

(⌬␯_expϷ0.01 cm^Ϫ1) is over four orders of magnitude higher

than TOF methods, resolving HF( ,J) P or R branch transi-

v

tions from adjacent rotational states by more than 4000-fold.

Indeed, the laser resolution (⌬␯_laserϷ0.0001 cm^Ϫ1) in these

studies is an additional two orders of magnitude below the

Doppler limit, and therefore also contains information on lab

frame velocity distributions of the HF( ,J) product. In yet

v

another development of combined laser and molecular beam

methods, Keil and co-workers^17,18have succeeded in using

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8406

J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nizkorodov et al.

perspherical potentials. In quasiclassical surface hopping

state resolution via direct IR absorption of a continuous-

wave single-mode (⌬␯Ϸ0.0001 cm^Ϫ1) F-center laser, multi-

passed 16–18 times through the jet intersection plane with a

cylindrical Herriot cell. Absorption due to reactively formed

75,76

*

studies of F ϩH₂, Tully

demonstrate the importance of

the nonadiabatic reaction channel and the intimately related

*

process of electronic quenching of F by collisions with H₂.

Gilbert and Baer, on the other hand, predict only a

Ϸ1%–2% effect,^61,62though their results, as well as the

calculations of Billing et al.,⁵⁹do demonstrate sensitivity in

the integral reaction cross sections to the single versus mul-

tiple potential surface nature of the theoretical treatment.

More recently, Alexander et al.⁵⁸have reported preliminary

results on full quantum reactive scattering calculations for

HF( ,J) is monitored by transient imbalance between signal

v

and reference IR laser beams on matched InSb detectors,

which is then sampled with a fast digitizer. Dual time gating

(⌬tϷ200 ␮s) of the signal before and during the gas pulse is

used to further discriminate against noncommon mode noise

on the signal beam due to low-frequency acoustic vibrations

in the multipass cell.

*

F/F ϩH₂, including all three adiabatic surfaces from the ab

The HF product states can be energetically formed in

initio work of Stark and Werner. Though only obtained for

J_totϭ¹₂and therefore not converged with respect to the partial

wave expansion, these calculations do represent a rigorous,

multisurface dynamical treatment of spin–orbit and Coriolis

coupling effects, and predict overall reaction probabilities for

_HFϭ0,1,2,3 and are probed by direct absorption on the fun-

v

damental (⌬ ϭϩ1) bands between 3600–3900 cm^Ϫ1. For

v

each HF( ,J ) HF( ,J ) probe transition, the absolute

v

Љ Љ

Ј Ј

absorbance of the laser is recorded as a function of laser

frequency and integrated over the full Doppler proﬁle ͑full

scan Ϸ2500 MHz, 3 MHz step size͒, rigorously yielding the

absolute column-integrated density difference between the

*

the F channel to be small but signiﬁcant. Speciﬁcally, Al-

*

exander et al. report nonadiabatic (F ϩH₂) versus adiabatic

(FϩH₂) reaction probabilities for forming HF in the

upper and lower HF( ,J) states. Since the HF( ϭ4) mani-

v

_HFϭ3 vibrational manifold on the order of 10% at E_com

v

fold is unpopulated by both adiabatic and nonadiabatic

Ϸ2 kcal/mole and, most importantly, dropping off much

*

F/F ϩH reaction channels, the ϭ4 3 absorbance signals

v

2

*

more slowly for F than F with center-of-mass collision en-

are readily related to the HF ( ϭ3,J) rotational populations.

v

ergy below the adiabatic reaction barrier.⁵⁸

The infrared laser power is kept below 60 ␮ W to ensure that

the signals are in the linear ͑i.e., unsaturated͒ absorption re-

gime; this is conﬁrmed by detailed calculations and explic-

itly veriﬁed by power-dependent studies for the strongest HF

transitions. Under these conditions, the single pulse experi-

mental detection sensitivity is 3ϫ10^Ϫ7per root Hz, corre-

sponding to a rms absorbance of 3ϫ10^Ϫ5in a Ϸ10 KHz

detection bandwidth. Though already within a factor of 3–4

from the shot-noise limit, this can be further improved by

signal averaging ͑2–4-fold͒ and integration over the full

Doppler proﬁle ͑10–20-fold͒. This degree of detection sen-

sitivity proves essential for collision-free detection of the

most weakly populated HF products, which as a result can be

observed down to concentrations Ϸ10⁷–10⁸molecules/

cm³/quantum state.³⁸

The hydrogen jet is generated by a piezoelectric trans-

ducer ͑PZT͒ pulsed valve based on the design of Proch and

Trickl⁸¹with argon/hydrogen mixtures maintained at a total

backing pressure of 900 Torr. The mole fraction of Ar with

H₂is varied from 0% to 40% to vary the H₂jet speed and

thereby the center-of-mass collision energy between F and

H₂. The H₂valve produces near-rectangular, 450 ␮s wide

gas pulses with a rise/fall time of roughly 30 ␮s, as moni-

tored in vacuum with a miniature hearing-aid microphone.

The effective nozzle diameter is determined to be 145

Ϯ5 ␮m from mass ﬂow rate measurements; this agrees quite

well with the actual nozzle diameter of 150 ␮m, conﬁrming

that the valve is fully open during the pulse. Under these H₂

backing pressure conditions and nozzle diameter, the total

column-integrated density of H₂4.5 cm away from the

nozzle is Ϸ1.0ϫ10¹⁴cm^Ϫ2, corresponding to a density of

Ϸ2.1ϫ10¹³cm^Ϫ3in the intersection region. Based on a total

reactive cross section of Ϸ3 Å², the reaction probability per

F atom is less than 3%, which makes the probability of sec-

ondary reactive encounters negligible.

In rather surprising contrast with these theoretical pre-

dictions, there have been no experiments until quite recently

that have unambiguously conﬁrmed the presence of the

nonadiabatic F ϩH₂reaction channel.^3,80As clariﬁed in this

*

work, this is most likely the result of relatively modest nona-

diabatic contributions predicted at collision energies near and

above the reaction barrier as well as limited quantum state

resolution in previous studies. A much more sensitive ap-

proach involves exploring the reaction at energies signiﬁ-

cantly below the adiabatic transition state barrier, where

FϩH₂reactions can be sufﬁciently suppressed to permit

*

nonadiabatic F ϩH₂channels to predominate. Preliminary

evidence for such nonadiabatic processes has been presented

elsewhere, based predominantly on reactive scattering stud-

ies at E_comϷ0.54(10) kcal/mole.⁸⁰Considerably more de-

tailed information on nonadiabatic versus adiabatic reaction

dynamics can be obtained by extending these studies over a

much wider range of collision energies. Such an energy-

dependent reactive scattering study forms the major thrust of

this paper, based on fully quantum state resolved HF( ,J)

v

product distributions obtained over a range of E_com

Ϸ2.4–0.3 kcal/mole, i.e., from both above to substantially

below the 1.9 kcal/mole barrier theoretically predicted for a

reaction on the lowest potential energy surface.

