  The wavefunction for the multiparticle Schr\"odinger equation is a function
of many variables and satisfies an antisymmetry condition, so it is natural to
approximate it as a sum of Slater determinants. Many current methods do so, but
they impose additional structural constraints on the determinants, such as
orthogonality between orbitals or an excitation pattern. We present a method
without any such constraints, by which we hope to obtain much more efficient
expansions, and insight into the inherent structure of the wavefunction. We use
an integral formulation of the problem, a Green's function iteration, and a
fitting procedure based on the computational paradigm of separated
representations. The core procedure is the construction and solution of a
matrix-integral system derived from antisymmetric inner products involving the
potential operators. We show how to construct and solve this system with
computational complexity competitive with current methods.
