  Ab initio quantum chemical calculations of Heisenberg exchange in linear
cuprate antiferromagnets are reported. For Sr2CuO3 I obtain Ja=-119 meV for the
intrachain coupling and Jb=-0.28 meV for the interchain coupling. For Ca2CuO3 I
find Ja=-119 meV and Jb=-0.52 meV. With these values, recent mean field theory
gives the staggered magnetic moments as 0.069 and 0.095 mB, in full agreement
with recent experiments. The experimental Neel temperatures are found to be
proportional to the ratio Jb/Ja to a high accuracy. This indicates that the
isolated chain is an antiferromagnet with vanishing Tn.