II. EXPERIMENT

The crossed-jet reactive scattering apparatus has been

described in detail elsewhere;³⁸only a brief description and

modiﬁcations relevant to the current study are mentioned

here. Two pulsed molecular jets, one containing ﬂuorine at-

oms formed in a pulsed discharge of F₂/rare gas and the other

supersonically cooled H₂in rare gas mixtures, are crossed at

right angles Ϸ4.5 cm downstream of the two nozzle oriﬁces

under low-density conditions. The HF( ,J) products formed

v

in the intersection region are probed with complete quantum

The ﬂuorine atoms are produced in a pulsed slit

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nonadiabatic reaction dynamics

8407

(300 ␮mϫ5 mm) discharge source described in detail in

Ref. 38. Two different mixtures containing ﬂuorine have

been used in present work, ͑i͒ 5%F₂/95%He and ͑ii͒

5%F₂/20%Ne/75%Ar. The two expansion conditions yield

two F atom velocities, i.e., ‘‘fast’’ ͓1.48͑15͒ km/s͔ and

‘‘slow’’ ͓0.59͑6͒ km/s͔, which, in conjunction with Ar dop-

ing of the H₂jet, conveniently result in two partially over-

lapping ranges of center-of-mass collision energies (E_com

ϭ0.3–1.7 kcal/mole and 1.0–2.4 kcal/mole͒. To initiate and

sustain the discharge, a negative pulse of ϷϪ700 V is ap-

plied across the expansion in a 500–700 ␮s time window

centered on the much longer ͑Ϸ2 ms͒ total gas pulse. Typical

discharge backing pressures range from 30 to 70 Torr, with

peak discharge currents from 100 to 500 mA. Under these

backing pressure conditions, both gas mixtures result in a

smooth, stable discharge producing roughly comparable den-

sities of ﬂuorine atoms, as directly monitored by the HF

absorption signals. The total column-integrated density of

the F atom source jet ͑including the 20-fold excess of rare

gas carrier͒ is less than 2ϫ10¹⁴cm^Ϫ2, with an estimated

number density of р5ϫ10¹³cm^Ϫ3in the intersection region.

Based on a 5% fractional F₂concentration in the discharge

mixture and an assumed Ϸ5% dissociation efﬁciency, this

corresponds roughly to Ϸ10¹¹cm^Ϫ3of F/F atoms. The par-

*

titioning between F and F atoms in the jet discharge is

unfortunately not possible for us to measure with the current

apparatus. However, based on the temperature and collision

frequency in the discharge region, one might anticipate the

FIG. 2. Schematic for measuring centerline jet speeds with the TOF method.

͑a͒ Nozzle–microphone separation versus arrival time of the gas pulse is

displayed for a series of Ar/H₂mixtures; the jet speeds are given directly by

the slopes. ͑b͒ Speeds of Ar/H₂mixtures are plotted versus the percentage of

added Ar. The dots represent experimental measurements, which agree ex-

tremely well with predictions ͑solid line͒ obtained from an ideal continuous

isentropic expansion. The small deviations between theory and experiment

are due to incomplete rotational cooling of H₂.

*

relative fraction of F:F to be close to the statistical limit of

4:2.

The primary focus of the present study is to measure

state-resolved cross sections for reactively forming HF (

v

ϭ3,J) as a function of collision energy. The rotational dis-

tributions of the HF ( ϭ3,J) products are ﬁrst established at

v

two reference collision energies, speciﬁcally for neat H₂ex-

pansions colliding with ‘‘slow’’ (F₂/Ne/Ar) and ‘‘fast’’

(F₂/He) ﬂuorine atoms. The rotational distributions are then

measured at a series of other collision energies by varying

the Ar/H₂mixture ͑for both fast or slow F atom sources͒,

with each data point referenced to the corresponding signals

obtained under neat H₂conditions. This offers a crucial ad-

vantage of permitting data to be compared quantitatively

over many hundreds of hours of data collection, which typi-

cally exceeds time between routine maintenance of the dis-

charge source. At such high detection sensitivity, extremely

weak background absorption can be observed due to trace

HF impurities excited in the F₂discharge. However, the

magnitude of this background is quite small ͑typically р

10% of the reactively formed HF signals͒ and readily com-

pensated for by background scans in the absence of the H₂

reagent jet.

studies, it is the angular distribution for the two jets that

plays the more important role. Two independent methods

have been developed to obtain these jet parameters, which

will be brieﬂy summarized here and described elsewhere in

more detail.⁸²The ﬁrst is based on monitoring the TOF pro-

ﬁle of the gas pulse with a small hearing aid microphone as

a function of the distance parallel and perpendicular to the jet

expansion axis. The mean jet speed is simply obtained by

translating the microphone along the jet axis and monitoring

the gas pulse arrival time as a function of the nozzle–

microphone separation ͑Fig. 2͒. The robust reliability of this

method can be gauged from the linearity of the individual

TOF curves ͓Fig. 2͑a͔͒, as well as from the small relative

scatter of speeds for various Ar/H₂mixtures plotted in Fig.

2͑b͒. As described elsewhere,⁸²these speed data agree quan-

titatively with detailed predictions of an adiabatic expansion

model for Ar/H₂mixtures, i.e., explicitly taking into account

͑i͒ additional energy release from rotational cooling and ͑ii͒

temperature-dependent heat capacities of the o-H₂, p-H₂and

Ar constituents.

III. CENTER-OF-MASS COLLISION ENERGIES

The center-of-mass collision energy distribution,

P(E_com), plays an important role in the discussion of the

present data. In a conventional crossed-beam experiment, the

width of the P(E_com) distribution is normally limited by the

spread in reactant speeds; for crossed-jet reactive scattering

The second method relies on high-resolution laser

Dopplerimetry, accomplished by seeding trace amounts of an

IR absorber ͑e.g., CH₄) into the expansion mix and recording

Doppler proﬁles of a single rovibrational transition for dif-

ferent orientations of the laser beam with respect to the jet

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8408

J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nizkorodov et al.

