J. Phys. Chem. 1993, 97, 2123-2127
2123
Stabilities and Lifetimes of Fluoroakyl Iodide and Fluoroallyl Iodide Collision Complexes+ Richard W. P. White, David J. Smith, and Roger Grice' Chemistry Department, University of Manchester, Manchester MI 3 9PL, UK Received: August 4, 1992; In Final Form: September 30, 1992
Translational energy threshold functions have been determined for the endoergic reaction of Fz molecules with CHsI, C Z H ~ Ic3H.11, , (CH3)2CHI, (CH3)3CI, and C ~ H Smolecules, I using a supersonic beam of F2 seeded in He buffer gas produced from an alumina nozzle source. The dissociation energies of the product FIR radicals determined from the translational threshold energies, are approximately constant Do(F-IR) 115 5 kJ mol-' with respect to F IR but vary from Do(F1-R) 70 f 10 kJ mol-' with respect to FI R for the alkyl iodides to Do(F1-R) 23 f 10 kJ mol-' for allyl iodide. Ratios of the lifetimes of FIR complexes formed in large impact parameter F IR reactive collisions to their rotational periods determined from angular distributions measured at an initial translational energy E 38 kJ mol-' are compared with ratios calculated from RRKM microcanonical transition-state theory. The predominant role of low-frequency transitional modes of vibration which are strongly modified as the FIR complex changes to the FI-R transition state compared with highfrequency constant modes which are largely unaltered is demonstrated by approximate comparison of theoretical and experimental lifetimes.
-
-
+
+
1.4
The reactive scattering of fluorine atoms with a range of alkyl and allyl iodides has recently beenstudied in detailI4 toinvestigate the role of persistent collision complexes which have lifetimes greater than one rotational period for the alkyl iodides and less than one rotational period for allyl iodide. F+IR+FIR-.IF+R (1) These results have been interpreted in terms of the extended microcanonical theory5 for the product angular and translational energy distributions arising from the dissociation of complexes via a product transition state which approximates to a prolate symmetrictop. However, these features of the reactivescattering are relatively insensitive to the stability and structure of the persistent collision complex provided that the lifetime is long enough to ensure energy randomization over the internal modes of the collision complex. The osculatingcomplex model6predicts that the lifetime of the collision complex will determinethe relative magnitude of scattering into the forward and backward directions. The stability of the fluoromethyl iodide radical has previously been determined by Farrar and Lee7 by measuring the translational energy threshold for the endoergicreaction of fluorine and methyl iodide molecules. This method is employed here for the range of alkyl and allyl iodides studied previously.I4 The estimated stabilities of the fluoroalkyl and fluoroallyl iodide radicals are used to correlate the lifetimes of the corresponding collision complexes using RRKM microcanonical transition-state theory.*
+ IR-.
FIR
*
-
Introduction
F,
-
+
I
1
I
I
I
-ap+
F,(He) +CH,I
I
I
I
80
100
120
I
I
I
F
1.2 1.0
?
0.8
E
0.6
1 1::
,d
F2
0.0 -20
0
-y
\
20
1
+3
A
40
60
LAB ANGLE 8 /degrees 1.4
1.0
1
I
I
I
I
1
0.6 0.4
+F
(2) 0.2
Experimental Metbod The apparatus was the same as that employed in previous work on the F IC1 reaction9with the F atom dischargesource replaced by an alumina nozzle heated up to a temperature lo00 K by an inconel clad thermocoax heating element. The beam of FZ molecules seeded in He buffer gas issued from a 0.25mm diameter nozzle using a stagnation pressure 100 mbar. The velocity distribution of the FZmolecule beam was measured as a function
+
-
-
' This paper is dedicated in fond regard to Dudley Herschbach on his 60th birthday, who, together with Walt Miller and Sanford Safron, first discovered long-lived complexes in a molecular beam reactive scattering experiment. 0022-3654/93/2091-2123$04.00/0
0.0
LAB ANGLE 8 /degrees
Figure 1. Laboratory angular distributions of FIR reactive scattering for the F2 + CH31 (upper panel), C2HsI (lower panel) reactions measured at initial translational energies of E 54 kJ mol-'. Solid lines show the fit of the kinematic analysis.
