edited by JOHNW. MOORE Eastern Michigan University. Ypsilanti. Mi 48197
Computer Animation of a Chemical Reaction Charles W. Eaker and Edwin L. J a c o b s University of Dallas, Irving, TX 75061
What actuallv takes d a c e in a chemical reaction is of great inttwit to leachers and students Ake. How is it that some ndiiion; lead tu reartim and uthers do nut? In our diicu;ii riasiical traiertorv. w . w. on our microcompresented the results as a moving puter graphics system. T h e details of the trajectory calculations will be given in the next section. Then we will describe the reaction animation on a microcomputer. Finally, we will discuss some of our results and conclusions.
+
Trajectory Calculations We have described the GDIM surface for HQelsewhere? For this surface the linear saddle point occurs a t the H-H bond length of 1.776 au with an energy 13.8 kcal above the Hz minimum energy. This compares to the "exact" values of 1.757 au and 9.8 kcal determined by Liu and Siegbahn." This GDIM surface was then incorporated into the REACTSZclassical trajectory program. This program solves the classical Hamiltonian equations of motion using a hybrid of the Adams-Moulton variable step size and Runge-Kutta fixed step size techniques. It is possible to set the initial conditions randomly or systematically. Since the purpose of this paper is to illustrate what occurs and must be considered in
a chemical reaction, we have chosen to select systematically the initial conditions. The output from this program gives the . . relative energies and Cartesian coordinates of each atom at swcitied ~ o i n t in s time. \Verenerilllv ~ r u d u r e drhisdatn evm. i.5 X 10-i5sec. The averagetraject6;lasted about 1.0 X sec. These calculations were done on the university's Hewlett-Packard HP-3000 minicomputer. The output was stored onto disk files which could be read by the microcomputer in the chemistry department for graphical display. Microcomputer Animation The chemistry department's microcomputer is a S-100 bus microcomputer system which uses the 2-80 central processor with 64k of memory and two double-density, douhle-sided floppy disk drives. The high resolution (512 X 640 pixels) graphics capability is provided by the Dynamic Blackboard system from Cambridge Development Labs. The video output is suitable for use with standard video monitors found in the classroom or lecture hall. All the figures in this paper were drawn on a Watanabe Digi-Plot x-y plotter interfaced to our microcompnter. T o provide an animation of the chemical reaction, we repesent the atoms as circles on a 12-in. video monitor. These circles are drawn on the screen as determined by the coordinates of the atoms stored on the disk file. They are then erased and redrawn a t the next location on the screen. T o draw (or erase) a circle takes about 0.01 sec, and so the reaction amears to proceed quite realistically. Optionally the programban be run in slow motion or stepped t h r o u ~ hmanually to allow for emphasizing various poi& in the trajectory. TO represent
'
Eaker, C. W. and Aliard, Lee R., J. Chem. Phys., 74, 1821 (1981). Parr, C. A,, Poianyi. J. C.. and Wong. W. H.. J. Chem. Phys.. 58,5
,.- . - . 119731 ,
Siegbahn, P. and Liu, B., J. Chem. Phys., 68, 2457 (1978).
Volume 59
Number 10 October I982
939
chemical bonding a line is drawn between any two atoms for which the centers are within 10 nm. In doing this type of animation, it is important to be able to draw and erase circles rapidly. T o do this we wrote two separate routines. The first, GENCIRCLE, generates a set of instructions for the relative movements of the cursor necessary for drawing a circle of radius R a t any location. The other, routine DRWCIRCLE, takes the results from GENCIRCLE and actually draws (or erases) the circle very quickly. The GENCIRCLE routine is relatively slow, hut it needs to he called only once in a program for each size circle that must be drawn. Results and Conduslons
T o represent this chemical reaction we have run anumber of trajectories in which the initial conditions are specified. These trajectories are of three basic types: (I) those in which the saddleooint occurs on the linear Hn surface: (11) those in which the k ~ d d l e ~ o ioccurs nt on the 60-degree H:,surface; and (.I l l.)those with saddlenoints between tvves .. I and ll.'l'he first type of trajectory arises from the linear collision of H with Hz. This is the lowest energy transition point for this reaction. On our surface this corresponds to point 13.8 kcallmole above the bottom of the Hz potential well. An example of this trajectory type is shown in Figure 1.The second trajectory type is indicated for a perpendicular attack of H to Hz. The lowest energy saddlepoint for this attack is 63.8 kcallmole above the Hz
