J. Phys. Chem. 1987, 91, 5496-5503
5496
Oscillating Reactivity of the Light Atom Transfer Reaction CI 4- HCI Dependence on the Nature of the Potentlal Energy Surface
-
CIH
+ CI:
Avigdor Persky* and Haya Kornweitz Department of Chemistry, Bar- Ilan University, Ramat-Gan 521 00, Israel (Received: March 23, 1987)
The hydrogen atom transfer reaction C1+ HC1- ClH + C1 was used as a model for investigatingthe occurrence of oscillations in the reactivity as a function of collision energy for reactions in which a light atom L is transferred between two heavy atoms H and H’, H + LH’ HL H’. Very extensive three-dimensional quasi-classical trajectory calculations, under a variety of conditions and employing three LEPS potential energy surfaces, were carried out for this purpose. The three surfaces have very similar properties for the collinear C1-H-C1 configuration but considerably different widths of the reactive cone of acceptance. Significant oscillations were obtained for two of the surfaces. The surface for which the strongest oscillations were observed is characterized by strong anisotropic attractive forces which lead to reorientation of the reagents to a nearly collinear configuration even when the initial orientation angle (the angle between the relative velocity vector and the axis of the HC1 molecule) is large. The results of this study indicate that the most promising experiments for detecting oscillations should be scattering experiments with oriented molecular beams.
-
+
1. Introduction
TABLE I: Morse Parameters for the Bonds H-CI and CI-CP parameter H-CI CI-CI
In recent years there has been increasing interest in the dynamics of reactions in which a light atom L is transferred between H L + H’ (see, for two heavy atoms H and H’, H + LH’ example, ref 1-6 and references therein). Reactions with such a mass combination exhibit several outstanding dynamic features due to the small skewing angle between the reactants and products valleys of the potential energy surface in mass-scaled coordinates. These features include, for example, the high degree of internal excitation of the products in exothermic reactions even on predominantly repulsive potential energy ~ u r f a c e s ’and * ~ ~oscillations ~ in the reaction probability as a function of collision energy. The oscillations which are of classical rigi in,^^^^^ resulting from the hopping of the light atom between the two heavy atoms, have been observed mainly in collinear quantum mechanical (C1 + HC1,2,i0 I HI,8J1 Br HC1,I2 F DBr3) and quasi-classical (C1 HCl,*J3 I HI,8,i40 HCli5) studies. The possibility of observing oscillations in three-dimensional calculations (3D) was discussed in several publications. Pollak et aL4 constructed a model for symmetric light atom transfer reactions which predicted oscillations in the 3D cross sections for reactions which occur on a collinearly dominated potential energy surface with a low barrier. Hiller et al.” expect to find oscillations in the energy dependence of the cross section at a fixed scattering angle, rather than for the total cross sections. Baer and Last performed 3D quasi-classical trajectory calculations for the reClH C113 and I H I IH 114using actions C1 HCl
-
+
+
+
+
+
-
+
+
0,A-’ re, 8,
-
TABLE II: Sato Parameters and Properties of the Potential Energy Surfaces 1-111 for the Collinear Confieuration CI-H-CI surface I surface I1 surface 111 A( H-C1)a 0.115 0.166 0.220 A(C1-CI)’ 0.115 -0.098 -0.241 r,2t = r23i,bA 1.467 1.478 1.488
p; kcal/mol
ust>,d cm-’ ~
~ cm-’ 1
,
uJ,d cm-l
~
8.55 341 13981 508
8.55 343 14361 612
8.55 345 14671‘ 691
OSato parameters. Interatomic distances at the saddle point. Barrier height. dVibrational frequencies of the transition state. TABLE 111: Barrier Heights for Different CI-H-CI Angles for the Potential Energy Surfaces 1-111
p,kcal/mol
+
(1) Polanyi, J. C.; Schreiber, J. L. In Physical Chemistry, an Advanced Treatise; Jost, W., Ed.; Academic: New York, 1974; Vol. 6A, Chapter 6. (2) Bondi, D. K.; Connor, J. N. L.; Manz, J.; Romelt, J. Mol. Phys. 1983, 50, 467. (3) Gertitschke, P. L.; Manz, J.; Romelt, J.; Schor, H. H. R. J . Chem. Phys. 1985, 83, 208. (4) Pollak, E.; Baer, M.: Abu-Salbi, N.; Kouri, D. J . Chem. Phys. 1985, 99, 15. (5) Klippenstein, S . J.; Babamov, V. K.; Marcus, R. A. J . Chem. Phys. 1986, 85, 1924. (6) Persky, A.; Broida, M. Chem. Phys. 1987, 114, 85. (7) Polanyi, J. C. Acc. Chem. Res. 1972, 5, 161. (8) Kaye, J. A.; Kuppermann, A. Chem. Phys. Lett. 1981, 77, 573. (9) Pollak, E. J. Chem. Phys. 1983, 78, 1228. (10) Abu-Salbi, N.; Kim, S. H.; Kouri, D. J.; Baer, M. Chem. Phys. Lett. 1984, 112, 502. (11) Hiller, C.;Manz, J.; Miller, W. H.; Romelt, J. J . Chem. Phys. 1983, 78, 3850. (12) Kaye, J. A.; Kupperman, A. Chem. Phys. Lett. 1982, 92, 574. (13) Baer, M.; Last, I. Chem. Phys. Lett. 1985, 119, 393. (14) Last, I.; Baer, M. J. Chem. Phys. 1987, 86, 5534. (15) Persky, A.; Kornweitz, H. Chem. Phys. Lett. 1986, 127, 609. (16) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand: New York, 1979; Vol. 4.
