  We have used an efficient new quantum mechanical method for radical pair
recombination reactions to study the spin-dependent charge recombination along
PTZ$^{\bullet+}$--Ph$_n$--PDI$^{\bullet-}$ molecular wires. By comparing our
results to the experimental data of E. Weiss {\em et al.} [J. Am. Chem. Soc.
{\bf 126}, 5577 (2004)], we are able to extract the spin-dependent (singlet and
triplet) charge recombination rate constants for wires with $n=2-5$. These
spin-dependent rate constants have not been extracted previously from the
experimental data because they require fitting its magnetic field-dependence to
the results of quantum spin dynamics simulations. We find that the triplet
recombination rate constant decreases exponentially with the length of the
wire, consistent with the superexchange mechanism of charge recombination.
However, the singlet recombination rate constant is nearly independent of the
length of the wire, suggesting that the singlet pathway is dominated by an
incoherent hopping mechanism. A simple qualitative explanation for the
different behaviours of the two spin-selective charge recombination pathways is
provided in terms of Marcus theory. We also find evidence for a magnetic
field-independent background contribution to the triplet yield of the charge
recombination reaction, and suggest several possible explanations for it. Since
none of these explanations is especially compelling given the available
experimental evidence, and since the result appears to apply more generally to
other molecular wires, we hope that this aspect of our study will stimulate
further experimental work.
