We discuss the unimolecular dissociations of three triatomic molecules
in their ground electronic states, HXO((X) over tilde) --> H + XO(n,
j) with X = C, N and O, using quantum mechanical methods, classical tr
ajectories and statistical theories. The calculations for HCO and HNO
employ new nb initio potential-energy surfaces and the investigations
for HO2 are performed on the DMBE IV potential. Our study focuses on t
wo issues: the differences in the dissociation rates for the three sys
tems and how they can be understood in terms of differences in the pot
ential-energy surfaces and, secondly, on the reliability of statistica
l theories (RRKM and SACM) in predicting the average rate. The interna
l vibrational motion of HCO is mostly regular, even at energies much g
reater than the threshold, which leads to a pronounced mode-specificit
y in the dissociation rates; the RRKM rate is found to be an upper lim
it for the quantum-mechanical rates with the average being overestimat
ed by roughly a factor of five. At the other extreme, the dynamics of
HO2 are essentially irregular, as confirmed by inspection of the wavef
unctions and analyses of the energy spectrum of the bound states; as a
consequence the fragmentation rates of HO2 are, on the average, well
described by statistical theories. HNO is a mixed case showing both re
gular and irregular motion; the RRKM rate is only a factor of two larg
er than the quantum-mechanical average. HCO has a potential with a cle
ar barrier at intermediate fragment separations and so exemplifies a s
ystem with a tight transition state. The HNO potential, on the other h
and, has a purely attractive exit channel and illustrates a system wit
h a loose transition state. Although the potential for HO2 has no barr
ier, the rapid change of the anisotropy between the inner and the oute
r regions leads to pronounced dynamical barriers so that this system,
too, belongs to the class of molecules with a tight transition state.