  A model-potential method is employed to calculate binding, elastic
scattering, and annihilation of positrons for a number of atoms and small
nonpolar molecules, namely, Be, Mg, He, Ar, H$_2$, N$_2$, Cl$_2$, and CH$_4$.
The model potential contains one free parameter for each type of atom within
the target. Its values are chosen to reproduce existing ab initio positron-atom
binding energies or scattering phase shifts. The calculations are performed
using a Gaussian basis for the positron states, and we show how to obtain
values of the scattering phase shifts and normalized annihilation rate $Z_{\rm
eff}$ from discrete positive-energy pseudostates. Good agreement between the
present results and existing calculations and experimental data, where
available, is obtained, including the $Z_{\rm eff}$ value for CH$_4$, which is
strongly enhanced by a low-lying virtual positron state. An exception is the
room-temperature value of $Z_{\rm eff}$ for Cl$_2$, for which the present value
is much smaller than the experimental value obtained over 50 years ago. Our
calculations predict that among the molecular targets studied, only Cl$_2$
might support a bound state for the positron, with a binding energy of a few
meV.