minimum energy. Figure 2 illustrates a trajectory of type 11. For trajectories of types I and 11, the impact parameter is set to zero corresponding to motion of the H atom directly toward the center of mass of the Hz molecule. The impact parameter for type 3 (Fig. 3) trajectories is set to 5.29 nm. The trajectories are -~ listed in the table. These trajector~escan help us understand what happens in a chrmicnl reaction. Traiwtorv 1 tsee Fie. " 1 ) shows huw the reaction can occur where the cacollisional (translational) energy is less than the activation enerrv. -. The additional enerw necessary to get over the barrier comes from the vibrational energy. However, vibrational energy is not always available to bring about the reaction. This is seen in trajectory 2 where we have changed the vibrational phase. For this trajectory the reaction is unsuccessful because the molecular HZis at a different point in its vibration when the attacking H atom reaches the transition point. Trajectory 3 leads to reaction where we increased the translational energy from trajectory 2. Students have a difficult time understanding how a reaction can he unsuccessful because the reactants collide with too much energy. This is shown in trajectory 4, which is the same as 1except the translational energy has been increased from 10 to 60 kcallmole. To make this concept clear, I have students look at the potential energy surface. With too much energy the trajectory goes up to the back wall of the reactant channel ~~~~~~
Trajectory Energy Data
-
Translationel
Traiectory
(
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
-
Figure 1.Stop action of trajectory 1
TIME
-
I.200L-ll SECONDS
llllf
-
I.BIOE-11
Type I I
I I I
I II I1 I1
II I1 I1 111 111 111 111
111
(kcall mole) 10.0 10.0 15.0 60.0 200.0 300.0 60.0 60.0 80.0 80.0 100.0 100.0 15.0 15.0 20.0 30.0 60.0
PLCOVOI
Figure 3.Stop action of trajectory 16. 940
Journal of Chemical Education
Vibra
Rota-
tional (kcall mole)
tional (kcall
Vibrational
mole)
Phase
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 90.0 90.0 0.0 0.0 0.0 0.0 90.0 0.0 90.0 0.0 90.0 0.0 0.0 0.0 0.0 0.0
6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 . 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3
0.0
0.0 0.0 0.0 0.35 0.35 0.35 0.0
and then rebounds out the entrance channel. The H? molecule does not have a chance to absorb the translational energy and convert it into vibrational enerm necessary to brinp.about the breaking of the hond for react&. This requirement for translational enerw to he absorbed by the molecule is also nicely shown in tr&ctories 5 and 6. Here we are attempting to break completely the Hz hond and produce three free atoms. We might expect that a collision of 200 kcallmole would certainly break a 105 kcallmole Hz bond. However. it takes a 300 kcallmole in a linear collision to cr~mplerelvfrer the atoms. These trujectories draniaricallv illustrate that it is im~urtantto consider hou, the enernv is directed in chemical reactions. The type I1 traiectories illustrate what haovens when the orientation of th;reactants changes. From the potential energy surface. w immedtately .+eet hsr r h acrivsrion ~ rnergy is much greater (13.8 versus 1.L8 kcal m d e ~in this "wurst case" urientariun. I r is very ciit'ficult t o hrinc about a reaction to form a new Hz molecule^ as seen by the fait that none of our selected trajectories, 7 through 12, are successful. This can be understood by looking a t the potential energy surface where there is a much smaller "window" for successful Hz formation. However, with trajectories of this orientation it is much easier, from an energy standpoint, to break the H2 hond. This is accomplished in trajectory 11, where 100 kcal/mole translational and 6.3 kcallmole vibrational energy combine to break the Hz bond and send the atoms in three different directions. Trajectory 12 with the same energies does not break the hond because the vibration is out of ohase. 'l'he type 111 trajectories represent the mnst common types of collisiuns. These culliaims occur on snrrnces intermediate between the "worst case" 60-degree surface and the."best case" 180-degree (linear) surface. We have allowed the H atom
--
to attack the Hp molecule off-center. The most striking thing we notice about these trajectories is the occurrence of vibrational and rotational excitation. In trajectory 13 there is no reaction, but the H2 molecule goes from 0.0 to 2.53 kcallmole rotational energy. By watching the animation of this trajectory, i t becomes obvious how this transfer of energy is accomplished. The H atom collides with one end of the Hz molecule. thus cansine" it to rotate. This t . w.e of enerev "" transfer does not always occur as shown in a very similar trajectory (14), where there is essentially no energy transfer between reactants. Trajectory 15 illustrates an unsuccessful reaction with vibrational energy excitation. Trajectory 17 has both vibrational and rotational excitation with no reaction. The different results of trajectories 13, 14, 15, and 17 are easily understood in the animation to he dependent on the orientation of the molecule and atom when the collision occurs, as well as dependent on the initial energies. Trajectory 16 (see Fig. 3) shows a successful reaction where the resulting Hz molecule is vibrationally and rotationally excited. When the animations of trajectories are observed, the many encounters which occur in any chemical reaction become real. This gives teachers and students a tremendous insight into how chemical reactions take place. This is one of the many applications of microcomputers now available to chemists. Acknowledgment
We would like to express our appreciation to Dr. Christo-
her Parr for makine available the REACTS classical trajectory program described in this paper. We would also like to thank the donors of The Petroleum Research Fund. administered by the American Chemical Society, for support of this research.
Volume 59 Number 10 October 1982
941