C1-H-CI. dee.
surface I
surface I1
surface I11
180 170 160 150 140 130
8.55 8.74 9.30 10.31 11.92 14.33
8.55 8.82 9.64 11.12 13.44 16.86
8.55 8.89 9.96 11.85 14.78 19.07
,
diatomics-in-molecules (DIM) type potential energy surfaces. The partial cross sections for nonrotating reactants for scattering in the angular range 160-180°, corresponding to collisions with very low impact parameters, revealed oscillations which seemed to follow rather well the oscillations observed in the corresponding collinear calculations. In an earlier publicationi5we reported results of collinear and 3D quasi-classical trajectory calculations for the reaction 0 + HCI(v=Oj=O) O H + C1, which is very similar to the C1+ HCI reaction with respect to energetics, kinetics, and mass combination. A LEPS (London-Eyring-Polanyi-Sato) potential energy surface was used for the calculations. It was shown that while the collinear results exhibit strong oscillations in reaction probability as a function of collision energy, no significant oscillations are observed in the 3D partial cross sections for scattering angles in the range 170-18O0, or even in the range 175-180°, as opposed to the results
-
0022-3654187 , ,12091-5496%01.50/0 0 1987 American Chemical Societv I
2.001 57.97 1.988
“Based on data from ref 16.
+
+
1.868 106.5 1.275
De, kcal/mol
-
Oscillating Reactivity of the C1
+ HCl Reaction
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5491
'1
h
-
O S
Y
L
60.4 F
2
W
U 00
-
Figure 1. Potential energy contours (in kcal/mol) of the potential energy surface I for the reaction C1 HCI CIH + C1 (linear configuration). The point indicates the position of the saddle point.
+
+
of Baer and Last13 for the C1 HCI reaction. Thus, the rather limited results available at present concerning the occurrence of oscillations in 3D calculations are not sufficient for indicating the properties of H + LH' systems for which oscillatory behavior can be expected. In order to reach a better understanding of the conditions for observing oscillations in 3D calculations, we have carried out an extensive study for the typical H LH' reaction C1 + HCI -., CIH + C1 using three LEPS potential energy surfaces and investigating the Occurrence of oscillations. The results of this study are presented and discussed in this publication.
+
2. Potential Energy Surfaces and Computation Procedure Three semiempirical LEPS potential energy surfaces were employed for the calculations. The Morse parameters used for constructing the surfaces are listed in Table I. The Sato parameters and some properties of the surfaces for the collinear Cl-H-C1 configuration are presented in Table 11. Surface I is the same potential energy surface which was used in ref 2 for collinear quantum mechanical and quasi-classical calculations, in ref 17 for accurate quantum mechanical cross section calculations and in ref 18 for variational transition-state-theory calculations. The Sat0 parameters for surfaces IT and I11 were chosen so that the barrier height v for the collinear Cl-H-CI configuration was the same as for the surface I, but the dependence of on the Cl-H-CI angle for bent configurations was significantly different. Barrier heights for different C1-H-Cl angles for the three surfaces are given in Table 111. The data in Table I1 indicate that the properties of the three surfaces for the collinear configuration are very similar, except for the bending frequency at the transition state which increases significantly in the order surface I < surface I1 < surface 111. This increase is in accord with the steeper increase, in the same order, in the barrier height with the deviation from the collinear configuration as indicated in Table 111. A contour diagram of surface I, for the collinear configuration, is shown in Figure 1. The corresponding diagrams for surfaces I1 and I11 (not shown here) are almost identical with Figure 1. The computation procedure is the same as that employed in our earlier study of the reaction 0 HC1.I5 As in ref 15 the statistics of the calculations were significantly improved by carrying out the calculations over limited ranges of the impact pa-
+
(17) Schatz, G. C.; Amaee, B.; Connor, J. N. L. Chem. Phys. Lett. 1986, 132, 1. (18) Bondi, D. K.;Connor, J. N. L.; Garrett, B. C.; Truhlar, D. G. J . Chem. Phys. 1983, 78, 5981.
Etr ( k d / m d )
-
Figure 2. Collinear reaction probabilities as a function of collision energy for the reaction C1 HCI(u=O) C1H C1 for the potential energy surfaces 1-111.