FIG. 4. Monte-Carlo simulation of the collision energy distributions. The

top and bottom panel show the results for the ‘‘fast’’ 1.48(15)

͓

ϫ10⁵cm/s and ‘‘slow’’ 5.9(6)ϫ10⁴cm/s F-atom jets, respectively, col-

͔

͓

͔

liding with different dilutions of Ar/H₂mixtures. The range of collision

energies covered in this experiment is from 2.4͑5͒ kcal/mole down to

0.31͑7͒ kcal/mole, where the width of the distributions is dominated by

angular divergence of the jets. Collision energies quoted in the text corre-

spond to averages over these Monte-Carlo distributions.

the angular and speed distributions of the IR chromophore,⁸⁰

sample data from which are shown in Fig. 3. It is worth

noting that the speed and the angular jet divergence obtained

from these more detailed Dopplerimetry measurements are in

excellent agreement with the much simpler microphone

based studies mentioned above.

With these jet speed and angular distributions estab-

lished, P(E_com) is calculated from a Monte-Carlo simulation.

This is accomplished by integrating over the jet intersection

volume and the known speed and angular distributions for

the F and H₂jets, with each collisional event appropriately

weighted by the local reagent densities (␳_H,␳_F), the relative

FIG. 3. High-resolution laser Dopplerimetry for measurements of super-

sonic jet speed and angular divergence. ͑a͒ The top panel shows scans over

the individual absorption lines of methane seeded into three different Ar/H₂

mixtures. Because of the parallel detection geometry, each individual CH₄

absorption line is split into a doublet, with the splitting and the width of each

feature providing information on the average and the width of the speed

distribution, respectively. The bottom panel shows least squares ﬁts for the

corresponding speed distributions. ͑b͒ The concept is quite similar to that in

͑a͒, except that in this perpendicular probe arrangement the absorption pro-

ﬁle ͑top͒ is determined primarily by the angular rather than speed distribu-

tions of the jet-cooled molecules ͑bottom͒.

velocity ( ), and the time spent in the probe laser beam.

v_rel

This additional weighting by time in the probe beam explic-

itly reﬂects the fact that a direct absorption method measures

column-integrated densities rather than ﬂuxes of HF( ,J)

v

products, i.e., the density to ﬂux transformation. Sample dis-

tributions for the crossed jet apparatus are presented for a

series of collision energies in Fig. 4. Mostly as a result of

favorable kinematics, the shapes of these P(E_com) distribu-

tions are fortunately quite insensitive to variations in the ﬁnal

axis ͓see Figs. 3͑a͒ and ͑b͔͒. For laser propagation parallel to

the jet axis ͓Fig. 3͑a͔͒, the absorption peak splits into two

symmetric features, the separation and width of which are

closely related to the average and width of the speed distri-

bution. For laser propagation perpendicular to the jet axis

͓Fig. 3͑b͔͒, the Doppler proﬁles are broadened by and there-

fore most sensitive to angular divergence in the jet. These

two Doppler proﬁles can be directly inverted to yield both

quantum state of the HF ( ϭ3,J) product,³⁸details of the

v

reaction differential cross section, and translational tempera-

tures of the jets.

Table I lists the jet speed combinations used in the ex-

periment along with the ﬁrst moments of the corresponding

P(E_com) distributions. It is worth noting that the average

values of E_comare about 10%–20% higher than energies

predicted for a perpendicular jet intersection geometry. This

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Nonadiabatic reaction dynamics

8409

TABLE I. Relative integral cross sections for Fϩn-H →HF( ϭ3)ϩH re-

v

2

actions. The ﬁrst and third columns give the centerline speeds for the F and

Ar/H₂jets and the second column provides the amount of Ar seeded into the

Ar/H₂jet. E_comis the average collision energy of the P(E_com) distribution

followed by its HWHM in parentheses. The ‘‘fast’’ and ‘‘slow’’ F atom jet

cross section data have been scaled for best agreement in the region of

overlapping collision energies, with 95 conﬁdence intervals in parentheses.

% Ar

␴

␷

E_com

F

H

2

in Ar/H₂

͑kcal/mol͒

͑arb. units͒

͑km/s͒

1.48͑15͒

0.0

0.7

1.7

3.0

5.0

2.58

2.44

2.26

2.09

1.89

1.67

1.56

1.39

1.21

2.58

2.38

2.21

1.99

1.80

1.55

1.32

1.10

0.89

2.35͑46͒

2.17͑44͒

1.95͑41͒

1.75͑37͒

1.54͑33͒

1.33͑29͒

1.24͑27͒

1.10͑24͒

0.98͑21͒

1.74͑23͒

1.50͑21͒

1.31͑19͒

1.08͑16͒

0.91͑14͒

0.71͑12͒

0.54͑10͒

0.42͑8͒

1.000͑25͒

0.942͑22͒

0.849͑23͒

0.762͑47͒

0.655͑16͒

0.638͑36͒

0.523͑23͒

0.468͑21͒

0.409͑16͒

0.810͑33͒

0.707͑65͒

0.570͑33͒

0.421͑37͒

0.352͑32͒

0.250͑17͒

0.195͑22͒

0.187͑42͒

0.186͑22͒

0.151͑30͒

Љ

8.0

10.0

14.0

19.9

0.0

1.0

2.1

0.59͑6͒

Љ

4.0

6.1

10.1

16.1

25.0

40.0

0.31͑7͒

FIG. 5. Sample nascent HF absorbance data on individual R-branch ϭ4

v

3 transitions at four representative collision energies. ͑a͒ 2.35͑46͒ kcal/

mole ͑‘‘fast’’ FϩneatH₂); ͑b͒ 1.74͑23͒ kcal/mole ͑‘‘slow’’ FϩneatH₂); ͑c͒

1.10͑24͒ kcal/mole ͑‘‘fast’’ Fϩ14%Ar/H₂); and ͑d͒ 0.71͑12͒ kcal/mole

͑‘‘slow’’ Fϩ10%Ar/H₂͒. Absorbance data have been obtained for a range of

18 collision energies and are used to extract state-resolved nascent HF

is due to a combination of ͑i͒ near-isoergic formation of the

HF( ϭ3) product and ͑ii͒ ‘‘heavyϩlight–light’’FϩH ki-

v

2

nematics. In essence, the HF product velocities in the labo-

ratory frame are close to those of F atoms in the jet, altered

only by the modest chemical energy release and the resulting

small kick due to light hydrogen atom recoil. Thus, the ma-

jority of reactive collisions between F and H₂resulting in HF

( ϭ3,J) populations as a function of E

͑see the text for details͒.

v

com

( ϭ3,J) signals occur for slightly obtuse angles, р 1 cm

v

prior to the probe laser region, which from the detailed

Monte-Carlo simulations yields a slight upward shift in the

average collision energy. As a ﬁnal test, we have also per-

formed these Monte Carlo calculations of P(E_com) for dif-

ferent angular spreads in the H₂and F atom jets, in an effort

to account for possible uncertainties in the jet angular diver-

gence that might arise from seeding the expansion with Ar.

