  Using the complex Kohn method, we have calculated variational values of phase
shifts and the annihilation parameter, Z_{eff}, for the elastic scattering of
positrons by molecular hydrogen. Our results are sensitive to small changes in
the accuracy of the wave function representing the target hydrogen molecule. We
have developed a systematic approach to demonstrate that, at low positron
energies, there are particular forms of the Kohn trial wave function for which
the results of variational calculations are not reliable, even when the target
wave function accounts for as much as 96.8% of the correlation energy of H_{2}.
We find that reliable results can be recovered if our calculations are extended
to admit more sophisticated target wave functions accounting for 99.7% of the
correlation energy. Remaining discrepancies between theory and experiment are
briefly discussed.
