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We determine the conditions in which negative differential resistance (NDR)appears in the C$_{60}$-based molecular device of [Phys. Rev. Lett. {\bf 100},036807 (2008)] by means of ab-initio electron-transport simulations. Ourcalculations grant access to bias-dependent intrinsic properties of themolecular device, such as electronic levels and their partial widths. We showthat these quantities depend on the molecule-molecule and molecule-electrodeinteractions of the device. Hence, NDR can be tuned by modifying the biasbehavior of levels and widths using both types of interactions.

Negative differential resistance in scanning tunneling microscopy: simulations on C$_{60}$-based molecular overlayers