Carbenes and fluorocarbenes are important intermediates in the hydrodechlorination of CFCs catalyzed by metal surfaces. However, the reaction mechanism at a molecular level is not completely understood. In this work, density functional calculations have been performed for the first-row transition-metal complexes M-CH2, M-CHF, and M-CF2 aiming to conbribute to the understanding of the metal/carbene interaction mechanism. Relative energies, geometries, and frequencies of the M-CXY complexes in different electronic states are reported. The binding mechanism is described through an analysis of the molecular orbitals. The binding energy of the M-CF2 is about 30% smaller than the respective M-CH2 binding energy. The electronic configuration of all complexes studied is presented in a diagram that allows one to predict qualitatively properties such as geometries, multiplicities, charge transfers, and relative bond lengths.