+
+
rameter b and the initial azimuthal orientation angle 8,, the angle between the molecular axis of HCl and the initial direction of the relative velocity vector. Thus, instead of randomly selecting 8, (according to cos e,) from the full possible range (0-180'), as is usually done in trajectory calculation^,^^ this parameter was se8,,, was appropriately chosen to lected between 0' and be somewhat larger than the highest orientation angle leading to reactive collisions with the products scattered in the angular range of interest. The calculated cross sections uR' were multiplied by a factor f to derive the same cross sections uR that would be obtained if 8, had been selected from the full possible range: ffR
f
=
Y2(1
=
(1)
- COS er,max)
(2)
Values of b,,, were also appropriately chosen to be somewhat larger than the highest impact parameter that leads to reaction with the products scattered in the angular range of interest. 3. Results and Discussion 3.1. Oscillations in Reaction Probabilities, Partial Cross Sections, and Total Cross Sections. Collinear calculations were carried out for the range of collision energies E,, between threshold and 80 kcal/mol. For each collision energy 250 trajectories were calculated. The results are displayed in Figure 2. Strong oscillations are observed with frequencies decreasing on going from surface I to surface 111. The threshold energies differ only slightly. They are 4.95,4.85, and 4.75 kcal/mol for surfaces I, 11, and 111, respectively. In the second stage of this study we performed 3D trajectory calculations for C1 HCl(v=Oj=O) and calculated partial cross sections for scattering in the angular range 170-180' (rR(17O180)). Preliminary calculations indicated that all the reactive scattering in this angular range, for the three surfaces and for all the collision energies of our calculations, result from collisions with impact parameters smaller than 0.35 A. We therefore used a value of b,, = 0.35 in all these calculations. Values of 8r,max
+
(19) Karplus, M.; Porter, R. N.; Sharma, R. D. J . Chem. Phys. 1965,43, 3259.
5498 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
Persky and Kornweitz
TABLE I V Values of the Largest Initial Orientation Angle Leading to Reaction for Different Collision Energies for the Potential Energy Surfaces 1-111
6r,1(170-180): E,,, kcal/mol 6.0 8.0 10.0 20.0 30.0 40.0
surface I 4.1 6.2
1.o
12.5 18.5 22.5
deg
surface I1
surface I11
surface I
13 18 19 23 26 34
42 49 45 42 40 38
17 21 30 40 53 59
( t ~ t a l )deg ,~ surface I1
surface I11
24 40 41
42 66 15 90 95 96
61 13
77
"Largest value of the initial orientation angle 0, leading to reactive collisions with scattering angles in the range 170-180°. b,,, = 0.35 8,. bLargestvalue of the initial orientation angle 0, leading to reactive collisions for all scattering angles. Appropriate values of b,, were used increasing with E,, up to 3.0 8, for E,, 3 20 kcal/mol.
CItHCI
suwm I
0.0 0
8
I
I
20
30
40
D.
0 0
20
O
33
L
40
50 ~
M
Etr (kcal/ml)
E,, (kcol/mol)
Figure 3. Partial cross sections for scattering angles in the range 170-180°, 0~(17&180), as a function of collision energy E,, for the reaction C1 t HCl(u=Oj=O) CIH + CI for the potential energy surface I. Error bars indicate one standard deviation in cross sections.
-
were also determined from preliminary calculations. Different values had to be used for the three surfaces under different conditions. These values were chosen to be somewhat larger than e,, the largest value of 6, leading to reactive scattering in the angular range of interest. Representative values of e,, for several collision energies for scattering angles in the range 170-180°, as well as for the total reactive scattering, are given in Table IV. Partial cross sections ff~(170-180) as a function of the collision energy E,, for surfaces 1-111 are displayed in Figures 3-5. Each point in these figures represents the results obtained from 2000 to 6000 trajectories. By examining Figures 3-5, it can be clearly seen that while no significant oscillations are present for surface I, prominent oscillations, well outside the statistical errors of the calculations, occur for surfaces I1 and 111. The largest number of oscillations occur for surface 11, but the most prominent one, with respect to the relative change in cross section, is observed for surface 111. The behavior for surface I is similar to that obtained previously for the 0 + HCI r e a ~ t i o n . ' In ~ both cases strong oscillations were obtained in the collinear calculations, but no significant oscillations were found in the 3D results. The occurrence of oscillations for scattering angles smaller than 170' was also investigated. Surface I11 was employed for these calculations. We calculated partial cross sections for the ranges of scattering angles 150-160°, 110-130°, and 90-110' (bR(150-160), aR(110-130), and ffR(9&110), respectively). We also calculated values of the total cross section ffR. For each range of scattering angles we used appropriate values of b,,, and 6r,max. In general, we had to use increasing values of these two parameters with decreasing scattering angle. Typical values used were b,,, = 0.80, 1.60, and 2.0 A and = 60°, 80°, and 80° for calculating ffR(15&160), ffR(1 10-130), and ffR(90-1 IO), respectively. Partial cross sections for different ranges of scattering angles as a function of the collision energy are displayed in Figure 6. The results obtained for the total cross section are shown in Figure 7. Each point in Figures 6 and 7 is the result of 2000-6000
Figure 4. Partial cross sections for scattering angles in the range 170-180', aR(170-180), as a function of collision energy E,, for the reaction C1 + HCl(v=Oj=O) CIH + C1 for the potential energy surface 11. Error bars indicate one standard deviation in cross sections.
