Kinetics of the Mu + H2 and Mu + D2 reactions from 610 to 850 K

Volume

KINETICS

1 November 1985

CHEMICAL PHYSICS LEI-PERS

121, number 1.2

OF THE

David M. GARNER.

Mu + H, Donald

AND

Mu + D, REACTIONS

G. FLEMING

’ and Randall

FROM

610 TO 850 K

J. MIKULA’

TRICJMF and Dcporrrrrer~ of Chemixry. Unicerxit~- of Brinslr Columhio. I’oncorrrvr. Brirish Colurnhia. Canodo V67 I Y6 Received

3 June 19BSr in final rorm 7 August

1985

rare conslanls for the thermal chemical reaclions 01 muonium (Mu): Mu + H2 + MuH + H and Mu+ D2 + measured in the temperalure range 610-650 K. For the hydrogen reaction. log A (err? molecule-’ fC,-13.8+1.5 kcol mole-‘. while for the druvxium rexCon log A (cm3 molecule-’ s-‘) = -9.12 1.2 and Ea = 17.22 4.1 kcal mole-‘. These results compare well with variational wmsition slate theory calcularions carried OULon the Liu-Siegbnhn-Truhlar-Horowitz potemial surface. The bimolecular

MuD+D. have been s-l)= -9.6&0.4md

1. Introduction In the 50 year history of the interplay between chemical reaction theory and experiment [ 141, the study of the isotopic variants of the elementary H + Hz exchange reaction has played a central role. The reas.Jns for this continued interest are clear: H3 is the simplest of all three-atom systems and, to date, it is the only system for which an accurate, truly ab initio potential energy surface exists [5,6]. Consequently, it is only for the isotopic variations of the H + Hz reaction that the predictive capability of reaction theories can be tested by comparison with experiment, free from ambiguities arising from inaccuracies in the surface itself. In this pursuit it is clearly important to have the widest possible variation in isotopic substitution. Traditionally this has been provided by experiments on hydrogen (HJ, deuterium (D) and tritium (T) substitution, in both bulk kinetic studies of thermal reaction rates [3,7--101 as well as in molecular beam [ 1 I] and hot atom [12] studies. In theoretical investigations there have no doubt been more papers published on the H + Hz reaction system than on any other [24,13-211. The muonium atom (Mu = p+e-) is a hydrogen ’ 1983/&l ’ Presenl P-0.

80

John Simon Guggenheim Fcllo~-. address: EM&R. Weswrn Research

Bag 1280.

Devon.

Album.

Canada

Laboralorier. TOC 1EO.

atom analogue in which the proton nucleus is replaced by a positive muon. Since the muon mass is only 1/9th of the proton mass (but 200 times the electron mass), muonium can simply be regarded as an isotope of the H atom, as demonstrarsd by several experimental [22] and theoretical investigations [23--271 of its gas-phase chemical reactivity during the past decade. The remark able mass ratio between Mu and H renders muonium a very sensitive probe of isotope effects in H atom reactions. The present paper reports the first complete measurements of the thermal bimolecular rate constants for the isotopic exchange reactions: Mu+H2-+MuH+H,

(RI)

Mu+Dz+MuD+D,

(I=)

which take place primarily from the ground (u = 0) vibrational state of the target molecule (at 850 K the fraction of molecules in vibrational excited states is =0.6% in D2 but only ~0.07% in Hz). The results cited herein were arrived at over an approximately three-year period, a combination of difficult experimental conditions and the pressures of accelerator beam time. They are compared with recent theoretical calculations for these reactions [24-271, carried out on the Liu-Siegbahn-Truhlar-Horowitz (LATH) potential surface [2,5,6] as well as with both experimental and theoretical results for the reactions 0 009-2614/85/S (North-Holland

03.30 0 Elsevier Science publishers B.V. Physics publishing Division)

Volume

121, number

1.2

CHEMICAL

PHYSICS

H+H2+H2+HH

W)

H+Da+HD+D,

(R4)

D+Hz+DH+H.