-
of nozzle temperature by a beam monitor quadrupole mass spectrometerdetector. Angular and velocity distributions of FIR reactive scattering were measured as a function of Fzbeam velocity using the rotatable mass spectrometerdetector and pseudorandom 0 1993 American Chemical Society
2124 The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
White et al. F2+n-C3H71. Et,,- 38.OkJ/wl and a- 1.0
I I
3.0
I I
I
I
I I
I
5.0
I I
I
I I
I
9.0
7.0
LAB VELOCITY io oms-’ Figure 2. Laboratory velocity distributions of FIR reactive scattering
I a“
0.0
22.0 2 6 . 0
S-
-
/
0.8-
.rl e,
?
4
0.6-
0
34.0
38.0
42.0
46.0
50.0
F2+2-C3H71. Et,,- 35.0kJ/mol and a- 1.0
1.0
1.OA
30.0
E kJ/mol
measured at the peaks of the laboratory angular distributions shown in Figure 1 for F2 + CH3I (upper trace), CzHsI (lower trace). F2+CH3I. Et,- 46.OkJ/mol and
0.2
leO
3-
I
U
0.6-
R rl
$
0.4-
Y U
a
0.2-
0.0
20.0 2 4 . 0 28.0 32.0 3 6 . 0 4 0 . 0 4 4 . 0 4 8 . 0 52.0 E kJ/mol
Figure4. Dependence of FIR reactive scattering on initial translational energy for F2 C3H71(upper panel), (CH3)zCHI (lower panel).
+
E kJ/mol F2+C2HSI. Et,,- 39.0kJ/mol and
8-
1.0 0
Results
0.8rl U
0.6--
R rl
9
0.4-
Y
U
a
0.2--
23.0
Laboratory angular distributions of FICH3 and FIC2Hs product scattering from the F2 CHjI, C2HJ reactions at initial translational energy E 54 kJ mol-l are shown in Figure 1 with thecorresponding laboratoryvelocitydistributionsshown in Figure 2. In both cases the reactive scattering measured at the IF+ fragment mass peak lies close to the velocity of the laboratory centroid vector and agrees closely with measurements made at the FIR+ parent mass peak. Kinematic analysis shows that the FIR reactivescattering favors the backward hemisphere in accord with previous mcasurementslo on the F2 + 12, IC1, and HI reactions. The intensity of FIR reactive scattering measured at the peak of the laboratory angular distribution is shown as a function of initial translational energy for FZ+ CHJ, C2HJ in Figure 3. Similar laboratory angular and velocity distributions of FIR reactive scattering were measured at the IF+ mass peak for the other FZ+ IR reactions and the corresponding intensities at the peak of the laboratory angular distributions are shown as a function of initial translational energy for FZ+ C3H71, (CH3)zCHI in Figure 4 and for F2 + (CH&CI, C3H.d in Figure 5 . In the case of these more complex alkyl and allyl iodides, reactive scattering was not detected at the FIR+ parent mass peaks.
-+
=!
$-
velocity distributions measured by the rotatable massspectrometer with the entrance aperture restricted to a horizontal slit of width -0.1 mm.
27.0 31.0
35.0
: : : : : : :
39.0
43.0
41.0
51.0
1 kJ/ml
Figure 3. Dependence of FIR reactive scattering on initial translational I panel) measured at energy for FZ+ CH3I (upper panel), C ~ H S(lower the peak of the laboratory angular distribution. Solid lines show the fit of the threshold function given by eq 3 with the parameters = 1 and the threshold energies &h given in Table 1.
time-of-flight analysis. The alkyl and allyl iodide molecule cross beam issued from a glass nozzle of diameter -0.25 mm with
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2125
Fluoroalkyl Iodide and Fluoroallyl Iodide Complexes
the velocity distributions of the incident beams
FZ+t-C4t191. Et,,- 37.OkJ/aol and a- 1 . 0
leO
0
T
0.4 U
0.0
23.0 27.0
31.0
47.0
35.0 3 9 . 0 4 3 . 0 E kJ/Wl
FZtC3ESI. Et,,- 3 8 . O k J / w l and
8-
51.0
1.0
where Eth denotes the threshold energy, s the number of internal degrees of freedom of the transition state, and Q.. the limiting reaction cross section at high initial translational energy. The best fit to the experimental data for F2 + CHJ which extends over the widest range of initial translational energy was obtained with the parameter s = 1 and this value was employed for all the other measurements. The values of the threshold energies Et,, thereby obtained are listed in Table I, and the fits to the experimental data are shown in Figures 3-5. The F-IR bond energy of the FIR radical may be calculated from Do(F-IR) = Do(F2) - Eth, where the bond energy Do(F2) = 154.6 kJ mol-' is taken from Huber and Herzberg.Iz This relationship requires that the threshold energy arise solely from the endoergicity of reaction 2 without involving any additional activation energy. The absence of an activation energy in the correspondingF atom reaction 1 has been attributed" to charge-transfer interactions of the form RI+F- and the electron affinity of the Fz moleculeI4 suggests that similar charge-transfer interaction RI+Fz- should also give a negligible additional activation energy for reaction 2. The FI-R bond energy of the FIR radical may then be calculated fromDo(FI-R) = Do(F-IR)-A&where thecxoergicitiesUo(F + IR I F + R) are taken from refs 1-4. This is illustrated by the potential energy profile for the F + IR reactions shown in Figure 6, with the resulting bond energiesand exoergicities listed in Table I. It is apparent from these values that the F-IR bond energies lie within a narrow range 11&120 kJ mol-' for all of the FIR radicals studied here. The FI-R bond energies also lie within a limited range -65-75 kJ mol-l for the FIR radicals, where R denotes an alkyl group, but the FI-R bond energy is much lower when R denotes an allyl radical due to the larger exoergicity of the F + C ~ H Sreaction. I According to the osculating complex model6 the lifetime of a persistent collision may be estimated from the relative magnitudes of reactive scattering into the forward 8 = Oo and backward 8 = 180° directions in centre-of-mass coordinates
-
-
0.4
t I
a!