-
CI t H C I
I
0%
?I
0.0
I
0
10
20
30
4c
5
E !r (kcal /mol)
Figure 5. Partial cross sections for scattering angles in the range 170-180°, uR(170-180), as a function of collision energy E,, for the CIH + CI for the potential energy reaction CI + HCI(v=Oj=O)
-
surface 111. Error bars indicate one standard deviation in cross
sections.
trajectories. As can be seen from Figure 6 , oscillations occur not only for partial cross sections for scattering angles in the range 170-180°, which correspond to collisions with very small impact parameters, but also for much smaller scattering angles which result from collisions with large impact parameters. However, the oscillations observed for low scattering angles are weaker than for high scattering angles. The range of E,, for which the oscillations occur is shifted to higher values with the decrease in scattering angle (less backward scattering). In view of the results shown in Figure 6 it seems that weak oscillations may be obtained even for scattering angles smaller than 90°. Figure 7 shows that the oscillatory behavior is washed out almost completely when the total cross section, which includes
~
Oscillating Reactivity of the C1
+ HCl Reaction
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5499
CI t H C l
SURFACE IU
8,=ao
-A
I
I
x,
m
E ,,
30
40
(kcal/mol)
Figure 8. Partial cross sections for scattering angles in the range 17C-18Oo, uR (170-180), as a function of collision energy E,, for the reaction CI + HCl(v=Oj=O) CIH + CI for an initial orientation angle Or = 20' for the potential energy surface 111. Error bars indicate one standard deviation in cross sections.
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CI + HCI SURFACE EI 8,= 20"
Figure 6. Partial cross sections for different ranges of scattering angles as a function of collision energy E,, for the reaction CI + HCl(v=Oj=O) -. CIH + CI for the potential energy surface 111: (A-A) scattering
angles 90-110°, uR (90-110); (A-.-A) scattering angles 110-130°, uR (110-130); (0---0) scattering angles 15C-160°, uR (150-160); (.---e) scattering angles 170-180°, uR (170-180). Error bars indicate one standard deviation in cross sections.
A
0.0
I
I
1
I
0
-
x
)
x)
M
80-
40
E +r (kcol/md)
Figure 7. Total cross sections uR as a function of collision energy E, for
the reaction CI + HCl(v=Oj=O) -.CIH + CI for the potential energy surface 111. Error bars indicate one standard deviation in cross sections. all scattering angles, is calculated. As shown in Figure 7 only a remnant of the oscillatory structure is preserved in the region of collision energies around 10 kcal/mol. Additional information about the Occurrence of oscillations was obtained by carrying out 3D calculations for a specific value of the initial orientation angle Or (oriented reagents). Calculations were carried out for surface I11 for Or = 20° in order to determine b,, = 0.35 A) and total partial cross sections ~ ~ ( 1 7 0 - 1 8 0(using ) cross section gR (using appropriate values of b,,, increasing with the collision energy up to b,,, = 3.0 8, for Et, 2 20 kcal/mol). This value of 6, is approximately in the middle of the range of 6 , leading to reactive scattering in the angular range 170-1 80' for surface I11 (see Table IV). The results are displayed in Figures 8 and 9, respectively. Figure 8 shows very strong oscillations which are much more pronounced than those obtained from the corresponding calculations for nonoriented reagents (Figure 5 ) , and their frequency is even higher than that of the oscillations observed in the collinear calculations (Figure 2). As can be seen from Figure 9, an oscillatory structure is also obtained for the total cross
.-.
N
'5
-
60-
8 -
i 5
4.0-
$
" p 2.0 -
0.0 0
D
20
30
40
50
E,, (kcal/mol)
Figure 10. Partial cross sections for scattering angles in the range 170-180°, ~ ~ ( 1 7 0 - 1 8 0 )as, a function of collision energy E,, for the reaction CI + HCl(v=Oj=O) CIH + CI, for an initial orientation angle 8, = loo, for the potential energy surface 11. Error bars indicate one standard deviation in cross sections.
-
section under the same initial conditions. Examination of Figures 8 and 9 shows that many of the features seen in Figure 8 are preserved to some extent in Figure 9, especially at the lower energy range.
Persky and Kornweitz
5500 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
T
1
- _
- _
t
0
40
m
80
w
.
----:
1m TlME / 3~10"~ S 40
80
160
40
80
.
I . . 120 160
-
Figure 11. Collision trajectories for CI + HCl(u=Oj=O). Interatomic distances (lower plots) and C1-H-C1 angle (upper plots) as a function of time, for surfaces 1-111 under identical initial conditions. Collision energy E,, = 12 kcal/mol, orientation angle 6, = 41°, and impact parameter b = 0.183 A. The collisions for surfaces I and I1 are nonreactive The collision for surface 111 is reactive.