(W

2. Experimental

technique

The experiments were conducted with the muon spin rotation &SR) technique, which has been extensively described elsewhere [22,28,29] _The @R method is based on the following: a beam of spin polarized u+ is stopped in the target of interest (here gaseous H-2

or D2)_ The target vessel is positioned between Hehnholtz coils which provide a magnetic field transverse to the beam direction, causing the muon spin to precess with a characteristic Larmor frequency (as in NMR). The muon undergoes radioactive decay with a mean life of 2.2 w into a high-energy positron 01” + e’v&,) that is ejected anisotropically, preferentially along the muon spin direction. The time evolution of the muon ensemble spin polarization appears as a time differential histogram of the number of decay positrons detected in a fmed direction, measured as a function of the survival time of the corresponding muons. Thus, a uSR histogram is a decay curve that is modulated by coherent muon precession, in complete analogy to free induction decay magnetic resonance experiments [28]. In an external magnetic field of less than 10 G, the

spin precession frequency of the muon in the paramagnetic Mu atom due to the muon-electron hyperfme interaction is 1.3 MHz G-l, which is 103 times the precession frequency of a muon in a diamagnetic environment, such as the MuH molecule. Hence, the coherent

precession of an ensemble of paramagnetic Mu atoms is exponentially damped as chemical reactions such as (Rl) place the muon into a diamagnetic environment at randomly distributed times. The relaxation rate (A = l/T-J of the muonium precession signal is linearly related to the bimolecular rate constant, k: 1=x,+k[X],

(1)

where [X] is the concentration of the reaction partner (Hz or D2) and b is a background relaxation measured in the absence of reagent [X] Three general features of the @R technique are noteworthy in the present study: (1) pSR is literally a one-atom-at-a-time technique that makes interfer-

LETTERS

1 November

1985

ences arising from, for example, Mu-Mu interactions, impossible_ Discussions of a “MU ensemble” or “Mu concentration” are ergodic concepts: a time-averaged ensemble is equivalent to a space-averaged ensemble. (2) Although, from the chemical viewpoint, muons enter the target with enormous (MeV) energies, their thermalization is rapid: typically of order 10 ns in gases at about an atmosphere pressure [29]. The present paper reports measurements observed on the microsecond timescale, over which thermal equilibrium of the muonium atom ensemble with the target gas is assured. (3) The timescale of phenomena accessible to study by @R [28] is limited by the 2.2 m muon lifetime to a range of 0.01-100 us, or less. It is the timescale limitation of @R that presented the most formidable problems to the present measure-

ments. Bimolecular rate constants of.muonium reactions in the range 1 O-1o-l 0-l” cm3 molecule-l s-l are experimentally easy to determine in gases at a few atmospheres [22,29]. For Mu + Hz, however, it was predicted [24] that k = lo-r6 cm3 molecule-1 s-l at 500 K with a reaction activation energy of about 14 kcal mole-l. Thus, measurements at high pressure and temperature were indicated for the present study. A cylindrical target vessel 90 cm long and 18 cm in diameter was fabricated of number 304 stainless steel. The outside surface of the vessel was fitted with ceramic-encased electrical heating coils rated to draw 3 kW of power. The target outer wrapping was a 3 cm thick ceramic fabric insulation. One end of the target vessel was fitted with a 0.13 mm thick Kapton window 4 cm in diameter supported by a 7 mm thick, water cooled, aluminum disk into which was drilled a close-packed array of 19 holes 7 mm in diameter. This arrangement provided the low-mass entrance windows necessary for the low-energy (surface) muon beam [22,29], which has a range of only about 150 mg cm -‘. So long as the thin Kapton window was kept cool (
Volume 121,

number 1,2

for pSR observations

CHEMICAL

PHYSICS

1 November

LmERS

1985

of Mu decays was from the cen-

20 cm of the target vessel. The temperature gradients in this region were constantly monitored by chromel-alumel thermocouples located at several points along the radius and length of the observation region, and it was found that these gradients could be maintained to within typically -C25 K at all temperatures. This rather large temperature uncertainty was only a minor contributor to the overall uncertainty of the experiments. The experiments were conducted on the M20 channel at TRIUMF, a meson factory adjacent to the campus of the University of British Columbia_ The evacuated target vessel was filled with a gas mixture of H2 (or D2) and argon, an tier-t moderator, to the desired pressures. The gases, obtained from Canadian Liquid Air, had the following manufacturer’s purity assays: Hz, 99.999%; D2,99.6% (largest impurity: Hz), Ar, 99.99%; and were used without further purification. Temperature equilibration of the target gas required typically 0.5 h. The @R spectrometer was essentially the same as described in refs. [22,29] _ The measurements were made with a magnetic field of 8.3 G. Two independent histograms were taken with “left” and “right” positron telescopes and the fmal results are reported as a weighted average. tral

