Cyclo[18]carbon (C18) is studied computationally at the density functional theory (DFT) and ab initio levels to obtain insight into its electronic structure, aromaticity, and adsorption properties on a NaCl surface. DFT functionals with a small amount of Hartree-Fock exchange fail to determine the experimentally observed polyyne molecular structure, revealing a cumulene-type geometry. Exchange-correlation functionals with a large amount of Hartree-Fock exchange as well as ab initio CASSCF calculations yield the polyyne structure as the ground state and the cumulene structure as a transition state between the two inverted polyyne structures through a Kekule distortion. The polyyne and the cumulene structures are found to be doubly Hückel aromatic. The calculated adsorption energy of cyclo[18]carbon on the NaCl surface is small (37 meV/C) and almost the same for both structures, implying that the surface does not stabilize a particular geometry.