Similar calculations of crR( 170-1 80) were carried out for surface I1 for 8, = 10". This value of 8, is approximately in the middle of the range for reactive scattering in the angular range 170-180O (see Table IV). The results are shown in Figure 10. Again, a very oscillatory structure is observed although the oscillations are not as pronounced as for surface 111. Similar calculations of aR(170-180), using b,,, = 0.35 A, for surface I did not reveal any significant oscillation even for very low orientation angles down to 8, = oo. To date, no experimental measurements showing oscillatory behavior have been reported. The results presented in this section can indicate the most promising experimental conditions for detecting oscillations in the reactivity for H LH' reactions, for nonrotating reagents (a high concentration of which can be obtained by using supersonic expansion techniques20,2'). If the nature of the potential energy surface for the reaction is conducive to oscillatory behavior, the most prominent oscillations should be observed in molecular-beam experiments using oriented molecules and measuring either partial cross sections for a limited range of scattering angles (Figures 8 and 10) or total cross sections (Figure 9). Impressive progress has been made in recent years in experimental scattering studies with beams of oriented molecules, for e ~ a m p l e . ~However, ~ - ~ ~ at present such studies are limited mainly to reactions involving symmetric-top molecules, or paramagnetic such as CF3Br + K23 and CHJ + Rb,25*26 molecules, such as NO 03."The orientation of such molecules is achieved by passing them through an inhomogeneous electric
+
+
~~
(20) Smalley, R. E.; Wharton, L.; Levy, D. H. Acc. Chem. Res. 1977, 10, 139. (21) Levy, D . H. Annu. Rev. Phys. Chem. 1980, 31, 197. (22) Jalinek, H.; Parker, D. H.; Meiwes-Broer, K. H.; Stolte, S.J . Phys. Chem. 1986, 90, 552. (23) Carman, H. S.;Harland, P. W.; Brooks, P. R. J . Phys. Chem. 1986, 90, 944. (24) Gandhi, S. R.; Curtis, J. J.; Xu, Q.X.; Choi, S . E.; Bernstein, R. B. Chem. Phys. Lett. 1986, 132, 6. (25) Parker, D H ; Chakravorthy, K. K.; Bernstein, R. B. J . Phys. Chem.
--. (26) Parker, D. H.; Chakravorthy, K. K.; Bernstein, R. B. Chem. Phys.
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TABLE V Total Cross Sections uR for the Reaction CI + HCI(v=OJ=O) CIH + c1 for the Potential Energy' Surfaces 1-111 E,,,
UR, A2
kcal/mol
surface I
6.0
(2.6 f 0.8) X (1.1 f 0.3) X (4.5 f 0.8) X lo-' (3.9 f 0.5) X 0.11 f 0.01 0.18 f 0.02
8.0 10.0 20.0 30.0 40.0
surface I1 (1.3 & 0.1) X (5.1 f 0.5) X 0.10 f 0.01 0.23 f 0.02 0.38 f 0.03 0.50 f 0.03
surface 111 0.14 f 0.01 0.60 f 0.03 0.73 f 0.03 1.06 f 0.07 1.08 f 0.05 1.07 f 0.05
field followed by a weak homogeneous electric field. However, for diatomic molecules with a closed electron shell it is very difficult to produce o r i e n t a t i ~ n . ~Significant ~.~~ oscillations, though less prominent than for oriented reagents, should be observed in measurements of partial cross sections using nonoriented reagents (Figures 4-6). This discussion is based on our results for nonrotating reagents. Rotational excitation of the reagents will probably weaken the ~scillations.'~The features of the potential energy surface that favor oscillatory behavior are discussed below. 3.2. Details of Individual Collision Trajectories. Some trends in the results presented in section 3.1 seem to be inconsistent with the properties of surfaces 1-111 shown in Table 111. Table 111shows that the increase in barrier height with the deviation from the collinear CI-H-Cl configuration becomes steeper on going from surface I to surface 111. One would therefore expect the range of leading to reaction, and correspondingly the reactivity, to decrease in the same order. The data in Table IV and in Figures 3-5 show that the opposite trend takes place. Values of Or,, and aR( 170-180) increase considerably from surface I to surface 111. Total cross sections also increase significantly in the same order, as shown in Table V. In order to resolve this seemingly contradictory behavior and to become more familiar with the properties of surfaces 1-111, individual trajectories were run and followed carefully. For every trajectory we recorded the three interatomic distances C1-H,
1981. 85. - - , 466 -~
Lett. 1982, 86, 113. (27) Van Ende, D.; Stolte, S . Chem. Phys. 1984, 89, 121.
(28) Brooks, P. R. Science 1976, 193, 11. (29) Stolte, S. Ber. Bunsenges. Phys. Chem. 1982, 86, 413.