o.2
0
23.0
/
21.0
. 31.0
0
35.0 3 9 . 0 4 3 . 0 E kJ/mol
41.0
0 51.0
Figure 5. Dependence of FIR reactive scattering on initial translational energy for FZ (CHI)JCI (upper panel), C J H ~(lower I panel). .............................................................................
+
1
(4)
E ,: I
where 7 denotes the lifetime and Trot the rotational period of the collision complex. Values calculated on this basis for the ratio ~ / 7 are , ~ listed ~ in Table I1 for the reactive scattering of F atoms seeded in He buffer gas with the sequence of alkyl and allyl iodide molecules14 and IC1.9 The precession of complexesthrough the forward and backward directions occurs in an entirely equivalent manner in the F IR reactions. Consequently, eq 4, which treats the scattering at 8 = Oo and 180° on an even handed basis, is preferred to alternative formulationslSJ6which assume that dissociation of complexes starts abruptly at 8 = Oo. According to RRKM theory? the lifetime of a persistent collision complex with total internal energy E* and angular momentum L is given by
+
/ % /J .................................. FIR
I
Figure 6. Potential energy profiles for the F + IR reactions at initial orbital angular momentum L = 0 (lower curve) and L = L, (upper curve). Energy annotation ignoring zero-point energies; initial translational energy E. well depth EO, reaction exoergicity ADO,initial and final centrifugal barriers B,, B',, rotational and internal vibrational energy of collision complex E,,,*, Eint*,internal energy of transition state Ei.2.
Discussion The translational energy threshold measurements shown in Figures 3-5 have been fitted by the equation for the dependence of the total reaction cross section on initial translational energy proposed by Mayer, Wilcomb, and Bernsteinl convoluted over
T (E
,L)= hp( E ,L)/ n( E',L)
(5) where h is Planck's constant, p(E*,L) denotes the density of states of the complex, and n(Et,L)the total number of states of the product transition state with the internal energy Et excluding the reaction coordinate. The density and the number of states both depend upon the energy which is distributed freely over vibrations and internal rotations excluding the energy of overall rotation. Both the collision complexes and product transition states are good approximations to prolate symmetric tops for all of these F + IR reactions.14 For collisions at the largest impact
2126
White et al.
