Although it has long been known that the classical notions of capacitance need modification at the nanoscale, in order to account for important quantum effects, very few first-principles investigations of these properties exist for any real material systems. Here we present the results of a large-scale ab initio investigation of the capacitance properties of carbon nanotube systems. The simulations are based on a recently developed real-space nonequilibrium Green's-function approach, with special attention being paid to the treatment of the bound states present in the system. In addition, use has been made of a symmetry decomposition scheme for the charge density. This is needed both to speed up the calculations and in order to study the origins of the induced charges. Specific systems investigated include two and three nested nanotube shells, the insertion of a capped nanotube into another, a connected (12,0)/(6,6) nanotube junction, and the properties of a nanotube acting as a probe over a flat aluminum surface. First-principles estimates of the capacitance matrix coefficients for all these systems are provided, along with a discussion of the quantum corrections. For the case of the nanotube junction, the numerical value of the capacitance is sufficiently high, as to be useful for future device applications.
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