3. Results The bimolecular rate constants obtained from simultaneous fits to eq. (1) of the relaxation rates from the two independent left and right histograms are listed in table 1 and illustrated in the Arrhenius plot of fig. 1, which includes ah.0 the theoretical rates (dashed hues) for reactions (Rl)-(R3) from ref. [24]. The temperature uncertainties in the data are the measured fluctuations and gradients; the rate constant uncertainties are primarily from counting statistics. The bimolecular rate constants were fit to the usual Arrhenius expression k = A exp(-&/RT) using the method of Cvetanovic and Singleton [30] to iterate the exact (lo) statistical weighting of ln k, yielding the results in table 2. There are several contributing factors to the large uncertainties reported in the data of tables 1 and 2. The temperature uncertainties have already been dir+ cussed. In addition, the aluminum support for the win82

0.01

1.0

I

I

I

I

L2

1.4

1.6

1.8

lDOO/Tempcralure

2.0

(K-3

Fig 1. Arrhenius plots of the experimental results for Mu + HP and Mu + D7 (solid lines) compared with the theoretical results from ref. [24] (dashed lines); the theoretical results for H + Hz are also shown (upper dashed line).

dow scattered 30 MeV positrons present as a contamination in the muon beam into the positron detectors. This creates a background that reflects the 23 MHz duty cycle of the TRIUMF cyclotron and increases the Table 1 Experimental and (R2)

bimolecular rate constants for reactions (Rl)

k

T(K) Mu+H2

Mu+&

(Rl)

(R2)

608 624 669 708 745 802

(lo-l4 2 -t * * f *

cm3 molecule-’

22 22 20 29 18

0.13 f 0.18 0.47 f 0.13 0.75 * 0.20 254 -c 0.90 2.22 f 0.38

36 845+24

5.39 f 1.31 6.09 * 0.97

674 f 19 749 f 17 773 f 21

0.05 -F 0.18 1.04 f 0.29

850 * 22

2.?2

1.16 f 0.43 * 0.72

i

5-l)

Volume 121, number I,2 Table 2

Arrhenius p-cten

for reactions (Rl) and (R2)

1ogA (cm3 molecule-’

s-‘)

E, (kcd mole-‘)

Mu+H2

-9.62+;:;;

+1.6 13.8_1_5

Mu+ D2

-9.17+;:-;

+4.9 17-2-3-s

correlations among the various fitting parameters. The greatest uncertainties, however, arose from the determination of the background relaxation, ho, which is measured in (chemically inert) pure argon. This is due primariIy to magnetic field inhomogeneity from two sources: (1) the Helmholtz coils themselves; and (2) the magnetic fields produced by the electrical heating coils. Unlike previous work for which X, was only an insignificantly small (in comparison with X) and reproducible quantity, for the present work the largest X was only 2Sh0, and the reproducibility of Lu was dependent upon the muon stopping power of the target gas mixture. Other studies [29] have shown that the muon stopping power is proportional to the gas mixture electron charge density, which was held constant in the present measurements. A series of experiments to investigate the uncertainties introduced by muon stopping power fluctuations indicated for the Hz reaction that systematic uncertainties range from about 7% at 850 K to 30% at 610 K; and for the D2 reaction, the systematic uncertainties range from about 20% at 850 K to 40% at 675 K.

