A new integral equation formulation is presented for molecular scattering. This is obtained by exactly transforming the common closehyphen;coupling theory into an equivalent nonlocal integral equation form which isnota set of coupled discrete basis equations. The integral equation is formally localized by the introduction of a translation operator, thereby leading to a Hamiltonian (or portion of it) that is a Fourier transform of the original kernel. The theory makesnouse of Greenrsquo;s functions and this overall approach has two attractive features. Firstly, an examination of the integral kernels allows the development ofoptimalquadrature schemes for each problem and, secondly, judicious approximations of the localized Hamiltonian operator lead to very attractive practical equations. As an illustration of the latter point, the method is applied to replace thedifferentialinternal Hamiltonian operator by an effective localfunctionwhich can act to correct the usual sudden approximation without excess computational effort. Various asymptotic limits of the theory are also discussed.
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