  The electronic contribution to the magnetically induced polarization in
orthorhombic TbMnO3 is studied from first principles. We compare the cases in
which the spin cycloid, which induces the electric polarization via the
spin-orbit interaction, is in either the b-c or a-b plane. We find that the
electronic contribution is negligible in the first case, but much larger, and
comparable to the lattice-mediated contribution, in the second case. However,
we how that this behavior is an artifact of the particular pattern of
octahedral rotations characterizing the structurally relaxed Pbnm crystal
structure. To do so, we explore how the electronic contribution varies for a
structural model of rigidly rotated MnO6 octahedra, and demonstrate that it can
vary over a wide range, comparable with the lattice-mediated contribution, for
both b-c and a-b spirals. We introduce a phenomenological model that is capable
of describing this behavior in terms of sums of symmetry-constrained
contributions arising from the displacements of oxygen atoms from the centers
of the Mn-Mn bonds.