4. Discussion and comparison 4.1. Perspective

1 November 1985

CHEMICAL PHYSICS LEIl-JZRS

with theory

on H + Hz

The availabiLity of a labclled atom (like Mu) clearly facilitates the measurement of H + H2 reactive scattering and there now exists accurate (z&20%) thermal rate constants, particularly for reaction (R5), over a very wide temperature range (==200-1200 K) [7-g]. These data provide an important basis for comparison both with theory and with the present results for the corresponding Mu reactions. Three broad types of theoretical calculations have been carried out: quantum mechanical reactive scattering calculations (QM) [13-

18,261, quasiclassical trajectory calculations (QCT) [19,20,27], and transition state theory (TST) calculations, particularly recent canonical and “improved” canonical variational treatments (CVT or ICVT) [21; 24,251. Although the main focus of most calcularions to date has been on state-to-state cross sections, with their direct applicability to molecular beam and recent hot atom results [11,12], the importance of continued studies of thermal rate constants must be kept in mind. Not only do these provide a reliable measure of absolute cross sections (which molecular beam experiments often do not), but they also provide a much more sensitive measure of the importance of quantum tunneling near threshold, an effect which can be particularly important in the reactivity of the Mu atom [22-261. In both QM and QCT calculations, the bimolecular rate constant can be related to the reaction cross section a(E) by the famihar expression k(7)

= (8/7r~)“2(k~T)-3’2

X s

a(E) E exp(-E/kgTJ

dE

(2)

0

Note that this equation contains a simple reduced mass factor which just reflects the mean rate of collision and is largely uninteresting_ Rather it is the deviations from this simple mass dependence that are of interest since these are indicative of cIynamicaZ effects contained in the cross section itself. In TST, the (textbook) expression for an atom (A)-molecule (BC) collision is given by

k(T) = I’-

h

Lexp(-EvAG/k~T),

(3)

QAQFX

where EVAG represents the ground-state

(u = 0) vibra-

tionally adiabatic barrier (in the notation

of ref. [21]),

I? is a transmission coefficient

and Q’,

QA and Qm

are the usual products of partition functions [3,31,32]. In recent years there has been renewed interest in the dynamical

interpretation

of TST. One focus has

been on (canonical) variational theory (CVT) in which the position of the dividing surface between reactants and products is varied in order to minimize the classical (l? = 1) reactive flux across it [21,24,25,3 1, 33]_ Another focus has been on how to properly include quantum tunneling along the reaction coordi-

83

CHEMICAL PHYSICS LETTERS

Volume 121, number I,2

nate. The usual method is via a factorization of the transmission coefficient (I’ = ~QMI'c~) and to calculate I'QM as a ID penetrability along the appropriate reaction path [21,24,25,3 l-331 _Both the tunneling correction to I? and the position and height of the VAG barrier depend sensitively on isotopic mass. Consequently, it has been of considerable interest to compare variational TST (ICVT) calculations for the isotopic variants of the H(Mu) + H2 reactions on the accurate LSTH surface with both experiment and with corresponding QCT and QM calculations. In the case of reactions (IU)-(R5) the level of agreement between theory and experiment is certainly impressive, the most exemplary case being the D + H2 reaction. For example, the QCT calculations of Mayne and Toennies [ 191, the CVT calculations of Garrett and Truhlar [21] and the 3DQM (adiabatic T matrix) calculations of Tang et al [16] all agree with experiment to typically better than 30% over six order rs of magnitude in k(7J (see also refs. [15,17]). At the same time it can be argued that these reactions do not provide a crucial test of theory since the H and D atoms differ by only a factor of two in mass. For example, QCT calculations [ 19,201, which do not include any tunneling, agree as well (or better) with the data at low temperatures as those theories that do include tunneling [15-17,211. This fortuitous agreement is likely a demonstration that the QCT calculation is less vibrationally adiabatic and hence gives rise to an unphysically low threshold energy [15,34]. 4.2. The Mu + H2 and Mu + D_7reactions There are a number of points alluded to above which are important to the present comparison with muonium. This is facilitated with reference to TST and in particular by expressing the basic result of eq. (3) as a ratio of the two rate constants for reactions (Rl) and (R3) (denoted as k&k&,

x 3Nfi7 [&(Mu)/2] ;=I

sinh[C$(H)/2]

sinh[Ur*(Mu)/2]

U:(H)/2

’

where Vi’ - hVi’/kBT and p* denotes the effective 84

(4)