As expected, these simulations indicate a completely negli-

gible sensitivity to angular divergence of the F atom, due to

the kinematic issues described above. Also, as expected,

there is some sensitivity of P(E_com) to the H₂jet divergence.

However, the incremental effects on the average E_comdue to

any further increase in this width is rather small, on the order

of 10%–20% for as much as an additional doubling of the jet

divergence.

noise ratios are approximately 30:1 for the most intense tran-

sitions, which are further enhanced by an additional 10-fold

from integration over the Doppler proﬁle. As a result, the

uncertainties in the HF state-to-state cross sections reported

herein ͓i.e., Ϸ3%–10% with respect to the cross section for-

mation of HF( ϭ3,Jϭ1) at E_comϭ2.35 kcal/mole͔ are inde-

v

pendent of peak absorption signal strength for all but the

very lowest collision energies. Furthermore, as a result of

modest kinetic energy release in the HF( ϭ3) manifold

v

͓i.e., m_HF/(m_Hϩm_HF)Ϸ95% of this excess energy is kine-

matically removed by light H atom recoil͔, the Doppler

widths are dominated by angular divergence in the jet and

therefore only weakly dependent on the ﬁnal product quan-

tum state. Thus, the qualitative trends in nascent populations

can be directly estimated from the peak absorption intensi-

ties, which, in turn, depend strongly on quantum state. Spe-

ciﬁcally, there is a clear peaking of the signal strengths at

low J values, with a systematic decrease with increasing ro-

tational state up to the energetic limit ͑i.e., JϷ6 for E_com

ϭ2.35 kcal/mole).

IV. RESULTS AND ANALYSIS

High resolution absorbance scans have been obtained

over a sequence of HF rovibrational transitions

ϭ4

͓v

3;R(0)–R(6) for 18 collision energies between E_com

͔

Since no products are formed in the HF( ϭ4) vibra-

tional manifold, the column-integrated densities of the na-

v

ϭ0.3 and 2.4 kcal/mole. Sample HF Doppler proﬁle data for

R(0) through R(6) at four representative collision energies

are shown in Fig. 5 and immediately indicate several points

worth noting. First of all, the raw peak absorbance to rms

scent HF ( ϭ3,J) can be rigorously obtained from the mea-

v

sured integrated absorbances, according to

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nizkorodov et al.

3

2

8␲ ␯ ͉m͉␮

0

A ␯͒d␯ϭ

ϫ

HF ϭ3,J ͒ dl, ͑1͒

͑v

͑

͓

͔

Љ

͵

3hc 2J ϩ1͒

͑

Љ

where ␯ is the transition center frequency, mϭJ ϩ1

Љ

0

(ϪJ ) for R-branch ͑P-branch͒ transitions, and ␮ is the tran-

Љ

sition dipole moment given in Ref. 83. As discussed in detail

in previous work,^38,80the ‘‘heavyϩlight–light’’ kinematics

for FϩH₂results in an essentially ﬂat density to ﬂux trans-

formation, especially so for the nearly isoergic formation of

the HF( ϭ3) manifold. Indeed, detailed Monte-Carlo simu-

v

lations indicate that the integrated signal absorbances are di-

rectly proportional to state-resolved integrated product ﬂuxes

at any given collision energy and for all product HF quantum

states to better than 5%–10% accuracy. In order to obtain

relative cross sections as a function of collision energy, how-

ever, one must scale for additional effects due to ͑i͒ relative

velocity and ͑ii͒ mole fraction of H₂in the Ar/H₂expansion

mixture, both of which are varied in order to tune E_com. The

relative integral cross sections into a given ﬁnal J state are

therefore calculated from

FIG. 6. Relative state-resolved reaction cross sections for HF ( ϭ3,J) for

several collision energies. The cross sections decrease smoothly with E_com

v

for every HF ( ϭ3,J) state, with a slight shift in the peak of the nascent

v

distribution from JϷ2 to JϷ1. Especially noteworthy is the quite modest

͑Ϸ2.5-fold͒ decrease in the cross section for collision energies up to 1 kcal/

mole below the Ϸ1.9 kcal/mole barrier height predicted for adiabatic FϩH₂

reactions.

decrease monotonically with decreasing collision energy, but

there is little evidence for an energetic threshold below 1.9

kcal/mole due to the adiabatic transition state barrier. This

unexpected shape of ␴(E_com) will be discussed more fully in

the context of detailed theoretical predictions in the next sec-

tion.

͐

HF ϭ3,J͒ dl

͑v

͓

͔

␴ E ͒ϰ

,

͑2͒

͑

J

com

ͱ

X E_com

where X is the mole fraction of H₂in the H₂/Ar mixture. As

described in Sec. II, all integrated absorbances and reaction

cross sections are measured with respect to ﬁxed reference

collision energy conditions, i.e., for a jet expansion of neat

hydrogen (Xϭ1). Since the absolute F atom populations in

the jet intersection region are not measured in the current

experiment, the data obtained under the two discharge con-

ditions ͑i.e., ‘‘fast’’ and ‘‘slow’’ ﬂuorine jets͒ are treated

independently, and then scaled with a single parameter in the

region of overlapping collision energies (E_com

Ϸ1.0–1.7 kcal/mole).

V. COMPARISON WITH THEORY

As a prelude to the present energy-dependent studies,

nascent FϩH₂distributions have been investigated for

HF( ,J) products in each of _HFϭ0,1,2,3 rovibrational

v

manifolds.³⁸Though only obtained at a single center-of-mass

The relative cross sections for forming HF ( ϭ3,J) as a

v

function of rotational state J are presented in Fig. 6 over a

sample range of collision energies, which demonstrates sev-

eral interesting trends. First of all, the reaction cross sections

decrease smoothly and systematically as a function of colli-

sion energy. Second, despite a more than fourfold change in

collision energy, the cross sections into a given ﬁnal J state

rise and fall in a qualitatively similar manner. On closer in-

spection, some sensitivity to collision energy becomes evi-

dent, with the most probable rotational state of HF( ϭ3)

v

systematically shifting toward lower J values with decreas-

ing E_com. For example, the maximum of the HF ( ϭ3,J)

