Spherical complex optical potential (SCOP) method, appropriately modified by our group for positron scattering, is employed to compute total elastic and grand total cross sections for astrophysical molecules. The cross sections for the present targets, viz. H2O, NH3, HCl, OCS and SO2 are reported for a wide energy range, spanning from 1 eV to 5000 eV. The elastic cross sections for HCl and OCS are reported for the first time. In the intermediate to high energy regime, results of most of the targets studied compare fairly well with the recent measurements, wherever available. Present cross sections would be useful for modelling astrophysical systems.