  The equilibrium structure and exchange constants of CaMnO$_3$ and LaMnO$_3$
have been investigated using total energy unrestricted Hartree-Fock (UHF) and
localised orbital configuration interaction (CI) calculations on the bulk
compounds and Mn$_2$O$_{11}^{14-}$ and Mn$_2$O$_{11}^{16-}$ clusters. The
predicted structure and exchange constants for CaMnO$_3$ are in reasonable
agreement with estimates based on its N\'eel temperature. A series of
calculations on LaMnO$_3$ in the cubic perovskite structure shows that a
Hamiltonian with independent orbital ordering and exchange terms accounts for
the total energies of cubic LaMnO$_3$ with various spin and orbital orderings.
Computed exchange constants depend on orbital ordering. UHF calculations tend
to underestimate exchange constants in LaMnO$_3$, but have the correct sign
when compared with values obtained by neutron scattering; exchange constants
obtained from CI calculations are in good agreement with neutron scattering
data provided the Madelung potential of the cluster is appropriate. Cluster CI
calculations reveal a strong dependence of exchange constants on Mn d e$_g$
orbital populations in both compounds. CI wave functions are analysed in order
to determine which exchange processes are important in exchange coupling in
CaMnO$_3$ and LaMnO$_3$.
