1. M. Raff' University of California Los Alomos Scientific Loborotory Los Alomos, New Mexico 87544
I I
Illustration of Reaction Mechanism in Polyatomic Systems via Computer Movies
The illustration of the actual dynamics of a chemical process is an educational problem throughout both the undergraduate and graduate curriculum. At the high school and freshman level students have little concept or physical feeling for the motion of the constituent atoms in a bimolecular chemical reaction. All too often, professors must rely on two-dimensional blackboard drawings, hand motions, and stationary models to give students concepts of atomic motion during chemical processes. In general, these illustrative techniques result in only marginal success not only because of their obvious dynamic limitations hut also because such illustrations are usually vastly oversimplified and often lead to erroneous concepts on the part of the student. At a more advanced level, questions such as (1) What is the nature of the transition state through which the reaction proceeds?; (2) Is an intermediate complex formed?; (3) If so, what is the lifetime of such a complex?; (4) Does the reaction mechanism involve motion of nonreacting groups?; (5) Are the processes which occur in a given reaction concerted or sequential?; (6) What is the nature of the spatial scattering that one would observe in a crossed-beam experiment?, are examples of questions that can he answered verbally in a classrwm hut which are extremely difficult to illustrate using the normal visual aids. The above problems may be solved in large measure by the use of accurate, quasiclassical trajectories represented by moving three-dimensional projections. During the previous decade both reactive and inelastic scattering processes have been studied in extensive detail by quasiclassical trajectory calculations. The experimental results obtained in thermal systems for rate coefficients, activation energies, and frequency factors have been computed with considerable accuracy, and the data produced by crossed-beam experiments have been calculated and explained in surprising detail. Since such computations accurately follow the detailed atomic motion throughout all open reactive channels, they are ideally suited for use as visual illustrations in the classroom of the dynamic characteristics of chemical reactions. A recentlv r e ~ o r t e dcalculation hv Raff on the hot atom (T* CH;/CD~) system ( I ) has now extended accurate, unadjusted, quasiclassical trajectory computations into the realm of polyatomic organic systems. In such a system, there are several open reactive channels
+
abstraction: displacement: fragmentation (A) ' fragmentation (B) :.
CH, CH, CH, CH,
+ T*
+ T* + T* + T*
--+
+
HT CH, CHjr H CH, H + T CH9T H H
+ + + +
(1) (21 (31
(4)
plus other less probable fragmentation modes. In Ref. ( I ) , the unadjusted computation of the reaction dynamics for each of these channels is reported. The six-body potential-energy surface was obtained
from the equilibrium thermodynamic and spectroscopic data for reactants and products coupled with the results obtained in a variety of quantum mechanical computations. These co.mputations included previously formulated three- and four-body valence-bond potential surfaces, all valence-electron INDO (Incomplete Neglect of Differential Overlap), and ab initio double-zeta, SCF (Self-Consistent Field) calculations, in which the molecular wave function is represented by a single determinant of molecular orbitals, and configuration interaction (CI) studies in which a large expansion of such determinants is used to represent the wave function. In the INDO calculations the molecular orbitals are generated from is, 2s, and 2p atomic orhitals centered on the carbon atom and a 1s orbital centered on each hydrogen atom. The molecular integrals are em~iricallvevaluated. The double-zeta SCF computations, bn the-other hand, form the molecular orbitals from two Is, two 2s, and two sets of 2p orbitals on the carbon atom and two 1s orbitals on each hvdroeen . . - atom. All intemals are numerically evaluated to the accuracy permitted by the comwter. The molecular orbitals employed in the CI calculat~onsare generated in the same fashion as the SCF orbitals. The computed transition-state geometries for axial ahstranion and for an S N displacement ~ with inversion (Walden inversion) were found to be in good to excellent agreement with previous (2) a b initio CI calculations. The energies of the transition state were in fair to good agreement, and the computed fundamental vibration frequencies for CHI were in excellent accord with ir and Raman data. The reaction cross-sections for processes (1)-(4) were computed, and the thresholds found to be in quantitative agreement with experiment (3). Hot-atom yields in (CD4 T*) systems, computed through solution of the integral reaction probability equation (4), were found to be in excellent accord with experiment a t all hot-atom energies (3,5, 6). This system is admirably suited for the classroom illustration of reaction dynamics. The most often asked questions can be posed in this system. For example
+
(1) In abstraction, does the reaction occur axially? That is, does
the transition state correspondg to axial abstraction along a C-H bond? (2) In displacement, does Walden inversion occur or does the reaction proceed through a frontside T attack with retention of CH, configuration? (3) Is an intermediate CHs complex formed? If so, what is its lifetime? (4) Is fragmentation concerted or sequential? That is, do we have CH, + T* CH, + H + T as opposed to T* -+ CH:,'P H CH, followed by T? CH5T*+ CH, (5) What type of molecular beam scattering would be observed in this system? (6) Haw does the energy of the collision affect the probability of motion into eachof the available open channels?
