  We calculate corrections to the fermion propagator and to the Green's
functions of all fermion bilinear operators of the form $\bar\Psi \Gamma \Psi$,
to one-loop in perturbation theory.
  We employ the Wilson/clover action for fermions and a family of Symanzik
improved actions for gluons.
  The novel aspect of our calculations is that they are carried out to second
order in the lattice spacing, $O(a^2)$. Consequently, they have addressed a
number of new issues, most notably the appearance of loop integrands with
strong IR divergences (convergent only beyond 6 dimensions). Such integrands
are not present in $O(a^1)$ improvement calculations; there, IR divergent terms
are seen to have the same structure as in the $O(a^0)$ case, by virtue of
parity under integration, and they can thus be handled by well-known
techniques. We explain how to correctly extract the full $O(a^2)$ dependence;
in fact, our method is generalizable to any order in $a$.
  The $O(a^2)$ corrections to the quark propagator and Green's functions
computed in this paper are useful to improve the nonperturbative RI-MOM
determination of renormalization constants for quark bilinear operators.
  Our results depend on a large number of parameters: coupling constant, number
of colors, lattice spacing, external momentum, clover parameter, Symanzik
coefficients, gauge parameter. To make these results most easily accessible to
the reader, we have included them in the distribution package of this paper, as
an ASCII file named: Oa2results.m ; the file is best perused as Mathematica
input.
