We identify a class of covalent functionalizations that preserves or controls the conductance of single-walled metallic carbon nanotubes.[2+1] cycloadditions can induce bond cleaving between adjacent sidewall carbons, recovering in the process the sp 2 hybridization and the ideal conductance of the pristine tubes. This is radically at variance with the damage permanently induced by other common ligands, where a single covalent bond is formed with a sidewall carbon. Chirality, curvature, and chemistry determine bond cleaving, and in turn the electrical transport properties of a functionalized tube. A well-defined range of diameters can be found for which certain addends exhibit a bistable state, where the opening or closing of the sidewall bond, accompanied by a switch in the conductance, could be directed with chemical, optical or thermal means.Chemical functionalizations of carbon nanotubes (CNTs) are the subject of intensive research [1,2], and could offer new and promising avenues to process and assemble tubes, add sensing capabilities, or tune their electronic properties (e.g., doping levels, Schottky barriers, work functions, and electron-phonon couplings). However, the benefits of functionalizations are compromised by the damage to the conduction channels that follows sp 3 rehybridization of the sidewall carbons [3,4], as evidenced by absorption spectra and electrical transport measurements [5,6,7]. We report here on a class of cycloaddition functionalizations that preserves instead the remarkable transport properties of metallic CNTs. In addition, we identify a subclass of addends that displays a reversible valence tautomerism that can directly control the conductance. We focus here on [2+1] cycloaddition reactions, where the addition of a carbene or a nitrene group saturates a double-bond between two carbon atoms, forming a cyclopropane-like three-membered ring. Such functionalizations have been reported extensively in the literature [8,9,10]. All our calculations are performed using density-functional theory in the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) [11], ultrasoft pseudopotentials [12], a planewave basis set with a cutoff of 30 Ry for the wavefunctions and 240 Ry for the charge density, as implemented in quantum-espresso [13]. We examine first the simplest members in this class of addends, CH 2 and NH. Fig. 1(a) and (b) show the two inequivalent choices available on a (5,5) metallic CNT; for convenience, we label these as "S" (skewed) and "O" (orthogonal), reminiscent of the relative positions of the sidewall carbons with respect to the tube axis. Our simulation cells include 12 n carbons for a given (n,n) CNT, plus one functional group. We use a 1×1×4 MonkhorstPack mesh (including Γ) for structural optimizations, and a 1×1×8 mesh for single-point energy calculations, with a cold smearing of 0.03 Ry [14].First, and for (n,n) metallic tubes, we highlight how strongly the reaction energies of these functionalizations depend on the curvature of the nanotubes, and on their ...