Oscillating Reactivity of the C1
+ HCl Reaction
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
5501
-
4 601
I l l \ ti
- m-
ti
I I I I it
0
tt
I:
/
40
/:
t
w
m
80
TI ME / 3x10"* S
Figure 12. Reactive collision trajectories for C1 + HCI(v=Oj=O). Interatomic distances (lower plots) and C1-H-CI angle (upper plots) as, a function of time, for surfaces 1-111 under identical initial conditions. Collision energy E, = 12 kcal/mol, orientation angle Or = 25O, and impact parameter b = 1.561 A. TABLE VI: Average Vibrational, Rotational, and Translational Energies of the Products of the Reaction CI + HCl(v=OJ=O) Different Collision Energies, for the Potential Energy Surfaces 1-111
Ed, kcal/mol
ER', kcal/mol
-
ClH
+ CI for
Et:, kcal/mol
E,,, kcal/mol
surface I
surface I1
surface I11
surface I
surface I1
surface 111
surface I
surface I1
surface I11
6.0 8.0 10.0 20.0 30.0 40.0
3.6 3.9 3.8 4.4 4.3 4.7
3.8 3.9 3.7 3.7 3.1 4.2
3.9 3.8 3.9 4.0 3.7 3.8
2.1 2.1 3.4 8.4 10.3 11.5
0.53 0.7 1 1.o 3.1 6.5 10.2
0.06 0.23 0.52 1.5 2.9 5.6
4.5 6.3 7.0 11.5 19.7 28.1
5.9 7.1 9.5 16.8 24.1 29.9
6.3 8.2 9.9 18.7 21.5 34.8
H-Cl, and Cl-Cl, and also the CI-H-Cl angle, as a function of time. Typical results for a collision energy of 12 kcal/mol are displayed in Figures 11-1 3. In each of these figures the initial conditions of the trajectories for all three surfaces are identical. Figure 11 shows trajectories with a very small impact parameter ( b = 0.183 A) and a large initial orientation angle (e, = 41'). A reactive collision occurs on surface I11 but not on surfaces I and 11. It can be clearly seen that for surface I11 reorientation takes place as the CI atom approaches the HCI molecule, probably due to strong anisotropic attractive forces, and at the time of reaction the Cl-H-Cl configuration is nearly collinear. For surfaces I and I1 the initial orientation angle is outside the range for reactive collisions (see Table IV), and repulsion occurs resulting in rotational excitation of the HC1 molecule. Figure 12 shows reactive trajectories for 6, = 25O and b = 1.567 A. For all three surfaces a nearly collinear configuration is achieved at the time of reaction. This behavior was found to be typical of reactive collisions for all three surfaces, but as mentioned above the reactive cone of acceptance increases considerably on going from surface I to surface I11 (see Table IV). A careful examination of Figure 12 shows distinct differences between the three surfaces with respect to the manner in which the products separate after reaction. For surface I11 a nearly collinear configuration is retained for some time after reaction, and the products separate with only a small amount of rotational energy (ER' = 0.06 kcal/mol). On the other hand, for surface I a configuration far from being collinear is achieved while the products are still close together, and the repulsion between them in this bent configuration leads to high rotational excitation (ER'
= 5.70 kcal/mol). The behavior for surface I1 (ER' = 0.54 kcal/mol) is more like that of surface I11 than for surface I. Low rotational energy (ER' = 0.07 kcal/mol) was also obtained for the reactive trajectory on surface I11 shown in Figure 11. The differences in rotational excitation discussed above are typical of surfaces 1-111. Values of average energies of the products for different collision energies, obtained from calculations of total cross sections, are presented in Table VI. As can be seen from Table VI, values of ER'are much larger for surface I than for surface 111, and values of Et; are lower. The values obtained for E,' indicate that the vibrational energy is approximately conserved in the reaction (the vibrational energy of the reagents is 4.2 kcal/mol) for the three surfaces up to very high collision energies. Recent quantum mechanical calculations of cross sections for the C1 HC1 reaction employing surface 117also indicated a high degree of rotational excitation of the products. Figure 13 shows nonreactive trajectories for 0, = 25O and b = 1.874 A. This value of Or is within the reactive cone of acceptance for collisions with large impact parameters for all three surfaces. A remarkable difference is observed between the three surfaces. For surface I repulsive forces lead to rotational excitation of the HCl molecule in the collision. This also occurs, to a smaller extent, for surface 11. On the other hand, for surface I11 attractive forces allow the C1 atom to approach the HCI molecule closely, and no rotational excitation of the HCl molecule takes place. This behavior was found to be typical of nonreactive trajectories on surface I11 for values of Or within the range for which reactive collisions can occur. Outside this range (which is very wide) repulsive forces dominate also for surface 111, and the behavior is similar to that
+
Persky and Kornweitz
5502 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
180 -_ 8-
"9
0,
-
0
4 0 8 o t ? 0 1 6 0
~
-
-160 3x10-'~ s
-.__-__--
40
TI ME
80
-
120
-~ -40
80
--
120
'63
Figure 13. Nonreactive collision trajectories for C1 + HCI(v=Oj=O). Interatomic distances (lower plots) and C1-H-CI angle (upper plot) as a function of time, for surfaces 1-111 under identical initial conditions Collision energy E,, = 12 kcal/mol, orientation angle Br = 2 5 O , and impact parameter b = 1.814 8,
found for the nonreactive collisions on surfaces I and 11. Figure 13 shows also that the nearest distance of approach of the C1 atom to the HCl molecule is shorter for surface I1 than for surface I. The results obtained in this study by following the details of individual trajectories show clearly the significant differences in the properties of surfaces 1-111. While the behavior for surface I11 is governed mainly by strong anisotropic attractive forces over a wide range of orientation angles, the behavior for surface I is governed mainly by repulsive forces. The properties of surface I1 are intermediate between those of surfaces I and 111. Because of these differences, the width of the reactive cone of acceptance, and correspondingly the values of reactive cross sections, increase considerably from surface I to surface 111, as shown in section 3.1. The strong anisotropic attractive forces for surface 111 lead to reorientation of the reagents to a nearly collinear configuration at the time of reaction, even for large initial orientation angles. The steep increase in barrier height with the deviation from the collinear configuration at the saddle point (Table 111) is of minor importance in this case. Because of this behavior, an angle-dependent line-of-centers model, which incorporates the dependence of the barrier height on the angle of a p p r ~ a c h ~and + ~which ~ was found useful for other systems, such as H + H234,35and K + CH31,36is not suitable to describe C1 + HCl collisions on surface 111.