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993
TABLE I: Enerdes/kJ mol-' of Fluoroalkyl Iodide and FluoroaUyl Iodide Radicals FIR and FICl from Ref IC CH3 46 109 65 44
Eih
Do( F-I R) Do( FI-R) ADo(F IR)
+
a
C2H5 39 116 76 40
CiH7 38 117 78 39
R (CHMH 35 120 75 45
(CH~IC 37 1 I8 64 54
CiH5 38 1 I7 23 94
CI 25 130 70 60
All values &5 kJ mol-' except Do(F1-R) f 10 kJ mol-'
-
TABLE 11: Ratios of Collision Lifetime to Rotational Period T / T , ~ for , Persistent Collision Complexes Formed in the Reactive Scattering of F Atoms with IR Molecules at an Initial Translational Energy E 38 kJ mol-' and Effective Number of Internal Demees of Freedom s
T/Trdexp) T/Trodeq 9)
1.7 1.7 4
S
2.8 2.8 5.5
3.6 3.9 6.5
2.8 2.7 6
parameters, the precessional motion of the collision complex and the product transition state lies close to the plane perpendicular to the initial orbital angular momentum L. Consequently, the potential energy profile for collisions with the maximum orbital angular momentum L, may be drawn including the energy of overall rotation as shown in Figure 6. This profile shows the product transitionstate located at the top of the centrifugal barrier in the exit valley of the potential energy surface. The reactive scattering arising from large impact parameter collisions peaks sharply in the forward and backward directionsi4 and hence represents the dominant contribution to the lifetime estimated from the experimental angular distributiona6 In this case the rotational period of the collision complex is given by
= 2?r12*/L, (6) where I,* is the moment of inertia of the complex for rotation about an axis perpendicular to the symmetry axis. If, for simplicity,we adopt the classical expressions for the number and density of states," the ratio of the complexlifetime to its rotational period may be written approximately Trot
7(E,L,) -=--
L,
II;-'v/
T ~ ~ ~ ( L , 2rI2* ) II;ui*
r
+ AD, + E, - Lm2/212* -' E + AD, - Lm2/212
I
(7)
where the products of vibrational frequencies vi*, u? extend over the s vibrational degrees of freedom of the complex and s - 1 degrees of freedom of the transition state excluding the reaction coordinate, where E denotes the initial translational energy, Eo the dissociation energy of the complex with respect to reaction products, 12+the moment of inertia of the transition state and ADo the reaction exoergicity. For the range of F + IR reactions being considered here, considerablecancellation may be expected between the products of vibration frequencies for modes of the hydrocarbon radical, which are little changed in passing from the complex to the transition state. The frequencies involved with the symmetric, asymmetric, and bending vibrations of the F-I-R bonds will undergo major change in passing from complex to transition state and the appropriate ratios in eq 7 are correspondingly uncertain. However, these ratios are likely to be quite consistent along the series of F + IR reactions. For this reason, the ratio of products may be replaced by the reciprocal of an average frequency for the purposes of this analysis. Similarly, the centrifugal energy of the transition state may be replaced approximately by the maximum centrifugal barrieri8which may in turn be equated to the peak product translational energies for these reactionsi4 Incorporating these approximations into eq 7 then yields an
2.2 1.9 7
0.8 0.1 1 7
0.5 0.25 3
expression which may be parametrized by the experimental data 7(E,L,) - L, Trot(Lm) - 2r12*v
- H
,
(E +
+
1-'
AD, E, - 12Ekk/12* E + ADo-Ekk
(9)
Calculations using structures for the FIR complexes with r(IF) = 2.1 A, r(C1) = 2.2 A, r(IC1) = 2.5 A and transition states of refs 1-4,9 indicate a ratio 12t/12* 1.2 f 0.1 for these reactions, although the magnitudes of the individual moments of inertia increase by a factor -2 along the homologous series. If it is assumed that the maximum initial orbital angular momentum L, remains constant, then the rotational period T,,~ for collisions at the largest impact parameter must increase by a factor -2 along the homologousseries of collision complexes. Ratios of the collision lifetime to the rotational period r(E,Lm)/TroI(Lm) calculated on this basis from eq 9 with L, = 200)r, I2*(FICH3) = 3.17 X 10-45kg m2 and = 1.1 X 1013 s-I are listed in Table 11,using the valuesof Eo= D(F1-R) from Table I. The calculated ratios T(E,L,)/~~~~(L,) follow the experimental values for the alkyl iodidesl-3 when thevalues of theeffective number of internal degrees of freedom s given in Table I and employed in eq 9 correspond to those previously deduced from analysis1-' of the differentialreaction crosssections. However,thecalculated ratios T(E,Lm)/Trol(Lm)for the allyl iodide4 and IC19J0 reactions lie below the experimental values when the effective number of internal degrees of freedoms 7,3 indicated by the differential reaction cross section data are employed. In all cases the effective number of internal degrees of freedom which are classically excitedi8J9are less than the total number of degrees of freedom of the collision complex and product transition state. Only lowfrequency vibration modes and internal rotations are expected to contribute significantly to the internal density of states.2, The classically excited degrees of freedom correspond mainly to transitional modes21v22 which undergo considerable change as the system passes from the persistent collision complex to the product transition state, with the high-frequency constant modes being largely unchanged. In principle, this may be checked by using the Whitten Rabinovitch semiclassical appr~ximationl~ to the internal density of states to gain in place of eq 9
-
-
+ AD, + E, + a*E,* - EIJ:1,2'* E + ADo + a+E; - E'pk
-' (lo)
I
where Ez*, E: denote the zero-point energies of the collision complex and transition state. However, calculationof the Whitten Rabinovitch parameters, a* and at, and zero-point energies requires detailed knowledge of the vibrational frequencies of the
Fluoroalkyl Iodide and Fluoroallyl Iodide Complexes collision complex and transition state. The effect of loosening of the transition state as reflected in decreasing vibrational frequencies for corresponding modes passing from the complex to the transition state decreases the lifetime calculated from eq 10 through the ratio of vibration frequencies but this may be partly offset through the zero-point energies and Whitten-Rabinovitch parameters. The lifetime predicted by eq 9 for allyl iodide in Table I1 is significantly less than the experimental value. Laser-induced fluorescence measurements23of the I F product vibrational state distribution indicate that energy redistribution over the internal modes of the collision complex is incomplete in the F + C3HJ reaction. When the lifetime of the collision is very much less than the rotational period as predicted for the F + C3HJ reaction by eq 9, the direction of scattering becomes dependent on the reactant impact parameter. In particular, theangular distribution of scattering from small impact parameters may be expected to be isotropic or even favor the backward direction24while scattering from large impact parameters favors the forward direction. Hence only a qualitative comparison of the lifetime of complexesformed in large impact parameter collisions is obtained for the most exoergic F + C3HJ reaction.