1 November 1985

mass of the barrier crossing trajectory. It is customary to denote r$ = (U/2)/sinh(U/2), indicating the inherent quantum nature of the vibrational partition functions [3,3 1,321. Although this expression invokes the assumption of harmonic vibrations, it is useful for discussion purposes. In general, if the VAG barrier is earlJI, the activated complex corresponds only to a slightly perturbed target molecule (“loose” complex), that displays a very weak dependence on isotopic substitution; I$Mu)/I$(H) + 1 and [p*(H)/p*(Mu)] l/2 + 3. This is the simple kinetic isotope effect referred to earlier and which enters directly into the collision theory expression of eq. (2). Conversely, if the VAG barrier is Zafe, the activated complex is a “tight” one which displays a marked dependence on isotopic substitution; I’$(Mu)/I’$(H) + 0 and [~‘(H)/~*(Mu)] II2 + 1. Such dramatic mass effects have their origin in the large zero-point energy differences between Mu and H substituted molecules at the transition state and dictate, for any reaction, that kp,lui 3kH. The only factor which can offset this result is quantum tunneling, contained in the transmission coefficient_ In general, rM”/rN s 1 only for an early barrier since it is only for such a barrier that translational energy is much more effective than vibrational energy at promoting reaction; in this case the reduced mass of the system is essentially just the mass of the incident atom. This is normally the situation in studies of Mu reactivity [22,23 ] _Conversely, for late (endothermic) barriers, the reduced mass of the system is much closer to that of the product channel, markedly offsetting the tunneling advantage of the much lighter Mu atom. These limits are clearly reflected in fig. 1 and in the trends exhibited in table 3, which presents, along with the experimental activation energies and rate constants for reactions (Rl) and (R2) from tables 1 and 2, the reaction enthalpies (w and the calculated positions of the VAG barriers (relative to s = 0 [21, 241) for the set of reactions (Rl)-(IU). The AHvalues for reactions (Rl) and (R2) have been arrived at from spectroscopic values for H2 and corrected by a simple harmonic mass dependence for substituted Mu. The well known propensity for exothermic reactions to correspond to the earliest (VAG) barriers and the lowest E, is clearly seen in table 3. This table also presents the reduced masses for the reaction systems (Rl)-(RS), assuming both an extreme early and an

Volume 121. number 1.2

CHEMICAL

Table 3 Reaction enthalpies (AH), experimental locations (r) for reactions (Rl)-(RS) ReXti0n

Mu+H2 (Rl) Mu+& (R2) H+H2 (R3) H+ 4 (R4) D+Ha (RS)

AH =) t&al mol-I) 7.6 9.2 0.0 1.0 -0.82

1 November 1985

PHYSICS LETTERS

activation energies (E3). rate constants at = 745 K, reduced masses (n), and CVT barrier

E, b)

k

(kcal mol-‘)

(IO-”

13.8 f 1.5 17.2 ? 4.2 a.5 f 0.5 9.4 -c 0.3 7.6 f 0.2

2.2 1.0 40.0 14.4 43.2

Jl(early) cm3 molecule-’

s-l)

d)

P(laW) d)

s (A) =)

0.526 1.03 0.667 1.20 0.750

0.38 (late) 0.53 (late) 0.0 0.056 (late) -0.095 (culy)

Cl 0.107 0.110 0.667 0.800

1.00

al Enthalpies calculated from measured spectroscopic values for Hz. HD and D2 and corrected by n- iI2 for substituted muonium. b, Experimental activation energies from simple Arrhenius fits, taken from the original papers: for (Rl) and (R2) from this paper (fig. 1, table 2), for (R3) from ref. [a], for (R4) and (R5) from ref. [ 7!_ Cl The experimental bimolecular mte constants at ==745 K. See footilote b). ‘1 Reduced masses assuming extreme early or late barriers_ e, Location of the VA barrier from the 3D CVT calculations of refs. [21,24], relative to r = 0 for reaction (R3).

extreme late barrier. From these values alone one na-

comparison

ively expects tunneling to be most important for reaction (Rl) regardless of the position of the VAG bar-

