We present a formulation for low-energy positron-molecule collisions b
ased on the Schwinger multichannel method (SMC) which was previously a
dapted for electron-molecule scattering. We have preserved very import
ant features of the SMC such as its ability to deal with electronicall
y inelastic scattering and its applicability to molecular targets of a
rbitrary geometry. Our implementation also allows for the inclusion of
a substantial number of closed electronic channels to represent polar
ization effects, which are very important at low impact energies. As a
n application, to illustrate the form with which polarization is repre
sented in this formulation, we have calculated elastic integral and di
fferential cross sections for e+-H-2 and e+-CH4 collisions. We include
d all possible single-particle excitations from the target and found s
ubstantial disagreement with respect to model potential calculations a
nd attenuated-beam experimental data. We discuss possible reasons for
these discrepancies.