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We develop a formalism for the evaluation of conduction eigenchannels ofatomic-sized contacts from first-principles. The multiple scatteringKorringa-Kohn-Rostoker (KKR) Green's function method is combined with the Kubolinear response theory. Solutions of the eigenvalue problem for thetransmission matrix are proven to be identical to eigenchannels introduced byLandauer and B{\"u}ttiker. Applications of the method are presented by studyingballistic electron transport through Cu, Pd, Ni and Co single-atom contacts. Weshow in detail how the eigenchannels are classified in terms of irreduciblerepresentations of the symmetry group of the system as well as by orbitalcontributions when the channels wave functions are projected on the contactatom.Comment: Revised version; under consideration in Physical Review

Conduction eigenchannels of atomic-sized contacts:Ab initioKKR Green’s function formalism