Rates of transient diffusion-limited chem
ical reactions in three dimensions are de
termined by Monte Carlo computer simu
lation. Particles are initially placed at
random on a cubic periodic Euclidean lat
tice and perform independent random
walks. Pairs of particles arriving at the
same site are reacted according to the
rules of particular types of chemical reac
tion; annihilation, bimolecular, and cata
lytic reactions are simulated. The compu
tational method involves searching par
tially ordered lists of the particles'
coordinates, to find any particles sharing
a lattice site. We observe the effects of
the diffusion coefficients and the stoichi
ometry of the reactive species on the rate
of reaction. The results strongly support
the contention that the Smoluchowski-
Noyes theory does not give a uniformly
accurate prediction of diffusion-limited re
action rates in three dimensions. The only
case of substantial disagreement between
the simulation results and the theory is
found for nearly equimolar bimolecular
reaction.
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