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We have adapted R-matrix theory to calculate phonon scattering across systemsof molecular to mesoscopic scale. The key novelty of this work is that the onlyrequired information about the scattering region are its normal modes, whichare evaluated only once for a system. Thus, R-matrix theory is acomputationally efficient and simple approach to calculate phonon scattering inlarger systems. To validate and to demonstrate the applicability of the theory,we apply it to two systems: a one dimensional chain of atoms and a graphenenanoribbon. In both cases, we discuss the effect of mass impurities on thermaltransport.

R-matrix theory for nanoscale phonon thermal transport across devices and interfaces