S vs O as a Neighbouring Group
In a first order analysis, a nucleophilic/electrohilic
interaction can be approximated by the interaction of two key
molecular orbitals; the HOMO (the nucleophile) donating a a
pair of electrons to the empty LUMO (the electrophile). This
interaction depends on:
 The energy gap between these two orbitals. The smaller
this gap, the better the interaction. Specifically, the
higher the energy of the HOMO (i.e the less negative) the better a nucleophile it
represents, whilst the lower the energy of the LUMO (i.e. less positive or more
negative) the
better the electrophile, and the combination of these two is
the HOMOLUMO gap.
 The spatial overlap of the HOMO with the LUMO.
These two effects can be probed by a molecular orbital
calculation on the two reactants, for which acetolysis for the S system shown below
is observed to be 10^{9} faster than for the O analogue.
The results (ab initio 321G* level) are as follows.
 S bicyclic: HOMOLUMO gap = 0.546 Hartree.
 O bicyclic: HOMOLUMO gap = 0.606 Hartree.
The difference amounts to 157 kJ (1 Hartree = 2624 kJ).
The spatial overlap can be seen below. On both counts, S wins over O.

S bicyclic 
O bicyclic 
LUMO 


HOMO 


Product Stability
One can test the above (reactant based) conclusions by calculating
the energy of the carbocation resulting from elimination of Cl^{}.
Thus the energy to create a cation from the O system is +980 kJ
whereas that for the S system is +898 kJ (AM1 calculations). Solvation and other
factors not withstanding, this difference of 82 kJ abundantly explains
the difference in solvation rates. Notice in particular that ring strain prevents
the O system from closing to form an oxonium ion, whereas the larger more flexible
S system does indeed so close.