  We study the properties of an anisotropically paired superconductor in the
presence of a specularly reflecting surface. The bulk stable phase of the
superconducting order parameter is taken to have $d_{x^2-y^2}$ symmetry.
Contributions by order parameter components of different symmetries vanish in
the bulk, but may enter in the vicinity of a wall. We calculate the
self-consistent order parameter and surface free energy within the
quasiclassical formulation of superconductivity. We discuss, in particular, the
dependence of these quantities on the degree of order parameter mixing and the
surface to lattice orientation. Knowledge of the thermodynamically stable order
parameter near a surface is a necessary precondition for calculating measurable
surface properties which we present in a companion paper.
