We report a detailed theoretical analysis of the structures of various crystalline phases of pure and hydrogenated carbon. Using first-principles density functional theory calculations, we propose possible structures for the experimentally observed phases of carbon nanocrystals through incorporation of interstitial hydrogen atoms, at proper concentrations, into cubic carbon lattices. The results of our analysis provide possible interpretations for the structures of i-carbon, a cubic phase with lattice parameter a = 4.25 angstrom, a body-centered cubic carbon phase with a = 3.1 angstrom, and n-diamond, a face-centered cubic phase with a = 3.57 angstrom. (C) 2009 Elsevier B. V. All rights reserved.