v

distribution shifts from Jϭ2 at E_comϷ1.8 kcal/mole to J

ϭ1 at lower collision energies (E_comр1.5 kcal/mole). Sub-

stantially more surprising, however, is the relatively modest

sensitivity of a reaction cross section to the center-of-mass

collision energy. Speciﬁcally, one might have expected a

sharp decrease in the reaction cross section at energies lying

below the theoretical transition state barrier predicted at

Ϸ1.9 kcal/mole. Instead, a signiﬁcant yield of HF products is

observed down to E_comϷ0.3 kcal/mol, i.e., the lowest colli-

sion energy of the present experiment. This point is explic-

FIG. 7. Total HF reactive cross sections into ϭ3 ͑i.e., summed over all

v

ﬁnal J͒ as a function of collision energy, E_com. The ‘‘fast’’ F-jet data ͑large

open squares͒ and the ‘‘slow’’ F-jet data ͑large ﬁlled squares͒ are analyzed

independently and scaled to each other in the overlapping E_comrange. The

theoretical curves reﬂect quantum mechanical scattering calculation on SW

PES for FϩH₂(j): jϭ0 ͑ﬁlled circles͒; jϭ1 ͑open circles͒; jϭ2 ͑triangles͒.

Also presented is the theoretical prediction for n-H₂at 200 K ͑thick solid

line͒. As discussed in the text, the theoretical calculations have been shifted

by 1/3⌬E_spin–orbitϭ0.38 kcal/mole to higher energy to account for the in-

crease in barrier height when spin–orbit effects are incorporated. The ex-

perimental data are in relative units while the theoretical cross sections are

reported in Å².

itly addressed in Fig. 7, where the total _HFϭ3 reactive cross

v

sections ͑i.e., summed over all rotational states͒ are plotted

as a function of E_com͑see also Table I͒. The cross sections do

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nonadiabatic reaction dynamics

8411

verged with respect to total angular momentum become

available.

collision energy E_comϭ2.4 kcal/mole, this nevertheless has

allowed a ﬁrst rigorous state-to-state comparison with ‘‘ex-

act’’ ͑i.e., fully converged͒ quantum calculations on the low-

est ab initio potential surface of Stark and Werner. These

direct comparisons have proven qualitatively very successful

in modeling the overall rovibrational distributions observed

experimentally, but also indicate signiﬁcant discrepancies,

The FϩH (jϭ0,1,2)→HϩHF( ϭ3) integral reactive

v

2

cross sections of Castillo et al.⁸⁴are plotted in Fig. 7 against

collision energy, which per the above discussion has been

approximately corrected for spin–orbit effects by a 0.38

kcal/mole energy shift. The theoretical cross sections are also

plotted for a n-H₂at 200 K, consistent with expected rota-

tional distribution of H₂in the jet. The experimental cross

sections have been normalized by a single parameter to

match the theoretical n-H₂data for the highest energies

sampled (E_comϷ1.9–2.4 kcal/mole), i.e., where the calcula-

tions are expected to depend least on details of the potential

surface, such as barrier widths, quantum tunneling contribu-

tions, etc. Qualitatively, the theoretically predicted and ex-

perimentally observed cross sections both exhibit a mono-

especially for states in the highest HF ( ϭ3,J) vibrational

v

manifold. Consequently, the current study has focused ex-

plicitly on the _HFϭ3 manifold, yielding ﬁrst quantum state

v

resolved cross sections for HF ( ϭ3,J) formation over a

v

broad range of collision energies, including those sampling

substantially below the adiabatic reaction barrier for FϩH₂

reactions. These energy-dependent data permit an even more

demanding comparison between experiment and theory, as

discussed below.

Arguably the best FϩH₂reactive scattering calculations

͑and most relevant to our experimental conditions͒ have been

performed by Castillo et al.^52,84on the fully ab initio poten-

tial energy surface of Stark and Werner ͑SW PES͒.³⁹In these

studies, the reaction has been treated adiabatically on the

tonic decrease with E_com

agreement with theory is rather poor. Speciﬁcally, theory

suggests vanishingly small reactivity below E_com

Ϸ1 kcal/mole, whereas signiﬁcant HF ( ϭ3,J) product

yields are observed in the experiment down to E_com

Ϸ0.3 kcal/mole. The experimental results suggest additional

; however, the quantitative

v

lowest-energy 1 ²A PES, i.e., without including any spin–

Ј

orbit effects. The calculations provide fully converged differ-

ential and integral state-resolved cross sections at a series of

center-of-mass collision energies especially well suited for a

comparison with the present experimental results.

HF( ,J) contributions from a lower threshold channel not

accounted for by purely adiabatic calculations on the ground

spin–orbit FϩH₂surface.

v

It is interesting to note that quantum tunneling in the

FϩH₂system is clearly quite important at these lower ener-

gies, which can be immediately recognized, since even the

theoretically predicted cross sections extend well below the

1.9 kcal/mole reaction barrier. Thus, based on the well-

known exponential sensitivity of tunneling effects, one might

be justiﬁably concerned that any discrepancies between

theory and experiment might be simply due to relatively

small errors in the potential surface near the transition state

geometry. We return to this important point in Sec. VI,

where threshold studies have been performed to explicitly

Theoretical studies agree that the spin–orbit interaction

can have a twofold effect on the FϩH₂reactive scattering

dynamics.³First of all, the spin–orbit interaction raises the

reaction barrier on the lowest adiabatic 1 ²A PES by ap-

Ј

proximately one-third the F atom spin–orbit splitting, i.e.,

from 1.54 kcal/mole to about 1.9 kcal/mole.⁵¹Second, it con-

tributes to the non-Born Oppenheimer, derivative coupling

between the low-lying zeroth-order PES’s, increasing the

3

*

probability of nonadiabatic reactions between F with H₂.

Fully converged quantum-mechanical calculations on mul-

tiple PES’s with rigorous treatment of nonadiabatic and

spin–orbit effects will ultimately be necessary to obtain the

most accurate picture of the reaction dynamics. Multisurface

calculations for atomϩdiatom reactive scattering represent a

eliminate this possibility by identifying HF ( ϭ3,J) quan-

v

tum states that are energetically inaccessible to purely adia-

batic reactions on the ground spin–orbit state surface.