-
+
+
+
This work has been supported in part by NSF Grant GP35869X and the US.Atomic Energy Commission. 1 On leave from the Department of Chemistry, Oklahoma State University, Stillwater. Oklahoma 74014. 712
/ Journal of Chemical Education
Each of these questions can he fully illustrated by reducing selected many-body trajectories to a 16mm color movie that represents the six-body motion in projected coordinates. Such a movie has been produced for the above system, and this paper reports the production procedure used and gives a detailed description of the contents of the movie. Production Procedure
The trajectories were computed on a CDC-7600 using a Runga-Kutta integration routine. The details of this procedure are fully described in Ref. (I). Since the carbon atom, the tritium atom, and the initial relative velocity vector between T and CH4 were chosen to he in the y-z plane, i t was most convenient, as well as best for illustrative purposes, to choose this plane as the projection plane. If (x,., y,, 2 , ) represent the Cartesian coordinates of the viewing point, the parametric equation of the line L connecting this viewing point with atom i are x = x
,
Y = Yr 2 = 2,
+ +
+
(x,
- x,Jt
( Y ; - yJt (z,
(5)
- 2,)t
Contents of the Movie
The (CH4/CD4 + T*) reaction dynamics have been illustrated by 14 selected trajectories. Ten of these involve CH4/T* collisions while the remaining four are trajectories with CDa. The following is a description of the salient features of each trajectory. The first three trajectories illustrate nonreactive collision events between T * and CH4. While such collisions do not contribute to the reaction cross-sections for processes (1)-(4), they are nevertheless extremely important in hotatom reactions in that they provide the major mechanism for hot-atom energy moderation. In each trajectory the zero-point vibrational motion of CHI is easily seen. This overall motion is the result of nine separate modes vihrating with four different frequencies. The integration step size in each case is 1.347 X 10-l6 s. Trajectory Number 7 This trajectory illustrates the most common type of collision event: the grazing collision a t large impact parameter, b. Such a trajectory is characterized by essentially forward T* atom scattering a t angles near 0" with little or no energy moderation. Figures l a and l b show two frames
where (I,,y,, z!) are the cartesian position coordinates of atom i. Line L intersects t h e y - z projection plane a t x = 0, that is a t
The projected coordinates for atom i are therefore given
i
For illustrative purposes, colored circles of variable radii centered a t (yo1, 2,') are drawn for the H (or D) and T atoms. It was found that the tetrahedral structure of CHn is more clearly evident if no circle was drawn for the carbon atom. Chemical honds, represented by lines, are drawn between atoms whenever they move into interaction range. This interaction range is arbitrarily taken to he 3.50 au for C-H bonds and 2.0 au for H-T honds. In order to represent motion in and out of the projection plane, the radius of the circle representing the atom was varied according to the distance from the viewing point. It was found empirically that a visually pleasing representation was given by
where r, is the radius of the circle for atom i, R, is the distance of atom i from the viewing point, and Rmor and Rmin represent the initial maximum and minimum values of the set [R,] (1 5 i 5 6), respectively. Equation (8) gives the circle radius in plotting units where one plotting unit is 0.01702 au. An inspection of the visual appearance of the projection a t different viewing points indicated that point (20.0, 0.0, 5.0) gave the best result. This viewing point was therefore employed for all trajectories. After each integration step the projected coordinates for all atoms were computed; the viewing point-atom distances and corresponding circle radii calculated; and one frame of 16mm color film generated on a General Dynamics 4020 plotting unit. Thus, there is a one-to-one correspondence between the trajectory projection time and the actual molecular collision time. For example, at an integration step size of 5.387 X 10-l7 s, 1 s of projection time a t 24 framesls corresponds to 1.293 x 10-l5 s of molecular collision time. The existence of this correspondence allows the determination of complex lifetimes by simply using a stopwatch while the trajectories are run.
