The structural, electronic, molecular and thermochemical properties of hypothetical [Tp(CO)2Mo≡C-Ph)]2+ (1) [Tp = hydridotris(pyrazolyl) borate] and [L(CO)2Mo≡C-Ph)]+ (2) [L=hydrido 2-phenoxybis(pyrazolyl) borate] carbyne complexes were investigated by quantum chemical calculations. The carbyne complexes were optimized at B3LYP/LANL2DZ/6-31G(d) level. Structural parameters, vibration spectra, electronic spectra and NMR spectra were computationally obtained. Environment geometry of the molybdenum atom was predicted to be distorted octahedral. Mulliken atomic charges, molecular electrostatic potential maps, molecular orbital energy diagrams and frontier orbital contour diagrams were calculated and interpreted to estimate the electronic properties of the complexes. In order to predict the molecular properties of complexes, some electronic structure descriptors were calculated and discussed. The thermal stability of the complexes was investigated. Thermochemical parameters of the complexes were found to increase with increasing temperature. Metal-carbyne bond dissociation energies of complex (1) and complex (2) were calculated as 955 and 912 K, respectively.