(FU)

rier, but to be markedly reduced for reaction (R2) relative to (R3) for the late barrier characterizing this reaction..However, any such tunneling enhancement in reaction (RI) is not enough to offset the effects of changes in zero point energy on the vibrational partition functions noted above, with the result that k3 5 kl > k2 over the whole temperature range (fig. 1). See also discussion in ref. [S] _ The combined effects of the location, height and width of the VAG barrier and the amount of tunneling are reflected in the experimental activation energies. A simple estimate of the zero-point energy difference between MuH;! and H3 in the (u = 0) transition state gives -4.5 kcal mol-l [7], or = 13 kcal mol-’ for the VAG barrier of reaction (Rl), ignoring the small contribution from quantum tunneling; a similar comparison between reactions (R2) and (R4) yields 2 16 kcal mol-l for the Mu + D2 reaction. These values can be expected to be roughly consistent with the experimental activation energies, as indeed they are (table 2) and represent the only cases yet seen in gas phase Mu chemistry where E&Mu) > E,(H). The qualitative trends outlined above are seen in the ICVT calculations of Garrett and Truhlar [24,25] and in the recently,subrnitted 3DQM (coupled states) calculation of Schatz [26]. The calculated rate constants from ref. [24] are shown as the dashed lines in

in

with

experiment

for reactions

(Rl)

and

the Arrhenius plot of fig. l_ These calculations

have utilized the Marcus-Coltrin tunneling path (MCP) but the transmission coefficients have been calculated semiclassically (SAG) rather than fully quantum mechanically (VAG); hence, the complete calculations are denoted ICVT/MCPSAG. It is expected that the results should not differ appreciably from the more accurate MCPVAG ones [21,24,33], although it is noted that Mu would likely be more sensitive to such changes than either H or D would be. The level of agreement between theory and experiment in fig. 1 is good (essentially within experimental error), for both reactions (Rl) and (R2), consistent also with that reported earlier for reactions @3)-(W) [21]_ The calculated activation energies from ref. [24] are 14.1 and 16.5 kcal mol-i for reactions (RI) and (R2), respectively, again in agreement with the experimental ones (table 2). Although the size ofthe experimental error bars in fig. 1 (table 1) must be kept in mind, it seems apparent that the rate constants calculated with the ICVT/ MCPSAG formalism tend to become progressively too small at lower and lower temperatures, notably for the Mu + Hz reaction. In fact, it seems generally to be the case for reactions (Rl)-(R5) that the CVT/MCP formalism

consistently

under-predicts

the experimental

This tendency indicates that either the MCPSAG transmission coefficients do not properly account for the required amount of tunneling, or that rate constants.

85

1 November 1985

CHEMICAL PHYSICS LETTERS

Volume 121. number 1,2

Table 4 TbeoreticaI and experimental rate constants for Mu + H2 T(K)

Experiment

608 624 669 708 745 802 845

1.3 f 4.7 + 7.5 f 2.5 f 2.2 * 5.4 f 6.1 *

=)

l-8(-15) 1.3 (-15) 2.0(--15) 0.9(--14) 0.4 (-14) l-3(---14) l.O(-14)

3DQhl (ES) b,

ICY-f/Morse ‘)

ICVT/WKB d,

3.6(-15) 4.8(-l% 9.7(--15) l-7(-14) 2.7(--14) X0(--14) 7.7(-14)

l-6(-15) 2.2(--15) 4.8(--15) 9.0(-15). 1.5(--14) 3.1(-14) 5.2(-14)

2.7(-15) =X4(-15) =7.7(-15) =1.4(-14) =2.5(-14) =5.2(--14) 7.9(-14)

3) From table 1, this paper. Units are in cm3 molecule-’ s-l with tbc power of ten given in parentheses b) From exact coupled states 3DQM calculations, table III. ref. [26]. c) From hlCPSAG (Morse approximation) calculations of ref. [24]. as plotted in fig 1. d, From LfCPSAG OVKB) calculations of ref. [25], table V. Approximate values obtained by interpolation the approximations

used to calculate

the vibrational

frequencies at the transition state are not accurate, or both. These points have recently been addressed by Garrett

and Truhlar

basic CVT Morse

theory

approximation

uate stretching particularly Considerable

in (further)