Additional evidence for nonadiabatic contributions to the

reaction dynamics is found in the HF product state distribu-

tions themselves. As shown in Fig. 8, for example, the aver-

*

state-of-the-art challenge in the ﬁeld, and in the F/F ϩH₂

reaction system have thus far only been performed⁵⁸for the

lowest value of total angular momentum, J_totϭ¹₂. Neverthe-

less, these initial results already have provided useful in-

sights into the inﬂuence of spin–orbit excitation on the ef-

fective barrier height. Speciﬁcally, the studies indicate that

the ground state F(²P_3/2)ϩH₂(jϭ0) integral cross sections

exhibit similar energy dependence as calculated for the un-

corrected PES, provided that the collision energy is refer-

enced with respect to the transition state barrier.^51,84Thus,

until more detailed multiple surface results for the spin–orbit

corrected PES become available, the best theoretical estimate

of the adiabatic energy-dependent cross sections is obtained

from the extensive adiabatic calculations already performed

for the spin–orbit uncorrected PES, shifting the collision

energy axis upward by the 0.38 kcal/mole change in barrier

height. It is worth stressing that we anticipate rapid theoret-

ical progress in this direction, such that direct comparisons

will be possible in the near future as calculations fully con-

age rotational energy

E

of products formed in HF(

v

͘

rot

͗

ϭ3) is found to be in relatively poor agreement with theory.

Speciﬁcally, the average HF ( ϭ3,J) rotational energy is

v

theoretically predicted to monotonically decrease with E_com

and essentially vanish for FϩH₂(jϭ1) below E_com

Ϸ0.7 kcal/mole. In contrast, the experimental E

values

͘

rot

͗

are 2–3-fold larger than predicted, with only modest ͑20%͒

fractional changes observed over the entire range of E_com

Ϸ0.3–2.4 kcal/mole. Interestingly, the theoretical curves ap-

pear to lie systematically lower than the experimental data

points by Ϸ0.2–0.3 kcal/mole, which is close to the amount

͑Ϸ0.2 kcal/mole^3,39͒ by which the SW PES is known to un-

derestimate the F(²P_3/2)ϩH₂reaction exothermicity. How-

ever, it would appear dynamically quite unlikely for this ex-

cess energy to be channeled exclusively into rotational

energy of the HF(vϭ3) products. The data therefore suggest

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nizkorodov et al.

since the most signiﬁcant discrepancies between theory and

experiment are observed at the lowest collision energies,

which are obtained in n-H₂mixtures with the greatest Ar

mole fraction (X_ArϷ20%–40%). As a result, T_rotр200 K

can be considered as a very safe upper limit for all Ar/H₂

mixtures employed in the present study, which translates into

р10% rotationally excited n-H₂in jу2.

Furthermore, for such a small fraction of reagent H₂(j

у2) to account for these population discrepancies would

require an extreme sensitivity in the FϩH₂(j) reaction cross

section to an initial H₂rotational state. However, the theo-

retical calculations do not indicate such a sensitivity. For

example, Fig. 7 reveals that at E_comр2 kcal/mol the theoret-

ical FϩH₂(j) integral cross sections drop with decreasing

energy at roughly comparable rates for jϭ0, 1, and 2.⁸⁴In-

deed, the FϩH₂(jϭ0) cross section predominates around

FIG. 8. Average rotational energy released into HF( ϭ3) product state,

v

calculated via

E

ϭ⌺ ␴(J)ϫE (J) /⌺ ␴(J), where ␴(J) is the rela-

͘

͕ ͖

rot J rot J

͗

tive cross section for forming HF ( ϭ3,J). The theoretical curves are fully

v

E

_comϭ1.5 kcal/mole, suggesting that H₂rotation is not as

converged QM scattering results on the SW PES. As discussed in the text,

the theoretical E_comvalues have been shifted to higher energy by

1/3⌬E_spin–orbitϭ0.38 kcal/mole to account for the increase in barrier height

when spin–orbit splitting effects are incorporated. Note that the nascent

efﬁcient as translation in terms of promoting a chemical re-

action. Though the reaction thresholds in Fig. 7 do shift to

lower E_comfor higher j, the calculated FϩH₂(jϭ2) cross

sections below E_comϭ1 kcal/mole are far too small to ac-

count for the experimental observation. Indeed, even a pure

beam of H₂(jϭ2) would not be sufﬁcient to make the

present experimental results compatible with the adiabatic

FϩH₂(j) predictions of Castillo et al.

HF( ϭ3) products are formed with substantially ͑2–3-fold͒ more rotational

v

energy than predicted by adiabatic theory.

some additional source of energy in the reagents that ulti-

mately appears in the HF ( ϭ3,J) products.

v

To explicitly demonstrate the lack of inﬂuence of H₂

rotational relaxation on the experimental cross sections, the

low E_commeasurements have been repeated under different

Ar/H₂expansion conditions, with p₀ϫd ranging from 5 to

20 Torr cm. According to the data of Pillard et al.,⁸⁵this

would translate into a decrease in the H₂(jу2)/H₂(jр1)

ratio by a factor of 2 for a neat hydrogen expansion. The

magnitude of this effect would be expected to be even larger

A plausible ﬁrst suspect for this source of excess energy

would be contributions from rotationally excited hydrogen,

which due to a large rotational constant (BϷ60 cm^Ϫ1) is

well known for its reluctance to cool in an expansion. The

situation is further aggravated by ortho–para nuclear spin

statistics, which preclude ⌬jÞ1 transitions and thus require

even larger energy changes ͓⌬E(jϭ2→0)Ϸ360 cm^Ϫ1and

⌬E(jϭ3→1)Ϸ600 cm^Ϫ1͔ to relax rotationally. On the other

hand, this anomalously large B constant also constrains the

initial rotationally excited populations in the stagnation re-

gion. Speciﬁcally, even at 300 K, у 80% of n-H₂resides in

the lowest para (jϭ0) and ortho (jϭ1) states, thus provid-

ing a rigorous upper limit on rotationally excited H₂(jу2)

populations in the expansion. The H₂reagent jet is actually

substantially colder than this worst case estimate. For ex-

ample, previous beam studies in neat H₂expansions indicate

that for comparable backing pressureϫoriﬁce diameter con-

ditions (p₀ϫdϷ13 Torr cm), the rotational distributions are

best characterized by a temperature of Ϸ200 K.^85–88Further-

more, the current data is predominantly obtained with Ar/H₂

mixtures, in which rotational relaxation is expected to be

considerably more efﬁcient. In any event, an upper limit of

200 K already translates into у90% population in H₂(j

ϭ0,1).

for the Ar-doped mixtures used herein to achieve low E_com

.

Within experimental uncertainty, neither the J-resolved reac-

tion cross sections ͑Fig. 6͒ nor the total integrated cross sec-

tions for ϭ3 ͑Fig. 7͒ are found to vary over this range of

v

p₀ϫd. As one speciﬁc example, Fig. 9 shows the experi-

mental ratio of state-resolved cross sections to form HF (

v

ϭ3,Jϭ2) at two different collision energies, E_com

Ϸ0.42 kcal/mole and Ϸ1.08 kcal/mole, with each cross sec-

tion scaled to the value obtained for a neat H₂expansion

(E_comϷ1.74 kcal/mole). As will be discussed in more detail

in the next section, E_comϷ0.42 kcal/mole corresponds to the

energetic threshold for the formation of HF( ϭ3,Jϭ2),

v

whereas E_comϷ1.08 kcal/mole is far above this threshold.

