Consider a compact manifold with boundary M with a scattering metric g or, equivalently, an asymptotically conic manifold . (Euclidean , with a compactly supported metric perturbation, is an example of such a space.) Let Δ be the positive Laplacian on , and V a smooth potential on M which decays to second order at infinity. In this paper we construct the kernel of the operator , at a non-trapping energy , uniformly for , small, within a class of Legendre distributions on manifolds with codimension three corners. Using this we construct the kernel of the propagator, , as a quadratic Legendre distribution. We also determine the global semiclassical structure of the spectral projector, Poisson operator and scattering matrix.