[25],

where

improvements

used previously

frequencies

to the

it is concluded

that

[21,24]

can be seriously

for those reactions involving improvement in comparison

the

to eval-

in error,

muomum. with colIin-

calculations is effected if the adiabatic eigenvalues of the reaction-path Hamiltonian are evaluated with the WKB method rather than the Morse approximation This improvement is also reflected in the calculated (ICVT/MCPWKR) rate constants, which are increased overall by a factor of = 1 S in comparison with the Morse approximation calculations, giving somewhat better agreement with experiment for both the Mu + H2 and Mu + D2 reactions than is seen in fig_ I_ This is shown in table 4, which compares the pres‘ent experimental rate constants for the Mu + II2 reaction with the ICVT calculation of ref. [24] (Morse) and ref. [25] (WKB) and with the 3DQM calculation of ref_ [26]. In both of the ICVT calculations, the values shown are taken from calculations with the MCPSAG transmission coefficients. The comparison between the exact 3DQM calculations and the ICVT (WKB) ones for reaction (Rl) shows that the latter calculation works extremely well, particularly at high temperatures. Both calculations give really excellent agreement with the experimental results although there is again an indication at the lowest temperatures cur quantum

86

that tunneling is not properly accounted for in the ICVT calculation. Better experimental data at temperatures g600 K would help to confirm this point. Such experiments are currently being planned with a newly designed target vessel and anew set of Helrnholtz coils of much higher intrinsic homogeneity than had characterized those available for the present study. These improvements should allow us to make measurements down to ~500 K for both reactions (RI) and (R2). In summary, the present comparison between theory and experiment for the Mu + H2 and Mu + D2 reactions has illustrated the dramatic impact that the ultralight Mu atom mass can have on H3 reaction dynamics. As a final example of this, we note that the QCT (forward trajectory) calculations for Mu + Hz [27] are in marked disagreement with the experirnental results by two orders or magnitude (too large), in complete contradiction to the agreement noted earlier for reactions (R+oS).

Acknowledgement One of us (DGF) would like to thank Dr. Peter Toennies and the MPI fir Stromungsforschung, Gbttingen, for their hospitality during most of a sabbatical year. DGF would also like to thank the John Simon Guggenheim Foundation for a fellowship and the Scientific Council of NATO for a Senior Scientist award. The continuing financial support of NSERC (Canada) is gratefully acknowledged. We would also like to thank Drs. Jonathan Connor and Donald

Volume 121. number 1.2

CHEhUCAL PHYSICS LETTERS

Truhlar for sending us their theoretical results prior to publication, and Dr. George Schatz for the receipt of a timely preprint (ref. 1261). Helpful comments on the manuscript by Donald Trublar were also appreciated.

References [II Proceedings of the Conference on 50 Years of Reaction Dynamics, Berlin, Ott 1981; Ber. Bunsenges Physik. Chem. 86 (1982)

348.

121 D-G. Truhlar, ed. Proceedings of the Conference on PO-

[31 [41 151 [cl 171 161

tcntial Energy Surfaces and Dynamics Calculations, ACS National Meeting, Las Vegas, Aug. 1980, (Plenum Press, New York, 1981). H-S. Johnston, Gas phase reaction theory (Ronald Press. New York, 1966). D-G. Truhlar and R.E. WyatS Ann. Rev. Phys. Chem. 27 (1976) I_ B. Liu. J. Chern Phys 80 (1984) 581; P. Siegbahn and B. Lti. J. Chem Phys 68 (1978) 2437. D.G. Truhlar and C.J. Horowitz, J. Chem. Phys. 68 (1978) 2466; 71 (1979) 1514@); B.R Johnson, J. Chem. Phys. 74 (1981) 754. A.A. Westenberg and N. de Haas, J. Chem. Phys 47 (1967) 1393. D-N. Mitchell and D-J_ LeRoy,

J. Chcm

Phys. 58 (1973)

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PHYSICS

E PoRak and P. Pechukas, J. Chem. Phye 79 (1983) 2814; E PolJack, MS. Child and P. Pechukas, J. Chem. Phys. 72 (1980) 1669; P. Pcchukas and F-J. McLafferty, J. Chem Phys 58 (1973) 1622 1321 A. Kuppennann, J. Phys. Chem. 83 (1979) 172; P. Pechukas. in: Dynamics of molecular collisions, modem theoretical chemistry, Part B, ed_ W.H. Miller (Plenum Press, New York, 1976) p. 239; W.H. Miller, Accounts Chem Rer 9 (1976) 306.

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mann_J. Chem. Phys 81._(!984) 3542;; B.C. Garrett and D:G. Truhlar, J. Chem.Phys 4931;. D-G. Truhlar and B.C. Garrett; Accounts (1980) 440. [ 341 G.C. Schatr, J. Chem

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5386.