1
i
Figure 1. Trajectory number 1: Nonreactive CH* collision with little moderation. Shaded circle representsT in all figures.
near the beginning and end of the trajectory. (The tritium atom is cross-hatched for identification purposes.) It is collisions of this type that are responsible for the strong peaking near E' = E of the energy moderation function given in Figure 23 of Ref. (1). In the trajectory shown, the initial T* lahoratory energy is 69 kcal/mole; the final T* lahoratory energy is 68.53 kcal/mole; and the impact parameter is 4.67au. Trajectory Number 2 This nonreactive collision involves a stronger T*-CHn interaction and hence both greater energy moderation and scattering angle. The initial T* lahoratory energy of 69 kcal/mole is moderated to 55.83 kcal/mole by the collision which occurs a t an impact parameter of 1.868 au. Trajectory Number 3
A very strong T*-CH4 interaction is shown in this trajectory. As a result, an unusually large T* energy moderation occurs along with a larger scattering angle (see Figs. 2a, b, c ) . A total of 35.52 kcal/mole of the initial 69 kcall mole T* laboratory energy is lost in the collision. After impact, the retreating T atom is seen to move more slowly and the vibrational amplitudes of CH4 are considerably enhanced due to the energy transfer. Such collisions are infrequent as shown by Figure 23 of Ref. (I). The impact parameter is 2.048 au. Trajectories 4, 5, and 6 illustrate the abstraction process a t low, intermediate, and high relative translational energy, respectively. In each case, the collision dynamics and spatial scattering is markedly different as shown by the data in Table 1X of Ref. (I) Since the integration step size is smaller in each of these traiectories than that employed for the nonreactive collisioni, the zero-point vibrational motion appears somewhat surpressed. Volume51
Number
1 1 . November 1974
/ 713
ICI
J Figure 2. Traiectory number 3: Nonreactive CH, collision with large enargy moderation.
Trajectory Number 4 In this collision the T * atom approaches CD4 a t an impact parameter of 1.293 au with 60 kcal/mole relative translational energy. As can be seen from Figure 3a, the approach is not axial. However, once the T* atom has moved into interaction range, as shown by the appearance of the C-T bond (see Fig. 3b), i t then moves into an almost perfect, axially oriented transition state (see Fig. 3c). Once having attained this state, axial abstraction occurs to form H T which scatters backwards a t an angle of 101.3". A total of 38.51 kcal/mole of the available 63.82 kcal/mole relative translational energy plus reaction exothermicity is partitioned into internal H T modes. The CD4T "complex" lasts 10-11 sec on the screen. Since the integration step size is 8.081 X 10-17 s, this corresponds to a molecular lifetime of (1.939-2.133) X 10-l4 s. It is interesting to note that the CH3 group is produced with a high degree of vibrational excitation. It does not exhibit its equilibrium planar sp2 geometry but rather a structure more like that of NH3. That is, the methyl group relaxation to the planar structure is very slow. Trajectory Number 5 This (T* CHI) collision occurs with a relative translational energy of 184 kcal/mole a t an impact parameter
+
Figure 3. Trajectory number 4: CD, abstraction through an axial transition state.
714
/ Journal of Chemical Education
Figure 4. Trajectory number 5: CHI abstraction that does not involve an axial transition state.