This ratio might therefore be anticipated to be especially sen-

sitive to p₀ϫd, if this excess rotational energy in the product

As described elsewhere,^80,82an independent conﬁrma-

tion of Ϸ200 K temperature estimate for neat n-H₂expan-

sions is obtained in our apparatus by comparing measured

and predicted jet speeds with an adiabatic expansion model

that explicitly treats rotational cooling and temperature-

dependent heat capacities of n-H₂. In addition, this analysis

also provides evidence for preferential cooling of n-H₂in

Ar-doped expansion mixtures, with rotational temperatures

as low as Ϸ100 K. This last point is particularly important,

HF( ϭ3) arises from adiabatic reactions of ground state F

v

atoms with uncooled H₂(jу2) in the expansion. By way of

contrast, both of these ratios remain constant within experi-

mental uncertainty over the full range of p₀ϫd ͑Fig. 9͒, with

most of the results reported in this paper conducted at 13

Torrϫcm ͑designated by an arrow͒. Thus, it is unlikely that

rotationally excited H₂(jу2) can be responsible for the ex-

cess HF( ϭ3) product state rotational energy and enhanced

v

reactivity at low E_com

.

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nonadiabatic reaction dynamics

8413

FIG. 9. Sample tests for contributions from H₂(jу2) levels. Shown are two

cross section ratios for HF( ϭ3,Jϭ2), corresponding to E_com

v

Ϸ0.42 kcal/mole ͑open circles͒ and Ϸ1.07 kcal/mole ͑ﬁlled circles͒, both

scaled to cross sections obtained under neat H₂expansion conditions at

E

_comϷ1.74 kcal/mole. The lower of these two collision energies ͑0.42 kcal/

mole͒ is near the energetic threshold for forming HF( ϭ3,Jϭ2) from

v

FϩH₂(jϭ1) and thus would be preferentially sensitive to any residual

H₂(jу2) population in the jet expansion. However, the reaction cross sec-

tions are found to be independent ͑within experimental uncertainty͒ of p₀

FIG. 10. Strategy for threshold studies. Shown is the energy level diagram

displaying relevant combinations of the reactant and product states. The

highest J state of HF( ϭ3) that can be produced from FϩH (jϭ1) at

v

2

ϫd for either ͑i͒ near the threshold or ͑ii͒ above threshold values of E_com

,

*

E

_comϷ0.5 kcal/mole is JϷ2, whereas reactions of F ϩH₂(jϭ1) under the

i.e., consistent with only negligible contributions from rotationally excited

H₂(jу2). The arrow designates typical p₀ϫd conditions for the rest of the

work reported in this paper.

same conditions can produce HF( ϭ3) up to JϷ5. Thus, quantum state

v

resolved, near threshold rotational distributions for the nascent HF( ϭ3)

v

*

products can provide a sensitive probe of the nonadiabatic F ϩn-H₂reac-

tion channel, based solely on ͑i͒ energy conservation and ͑ii͒ the well-

known asymptotic energy levels of H₂and HF.

VI. THRESHOLD STUDIES

The results in the previous section clearly identify two

important discrepancies between experiment and adiabatic

theoretical predictions for FϩnϪH₂(jϭ0,1). First of all, re-

products, and provides an especially good opportunity for

obtaining additional dynamical insights from threshold prod-

uct state studies.

active cross sections into the _HFϭ3 manifold drop off far

v

more slowly with E_comthan predicted from fully converged

For example, Fig. 10 displays the maximum product lev-

*

adiabatic calculations. Second, 2–3-fold more rotational en-

els energetically accessible to F, F , and H₂(jϭ0,1) reac-

ergy is experimentally observed in the HF ( ϭ3,J) product

tants at E_comϭ0.5 kcal/mole, i.e., where all the incident en-

v

manifold than theoretically predicted from FϩH₂calcula-

tions on the lowest adiabatic potential surface of Stark and

Werner. It is important to note that the quantum calculations

of Castillo et al. are numerically ‘‘exact’’ and based only on

two assumptions: ͑i͒ a given ab initio potential energy sur-

face, and ͑ii͒ purely adiabatic reaction dynamics on that po-

tential surface. It is always possible that discrepancies in the

cross sections and product state distributions at low E_com

could arise simply from errors in the SW potential energy

surface. Indeed, the reaction dynamics this far below the bar-

rier are dominated by quantum tunneling, which leads one to

expect exponential sensitivity to potential surface inaccura-

cies in the transition state barrier height, width, curvature,

etc. However, as described in this section, these studies have

also been performed in a regime that eliminates the possible

inﬂuence of inaccuracies in the potential energy surface, and

thereby permits one to focus explicitly on the role of adia-

ergy (⌬EϩE_com

rovibrational energy of the HF( ,J) product. The initial

translational energy distributions of F and F are assumed to

be identical, but with an internal energy difference equal to

the spin–orbit splitting, ⌬E_spin–orbitϭ1.15 kcal/mole. Since

the width of the experimental E_comdistribution (FWHM

Ϸ0.2 kcal/mole at E_comϭ0.5 kcal/mol) is less than or com-

parable to the relevant rotational energy spacings, this allows

a rigorous prediction of the highest HF ( ϭ3,J) product

state that could be formed, corresponding to zero kinetic en-

ergy recoil of the products. For example, at E_com

ϭ0.5 kcal/mol, F can energetically access only up to HF(

ϭ3,Jϭ2), whereas F at the same collision energy can pro-

duce three additional rotational levels up to HF( ϭ3,J

)

has been converted into internal

v

*

v

*

v

ϭ5). Thus, the full quantum state resolution of the present

experiment can allow one to sensitively differentiate between

adiabatic and nonadiabatic reactive channels by examining

the product state distributions obtained near the energetic

threshold.

*

batic (FϩH₂) versus nonadiabatic (F ϩH₂) contributions to

the reaction dynamics.

