Caution in Using Monte Carlo Kinetics Modeling Students often have a tendency to he uncritical of experimental data, and this problem is exacerbated when the data comes from a computer. An example of this situation is provided by the computer-simulated kinetics scheme for the photo-oxidation of anthracene given recently by Dixon and Shafer.' Figure 1 shows the result of a computer run for that mechanism using the Monte Carlo strategy of those authors. Certain of the concentrations, as claimed by the authors, do show an oscillatory behavior reminiscent of that seen in genuine oscillating reactions. However, a second run with identical input parameters (Fig. 2) shows that the oscillations are, in fact, statistical fluctuation^.^ Indeed, the mechanism given does not include the autocatalytic or inhibitory steps required for oscil1ation.a
Figure 1 . Simulated phota~oxidation of anthracene, using the Monte Carlo strategy of D x o n and Shafer. ldentfication of Species and units will be found in Figure 1 of that paper.
FigureZ.
O u p l c a t e r u n of the reaction shown in Figure 1
The fluetuations seen in the above example can be viewed, not as a defect of the Monte Carlo method, but as a manifestation of the statistical fluctuations expected for small systems. In a sample containing loz3 molecules, we would not observe these fluctuations; but for the numbers of molecules often used in pedagogical computer simulations to maintain reasonable running times,2 these fluctuations can become significant. The failure to recognize this characteristic of Monte Carlo modeling is a potential pitfall for unsuspecting students. We thank Dr. Peter G . Bowers of Simmons College for clarification of the mechanistic requirements for oscillating reactions.
' Dinon, D. A., and Shafer, R. H., J. CHEM. EDUC., 50,618 (1973).
These two runs were made using 10' "trials" and a "container size" of lo3, in the terminology of Dixon and Shafer, with all rate constants equal to unity and [A10 = [O& = 0.5. The runs each required approximately 9 min on a Hewlett-Paekard 2WOC' time sharing system, including the generation of the graphic plots on a Tektronix 4010 graphics terminal cammunicating with the computer at 300 baud. (Points were plotted every 1W trials.) The pseudo-ascillations can he smoothed out by increasing the container size to l(r (effectively increasing the starting population by a factor of lo), hut then 105 trials are required to get to the same stage in the reaction, and the running time is increased proportionately to about 90 min, an unacceptably long run far most teaching purposes. Degn, H., J. CHEM. EDUC., 49,302 (1972). Leonard J. Soltzberg Faye Goldman Waber Simmons College Boston, Massachusetts 02115
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