Extensive ab initio molecular orbital calculations are reported for mo
nomeric MgF2 and CaF2, at both SCF and correlated levels of theory, co
ncentrating on the shapes and bending potentials. In particular, caref
ul attention has been paid to details of the basis sets used, which ha
ve been extended until convergence was obtained. Polarization exponent
s for the molecular environments have been optimized for both d- and f
-type functions. They are quite different from those obtained variatio
nally for isolated atoms or ions. They are also different at SCF and M
P2 levels of theory. MP2 and QCISD theories were shown to give very si
milar results for MgF2. While our final SCF and MP2 results for MgF2 d
iffer only marginally, we have shown that f-type functions are necessa
ry on Mg if reliable results are to be obtained in correlated calculat
ions. The bending potential for MgF2 in an argon matrix is shown to be
seriously perturbed by matrix effects, but the frequency reported fro
m IR emission at high temperature is found to be reliable. A very larg
e d basis set has been shown to be necessary for Ca; five sets are nee
ded at the SCF level, and at least seven in MP2 calculations. The resu
lts for CaF2 are remarkably sensitive to the particular exponent value
s used, even for multiple sets. Our best estimate of the bond angle in
CaF2 is 154 degrees, but the linear transition state is only 0.7 kJ m
ol(-1) higher in energy. The factors responsible for the non-linearity
of monomeric CaF2 are discussed, and the importance of core polarizat
ion is stressed. It is important to note that the exponents for d-type
functions which maximize the polarizability of the isolated Ca2+ ion
are very similar to those optimized variationally for molecular CaF2.