The results obtained in this study indicate that oscillations in reactivity for the C1 + HCl reaction are the most significant for the potential energy surface which is characterized by strong anisotropic attractive forces over a wide range of orientation angles. ~
~~
~~~
(30) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: London, 1980. (31) Smith, I. W. M. J . Chem. Educ. 1982, 59, 9. (32) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University Press: Oxford, 1987. (33) Levine, R. D.; Bernstein, R. B. Chem. Phys. Lett. 1984, 205, 467. (34) Blais, N. C.; Bernstein, R. B.; Levine, R. D. J . Phys. Chem. 1985, 89, 10. (35) Schechter, I.; Levine, R. D. Int. J . Chem. Kinet. 1986, 18, 1023. (36) Blais, N. C.; Bernstein, R. B. J . Chem. Phys. 1986, 85, 7030.
Additional studies, for other systems, employing different potential energy surfaces have to be carried out in order to determine whether this conclusion is general for light atom transfer reactions. 4. Summary The hydrogen atom transfer reaction C1+ HC1- C1H + C1 was used as a model for investigating the occurrence of oscillations in the reactivity as a function of collision energy for reactions in which a light atom is transferred between two heavy atoms, H LH' H L H'. Very extensive three-dimensional quasiclassical trajectory calculations, under a variety of conditions and employing three LEPS potential energy surfaces having the same barrier height for the collinear C1-H-Cl configuration (surfaces I-III), were carried out for this purpose. All the calculations were performed for the ground vibrational and rotational states of the HC1 molecules. These calculations gave some indications as to conditions under which the observation of oscillations is most likely and the nature of the potential energy surface most favorable for such behavior. The strongest oscillations were found for surface 111, somewhat less pronounced oscillations were found for surface 11, and no significant oscillations were obtained for surface I. The most remarkable oscillations were observed in calculations of partial cross sections for the range of scattering angles 170-180°, which corresponds to collisions with very small impact parameters, for a specific value of the orientation angle 0,. Strong oscillations were also observed for the total cross sections, which include all scattering angles, under the same conditions. Less pronounced oscillations, but still quite marked, were obtained in calculations of partial cross sections for the range of scattering angles 170-180°, for a random distribution of orientation angles Or which includes all values of Or that contribute to reactive scattering in this angular range. For surface I11 such oscillations were also obtained for other ranges of scattering angles down to 90" (150-16O0, 1 10-130°, and 90-1 lo"), corresponding to collisions with increasing values of the impact parameter b. However, the oscillation observed for low scattering angles are weaker than for high scattering angles. The range of collision energies for which these oscillations were found was shifted to higher values with the decrease in scattering angle. The oscillatory behavior was
+
-
+
J. Phys. Chem. 1987, 91, 5503-5509 washed out almost completely in calculations of total cross sections under the same conditions. Detailed studies of individual trajectories showed that surface 111, for which the strongest oscillations were observed and for which the reactive cone of acceptance and the reactive cross sections were largest, is characterized by strong anisotropic attractive forces over a wide range of orientation angles. These forces lead to reorientation of the reagents to a nearly collinear configuration at the time of reaction, even when the initial orientation angle is large. A nearly collinear configuration is also retained for some time after reaction. On the other hand, the behavior for surface I, for which no significant oscillations were found even under the most favorable conditions and for which the reactive cone of acceptance and the reactive cross sections were smallest, is governed mainly by repulsive forces. The behavior for surface
5503
I1 is intermediate between that of surfaces I and 111. These results show that the occurrence of oscillations in H LH' reactions depends mainly on the nature of the potential energy surface and not just on the mass combination for the reaction. Additional studies of other H + LH' reactions are under way. Such studies will show whether the conclusions derived here, about the correlation between the nature of the potential energy surface and the occurrence of oscillations and about the conditions which are most conducive to oscillatory behavior, are general for light atom transfer reactions. Hopefully, the results obtained from 3D quasi-classical trajectories will stimulate experimental studies of this novel dynamic behavior.
+
Registry No. CI, 22537-15-1; HCI, 7647-01-0.
