  The Complex Kohn variational method for electron-polyatomic molecule
scattering is formulated using an overset grid representation of the scattering
wave function. The overset grid consists of a central grid and multiple dense,
atom-centered subgrids that allow the simultaneous spherical expansions of the
wave function about multiple centers. Scattering boundary conditions are
enforced by using a basis formed by the repeated application of the free
particle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the overset
grid in a "Born-Arnoldi" solution of the working equations. The theory is shown
to be equivalent to a specific Pad\'e approximant to the $T$-matrix, and has
rapid convergence properties, both in the number of numerical basis functions
employed and the number of partial waves employed in the spherical expansions.
The method is demonstrated in calculations on methane and CF$_4$ in the
static-exchange approximation, and compared in detail with calculations
performed with the numerical Schwinger variational approach based on single
center expansions. An efficient procedure for operating with the free-particle
Green's function and exchange operators (to which no approximation is made) is
also described.
