We present a more efficient way of treating polarization effects in the scattering of low-energy electrons by molecules within the Schwinger multichannel (SMC) method. We propose to expand the scattering wave function in a set of functions of N + 1 electrons that describe the scattering in an effective way, which allows the use of a small number of functions to describe the polarization effects. As a first test, we apply the method to the scattering of electrons by the H-2 molecule. We calculate elastic integral and differential cross sections, and we obtain excellent results with a reduction in the number of configurations of up to 98% when compared to the traditional method used in the SMC method. This is a substantial size reduction of all matrices involved in the SMC method and, as a consequence, it represents a promising technique for treating more complex molecular systems.614