of 2.300 au. As can he seen in Figs. 4a, b, and c, the T* atom approach is not axial, and the abstraction occurs without an axial transition state ever being attained. This illlustrates the fact that when the reacting system has energy in considerable excess of that required to traverse the potential-energy barrier, the mechanism need not include motion though the normal transition state. At this higher energy, the scattering becomes more forward with H T scattering at an angle of 30.3". The internal HT excitation is 29.2 kcal/mole, and the integration step size is 8.081 x 10-11 s. Traiectory Number 6 This trajectory shows a (CHI T*) collision a t 346 kcal/mole relative translational energy. In order to ahstract a hydrogen atom at such a high energy, i t is necessary for the T* atom to dissipate a great deal of this energy to CHI so that its velocity is slowed sufficiently to allow the abstracted hydrogen atom time to move out in concert with the tritium atom. To obtain such a large energy transfer, the tritium atom must drive directly into the body of the CHI molecule a t small impact parameter. In the present case (see Fig. 5a) the impact parameter is 0.337 au. In the movie, one can easily see the inner repulsive T-CHI interaction bring the tritium atom to a dead stop (see Fig. 5b) after which the H T scattering is almost directly backwards a t an angle of 157.2". For a moment (see Fig. 5c) it appears as if the collision will result in fragmentation, but the energy transfer allows
+
L Figure 5 . Trajectory number 6: High energy CHI abstraction
HT to he formed in a highly excited internal state (64.8 kcal/mole internal excitation). In the movie, this large internal excitation is visually evident by the large H T vihrational amplitude that oscillates in and out of the defined interaction range. The integration step size employed in this trajectory is 5.387 X 10-l7 s. Trajectories 7 and 8 illustrate the mechanism by which displacement occurs in the (T* + CDI) system. It might take place via a backside attack followed by Walden inversion of the CD3 group, or i t might occur by means of a frontside attack with the backside CDJ group retaining its configuration. Trajectory Number 7 The collision takes place a t 60 kcal/mole relative translational energy a t an impact parameter of 0.784 an. The integration step size is 8.081 x 10-l7 s. In Fig. 6a we see the tritium atom approaching. In Fig. 6b the CD4T "complex" is formed, and in Fig. 6c, a frontside displacement is seen to occur with the CD3 group retaining its configuration. This is the typical CD4 displacement mechanism.
Figure 7. Trajectory number 9: Concerted fragmentation of CH4 to form H f T. CHn
+
Trajectory Number 10 Fragmentation of CHI by reaction (4) is shown. This type of fragmentation occurs much less often than reaction (3) since it requires a suhstantial energy transfer to the CH4 molecule. The relative translational energy, impact parameter, and integration step size are 231 kcal/mole, 1.550 au, and 8.081 X 10-IT s, respectively. In Figures 8a and 86 we see the tritium atom approach and displace the first hydrogen atom. The highly excited CHJT molecule (see Fig. 8c) lives for about 10-11 s screen time, (1.939-2.133) x 10-l4 s actual molecular time, and then (see Fig. 8d) the second hydrogen atom is displaced. Thus, the process is sequential
Figure 6. Trajectory number 7: CD, displacement via frontside attack with retention of CD3 configuration.
Trajectory Number 8 This trajectory also illustrates that CD4 displacement occurs via a frontside attack with retention of the CDX configuration. The relative collision energy is 184 kcallmole; the impact parameter is 1.633 au; aKd the integration step size is 5.387 X lO-"'s. Traiectories 9 and 10 illustrate fraementation hv " . nrocesses (3) and (4), respectively. In such reactions the process may he concerted with both atoms fragmenting a t essentially the same instant, or the process may he sequential.
This is typical for reaction (4). As one might expect from the energy transfer required for such a reaction, the CHzT radical contains a suhstantial amount of internal energy as evidenced by its large vibrational amplitudes and rotation speeds. It may be noted that the CHzT group is, of r course. not in its eauilibrium ~ l a n a confimration. ~rajkctories l l ' a n d 12 illustrate t i e most common events whenever the collision enerpy is very high (>I000 kcal/mole) as is the case whenevertritium is obtained via nuclear recoil techniques. At such high energies, ahstrac-
.
Trajectory Number 9 A concerted CHI fragmentation by process (3) is illustrated in this trajectory. The relative collision energy, impact parameter, and integration step size are 184 kcall mole, 1.984 au, and 8.081 X lo-" s, respectively. In Fig. 76 the tritium atom has displaced a hydrogen atom by frontside attack. An instant later (see Fig. 7c) the C-T bond breaks, and a concerted fragmentation has occurred. This is the most common mechanism for reaction (3). It should he noted that in such processes most of the kinetic energy is carried away by the atoms rather than by the CH3 fragment. This is visually clear from the fact that the H and T atoms move rapidly off the screen while the CH3 radical moves slowly away.
Figure 8. Trajectory number 10: Sequential fragmentation of CHr to form CH2T 2H.
