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The Complex Kohn variational method for electron-polyatomic moleculescattering is formulated using an overset grid representation of the scatteringwave function. The overset grid consists of a central grid and multiple dense,atom-centered subgrids that allow the simultaneous spherical expansions of thewave function about multiple centers. Scattering boundary conditions areenforced by using a basis formed by the repeated application of the freeparticle Green's function and potential, $\hat{G}^+_0\hat{V}$ on the oversetgrid in a "Born-Arnoldi" solution of the working equations. The theory is shownto be equivalent to a specific Pad\'e approximant to the $T$-matrix, and hasrapid convergence properties, both in the number of numerical basis functionsemployed and the number of partial waves employed in the spherical expansions.The method is demonstrated in calculations on methane and CF$_4$ in thestatic-exchange approximation, and compared in detail with calculationsperformed with the numerical Schwinger variational approach based on singlecenter expansions. An efficient procedure for operating with the free-particleGreen's function and exchange operators (to which no approximation is made) isalso described.

Variational treatment of electron-polyatomic molecule scattering calculations using adaptive overset grids