The strategy is based on the conservation of energy,

which relies only on the accurately characterized asymptotic

properties of the FϩH₂potential energy surface. The exo-

The results presented in Fig. 11 explicitly highlight such

threshold effects. The HF ( ϭ3,J) rotational distributions

v

obtained at a given E_comhave been plotted as a function of

threshold energy (E_thr), deﬁned as the minimum collision

thermicity of the FϩH₂reaction ⌬Eϭ32.001(14) kcal/

͓

mole͔ is determined by the difference in HF and H₂disso-

ciation energies, which are both known to unusually high

precision ͑Ϯ0.014 kcal/mole͒ from previous spectroscopic

measurements.^89,90This uncertainty is already much smaller

than the relevant internal energy spacings in reactants or

energy required to energetically access HF ( ϭ3,J) from

v

adiabatic reactions of FϩH₂(jϭ1). The advantage of such

an abscissa is that all states with E_thrуE_comare rigorously

closed for the adiabatic FϩH₂reaction channel and can only

*

be produced from nonadiabatic F ϩH₂events. For compari-

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8414

J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nizkorodov et al.

where the normally dominant adiabatic channel is suppressed

by the reaction energetics. As the ﬁrst and the most convinc-

ing experimental ﬁnding, HF( ,J) product states are de-

v

tected that are energetically inaccessible from the adiabatic

*

FϩH₂reaction but remain open for the corresponding F

channel. The second conﬁrmation comes from the results of

converged QM calculations on the best available PES.^52,84

The calculations predict vanishingly small cross sections for

the FϩH →HF( ϭ3)ϩH reaction in the energy range of

v

2

E

_comϭ0.3–0.6 kcal/mole, in contrast to the reaction cross

sections measured experimentally. It is also demonstrated

that an alternative explanation based on reactions with rota-

tionally excited H₂(jу2) is much less credible, based on the

small cross sections at low E_com, the weak dependence of

these cross sections on H₂rotational excitation, and the re-

sults of extensive experimental tests. In this section we

*

speculate on the possible mechanism of the F reactivity and

give some suggestions for future directions that would be

required to provide a more quantitative description.

One physically appealing but clearly speculative mecha-

*

nism for the F ϩH₂reaction dynamics would involve nona-

*

diabatic quenching of F followed by a reaction on the adia-

batic FϩH₂surface in a single collision event. The ﬁrst step

in such a process could be signiﬁcantly enhanced by near-

FIG. 11. Rotational distributions of HF( ϭ3) products at several represen-

tative lower collision energies. The distributions are plotted as a function of

v

resonant (⌬j_Hϭ2) electronic-to-rotational ͑E–R͒ energy

2

60,70,72,77,78

the minimum E_comrequired to produce a given state of HF( ϭ3) from

v

*

exchange between F and H₂,

FϩH₂(jϭ1) reactions, based on a rigorous lower limit of zero product

kinetic energy recoil in the center-of-mass frame. Also shown for each case

is the experimental distribution of E_comobtained from Monte-Carlo simula-

tion. The shaded symbols represent states that would be energetically inac-

cessible via adiabatic FϩH₂(jϭ1) reactions and can only be produced via

*

F ϩH jϭ0͒→ F---H jϭ2͒ →HF ,J͒ϩH,

͑3͒

͑

2

͓

͑

2

͔

͑v

although some calculations⁶²predict the pure quenching pro-

cesses (⌬j_H₂ϭ0) also to occur with comparable rates. We

*

nonadiabatic reactions with F . Note that the net cross sections for forming

wish to emphasize that this is only one of many possible

mechanisms⁹¹for interpreting such a nonadiabatic event.

However, there are several precedents for such behavior in

the literature, at least for the heavier halogen species where

spin orbit coupling effects are more signiﬁcant. For example,

related studies of rapid electronic–vibrational ͑E–V͒ energy

HF ( ϭ3,J) is dropping off rapidly over this range of collision energies; for

v

visual ease of comparison, the data for each energy have been rescaled to

the same maximum value.

son, the distribution of center-of-mass collision energies ob-

tained from the Monte-Carlo simulations are also shown.

Figure 11 clearly shows that as the average collision energy

transfer from spin–orbit excited Br(²P_1/2) to H ( ϭ1)⁹²

v

2

demonstrate the importance of nonadiabatic ͑albeit highly

efﬁcient͒ E–V transfer in the entrance channel, followed by

is decreased, more HF ( ϭ3,J) product states are evident

v

that are not energetically accessible to adiabatic reactions of

ground state F atoms with n-H₂(jр1). For example, one,

two, and three such states are clearly discernable at E_com

ϭ1.31, 0.91, and 0.54 kcal/mole, respectively. Finally, no

product state is observed with more than ⌬E_spin–orbit

ϭ1.15 kcal/mole beyond this adiabatic limit at each center-

of-mass collision energy. In other words, all the above

subsequent H atom abstraction from vibrationally excited

H₂,

*

Br ϩH ϭ1͒→ Br---H ϭ2͒ →HBrϩH.

͑4͒

͑v

2

͓

͑v

2

͔

Similar evidence for nonadiabatic reaction dynamics has also

been obtained in the reverse direction from studies by Pola-

nyi and co-workers for FϩHBr→HF( ,J)ϩBr,⁹³which

v

threshold HF( ,J) products are energetically consistent with

v

*

demonstrated a product Br/Br ratio independent of the F/F

*

the nonadiabatic F ϩH₂(jϭ1) channel. In summary, these

ratio in their thermal source. This was interpreted as hydro-

gen abstraction to form HF( ), followed by near resonant

threshold results, based solely on the conservation of energy,

constitute strong additional evidence for the presence of

v

V–E transfer from HF( ) to ground state Br atoms in the

v

*

nonadiabatic reaction pathways in F ϩH₂.

exit channel, i.e.,

*

FϩHBr→ HF ͒---Br →HF Ϫ1͒ϩBr .

͑5͒

͓

͑v ͑v

͔

VII. DISCUSSION

The present work provides the ﬁrst experimental evi-

These studies provide intriguing examples of efﬁcient

nonadiabatic relaxationϩreaction mechanisms occurring in a

single collisional event. Such nonadiabatic reaction pro-

cesses with spin–orbit excited states could have a signiﬁcant

impact on the kinetics of these and other halogen/hydrogen

abstraction reactions, especially for low collision energies/

2

*

dence for ﬁnite nonadiabatic reactivity between F ϭF( P_1/2

)

and H₂, though such behavior has been long predicted by

theorists. This conclusion is primarily founded on two ex-

perimental observations, both of which are made at collision

energies lying below the reaction barrier ͑Ϸ1.9 kcal/mole͒,

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J. Chem. Phys., Vol. 111, No. 18, 8 November 1999

Nonadiabatic reaction dynamics

8415

temperatures where the reaction may be insufﬁciently ener-

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Energy-dependent cross sections and nonadiabatic reaction dynamics in F(2P3/2,2P1/2) + n - H2→HF(v,J) + H

DOI: 10.1063/1.480182

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