+
Voiume51. Number 11. November 1974 / 715
Figure 9. Trajectory number 11: Nonreactive collision at 1084 kcal/mole relative translational energy.
tion and displacement never occur because the tritium atom can not transfer a sufficient amount of its energy to allow it to become bonded to either CH3 or H. In fact, nonreactive events are the usual result of collision even a t small impact parameter. Trajectory Number 11 Such a nonreactive collision is shown here. The relative translational energy is 10% kcal/mole, and the integration step size is 5.387 X 10-l7 s. Figures 9a and 96 show the trajectory details. Superficially, they appear very similar to those of trajectory number 1. The difference however lies in the fact that this collision occurs with an impact parameter of 1.897 au rather than 4.67 au. Even though there exists a significant T-CHI interaction a t this impact distance, the tritium atom moves in an almost undeviated trajectory past the CHa molecule. This type of trajectory is typical a t this energy.
Figure 10. Trajectory number 13: Sequential fragmentation of CDI to lorm CD3 T D that goes through a long-lived CDzT intermediate.
+ +
The fragmentation is seen to he concerted. The collision energy, impact parameter, and integration step size are 1084 kcal/mole, 1.241 au, and 5.387 X 10-1" s, respectively. Trajectory 13 illustrates what may he thought of as complex formation. Although such collisions do not occur often enough to be statistically significant in this system, the trajectories serve to illustrate the nature of such processes.
quently reforms CDsT* (see Fig. 10c). This excited molecule lives for 63 s on the screen, corresponding to 8.145 X 10-14 s of molecular time, a t which point it dissociates to form CD3 + T (see Fig. 10d). The reaction cross-sections for abstraction, displacement, and fragmentation computed from 11,000-12,000 trajectories are given in Figures 16-20 of Ref. (1). The results for (CH4 + T*) are now dynamically drawn on a common graph in the movie with each cross-section curve being shown in a different color. Such a presentation clearlv shows that abstraction is the low-enerw. thermal proceis followed by displacement and then fragmentation. Finallv. .. the film illustrates to the student that the reaction cross-sections computed from trajectories of the foregoing type allow accurate computation of experimental laboratory yield ratios. This is accomplished by dynamically plotting the experimental and calculated ahstraction/displacement yield ratios as a function of initial T* laboratory energy for both recoil tritium and TBr photolysis experiments. The results shown are Figures 24 and 25 of Ref. (I). In complete form the movie consists of about 750 f t of 16mm film and has a running time of 18.5 min a t 24 framesls. At the present time, it is scheduled for presentation a t the 1974 spring ACS meeting to be held in Los Angeles, California. Upon request, copies of the film will be made available a t cost.
Tralectory Number 13
Acknowledgment
In this trajectory reaction (3) is shown to occur by a sequential mechanism
Special thanks are due to Dr. D. L. Thompson of the CNC-4 group, Los Alamos Scientific Laboratory, for his helpful advice relating to the use of the photographic facilities of the computer center, and to Mr. R. Gordon and Mr. B. Clayhrook for their expert editing of the raw film.
Trajectory Number 72 Occasionallv, fragmentation will occur in high energy collisions. Trajectory number 12 illustrates an unusual fragmentation at high collision energy
T*
CD,
+ CH,
+P
+
+
CH,
+ 2H + T
+
CD3F D L CD,
+T
The collision energy is 184 kcal/mole; the impact parameter is 1.724 au; and the integration step size is 5.387 X 10-1' s. The initial T*-CDa impact appears to lead to reaction (3) via a concerted mechanism. This is shown in Figures 10a and lob. The tritium atom, however, does not have sufficient energy to escape the CD3 group and suhse-
716
/ Journal of Chemical Educafion
Literature Cited (I)R d f . L M ...J Chem Phyr., 60.222U(lY74). (21 Morokurna. K..andUauir. R.E.. J. Amer Chpm Sor., 94. 1059 119121. 131 Chou. C. C..sndRowlandF.S.. J. Chsm. Phy. .. 50.2163 (19691. 141 P0rter.R. N..J Chem. Phus.. 15. ?2&1l19ffil. (5) Seewald, D..and Wolfeang. R..J Chem Phya.. 17.143 (1961). 16) Root. J. W..and Rowland. F. S . , J Cham Phyr., 46,4299119611.
