We show how to extract the orbital contribution to the transport eigenchannels from a first-principles quantum transport calculation in a nanoscopic conductor. This is achieved by calculating and diagonalizing the first-principles transmission matrix reduced to selected scattering cross sections. As an example, the orbital nature of the eigenchannels in the case of Ni nanocontacts is explored, stressing the difficulties inherent to the use of nonorthogonal basis sets.
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