Quantum Mechanical Studies of Ion-Molecule Reactions: The He H,)' Systems
+ H,+
and the (Ar
+
Michael Baer* Soreq Nuclear Research Center, Yavne 70600, Israel
and Hiroki Nakamura Division of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444, Japan (Received: January 26, 1987)
A quantum mechanical study within the reactive infinite-order sudden approximation for the two prototype ion-molecule reactions He + H2+and (Ar + H2)+was carried out. He + H2+was studied in the energy range 1.3 5 E, 5 1.8 eV and the two most characteristic features for this system in the above-mentionedenergy range, namely the existence of the vibrational propensity rule and the spectator stripping mechanism for exchange, were fully reproduced. The study of (Ar + H2)+was carried out for one energy value, E, = 0.6 eV. All four possible channels for chemical reactions and charge-transfer processes were treated simultaneously. Integral and differential cross reaction were calculated. Qualitative agreement with experiment was found for both. The study of these two ion-molecule reactions revealed the existence of a steric factor which is not associated with the potential but with the kinematics of the exchange process.
I. Introduction The experimental study of ion-molecule reactions is, to a certain extent, more convenient than the study of atom-molecule reactions due to the facts that the reagents can be prepared with any well-defined translational energy and the products can be easily detected. Since the experimental results under these circumstances are quite reliable, the relevance of various theories can be examined and nice models can be devised. As examples we refer to the Langevin formula for the rate constant' and to improved versions of that approach2 and to c l a ~ s i c a and l ~ ~quantum ~~ mechanical approximate treatments4 as well as to the stripping spectator model to determine final energy d i ~ t r i b u t i o n . ~ , ~ In this paper we report on quantum mechanical results regarding two of the most important ion-molecule reactions, namely He H2+(u,) HeH+ + H (ref 7, 8) (1)
+
(Ar
-
+ H2)+
ArH+ + H
(ref 9)
(11)
(1) Langevin, P. M. Ann. Chem. Phys. 1905, 5 , 245. (2) (a) Su,T.; Bowers, M. T. J . Chem. Phys. 1978,58, 3027. (b) Quack, M.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1978, 78, 240; 1975, 79, 170,469. (c) Troe, J. Chem. Phys. Lett. 1985, 122, 425. (3) Chesnavich, W. J.; Bowers, M. T.Prog. React. Kinet. 1982.11, 137. (4) Clary, D. C. Mol. Phys. 1985, 54, 605. Clary, D. C.; Smith, D.; A d a m , N. G. Chem. Phys. Lett. 1985, 119, 320. ( 5 ) Henglein, A,; Lachmann, K.; Jacobs, G. Ber. Bunsen-Ges. Phys. Chem. 1965, 64, 279. Hierl, P. M.; Hermann, Z.; Wolfgang, R. J . Chem. Phys. 1970, 53, 660. ( 6 ) Turner, T.; Dutuit, 0.;Lee, Y. T. J . Chem. Phys. 1984, 81, 3475.
0022-3654/87/2091-5503$01.50/0
The calculations were carried out within the reactive infinite-order sudden approximation (RIOSA). He H2+is one of the simplest ion-molecule reactions because the system contains only three electrons. This fact, as well as the fact that this reaction was frequently studied experimentally68'J0 makes it an attractive candidate for comparing theory with experiment (Ar H2)+ may not be as simple as the previous one but it is of no less interest. This system was studied e ~ p e r i m e n t a l l y ' ~ - ~ ~
+
+
.'z8s1
(7) Baer, M.; Suzuki, S.; Tanaka, K.; Kayano, I.; Nakamura, H.; Hermann, 2.;Kouri, D. J. Phys. Reu. 1986, 34, 1748. (8) Baer, M.; Nakamura, H.; Kouri, D. J. fnt. J. Quantum Chem. Quantum Chem. Symp. 1986, 20, 483. (9) Baer, M.; Nakamura, H.; Ohsaki, A. Chem. Phys. Lett. 1986,131,468. Baer, M.; Nakamura, H. J . Chem. Phys., in press. (10) Chupka, W. A,; Russell, M. E. J . Chem. Phys. 1968, 49, 5426. Chupka, W. A. In Ion-Molecule Reactions; Franklin, J. L., Ed.; Plenum: New York, 1972; Vol. 2, Chapter 3. Chupka, W. A.; Berkovitz, J.; Russell, M. E. Proceedings of the 6th fnternational Conference on the Physics of Electronic and Atomic Collisions, 1969; MIT.: Cambridge, MA, 1969; p 21 (11) Kouri, D. J.; Baer, M. Chem. Phys. Lett. 1974, 24, 37. (12) Whitton, W. N.; Kuntz, P. J . J . Chem. Phys. 1976, 64, 3624. (13) Schneider, F.; Havemann, U.; Zulicke, L.; Hermann, Z . Chem. Phys. Lett. 1977, 48, 439. (14) Joseph, T.; Sathyamurthy, N. J . Chem. Phys. 1984,80, 5332. Joseph, T.; Sathyamurthy, N. J. Chem. Phys. 1987, 86, 704. (15) Wagner, A. F.; Truhlar, D. G. J . Chem. Phys. 1972, 57, 406. (16) Lacmann, K.; Henglein, A. Ber. Bunsen-Ges. Phys. Chem. 1965, 69, 286. (17) Amme, R. C . ; McIlwain, J. F. J . Chem. Phys. 1966, 45, 1224.
0 1987 American Chemical Society