Acknowledgment. Support ofthis work by SERC, the European Commission, and NATO is gratefully acknowledged. References and Notes (1) Jarvis, R. D.; Firth, N. C.; Smith, D. J.; Grice, R. J. Chem. SOC. Faraday Trans. 1990,86. 2059. (2) Harkin, J. J.; Jarvis, R. D.; Smith, D. J.; Grice, R. Mol. Phys. 1990,
71, 323.
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2127 (3) Harkin, J. J.; Smith, D. J.; Grice, R. Mol. Phys. 1991, 72,95. (4) Harkin, J . J.; Smith, D. J.; Grice, R. Mol. Phys. 1991, 72,763. (5) Jarvis, R. D.; Harkin, J. J.; Smith, D. J.; Grice, R.Chem. Phys. Lett. 1990,167,90. (6) Fisk, G . A.; McDonald, J. D.; Herschbach, D. R. Discuss. Faraday SOC.1967,44,228. (7) Farrar, J . M.; Lee, Y. T. J. Chem. Phys. 1975,63,3639. (8) Marcus, R. A. J. Chem. Phys. 1952,20,359; 1965,43, 2658. (9) Jarvis, R. D.; White, R. W. P.; Zhu, 2.Z.; Smith, D. J.; Grice, R. Mol. Phys. 1992,75. 587. (10) Valentini, J. J.; Coggiola, M. J.; Lee, Y. T. J. Chem. SOC.Faraday Discuss. 1977,62,232. ( 1 1) Mayer, T. M.; Wilcomb, B. E.; Bernstein, R. B. J. Chem. Phys. 1977, 67,3507. Gonzalez Urena, A. Mol. Phys. 1984,52, 1145. ( 1 2) Huber, K. P.; Herzberg, G . Constantsfor Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (13) Loewenstein, L. M.; Anderson, J. G. J. Phys. Chem. 1987,91,2993. (14) Chupka, W. A.; Berkowitz, J.;Gutman, D. J. Chem. Phys. 1971,55, 2724. (15) Bullitt, M. K.; Fisher, C. H.; Kinsey, J. L. J. Chem. Phys. 1974,60, 478. (16) Stoke, S.;Procter, A. E.; Bernstein, R. B. J. Chem. Phys. 1976,65, 4990. (17) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; WileyInterscience: New York, 1972. (18) Safron, S. A.; Weinstein, N . D.; Herschbach, D. R.; Tully, J. C. Chem. Phys. Lett. 1972,12,564. (19) Marcus, R. A. J . Chem. Phys. 1975,62,1372. Worry, G.; Marcus, R. A. J. Chem. Phvs. 1977,67. 1636. (20) Cheung, J.-T.; McDonald, J. D.; Herschbach, D. R. Faraday Discuss. Chem. SOC.1973,55, 377. (21) Wardlaw, D. M.; Marcus, R. A. Adu. Chem. Phys. 1988,70,231. (22) Klippenstein, S.J.; Marcus, R. A. J. Phys. Chem. 1988,92, 3105, 5412. (23) Collins, S.T.; Trautmann, M.; Wanner, J. J. Chem. Phys. 1986,84, 3814. (24) White, R. W. P.;Smith,D. J.;Grice,R. Chem. Phys.Lett.l992,193, 269.
