The relation between vertical and adiabatic singlet-triplet gaps and the generalized spin-dependent global response coefficients is presented. Local, semilocal, and hybrid density functional calculations of these quantities for the halocarbenes CXY, where X and Y are H, F, Cl, Br, and I, show that the vertical gaps are better reproduced at the local level. Hybrid functionals overestimate them considerably. For the whole series of halocarbenes considered, except CHI, calculations predict the singlet (1)A(1) as the ground state. The only exception found is for the hybrid calculation of CHI that predicts B-3(1) as the ground state for this halocarbene. For all functionals, there is a linear relation between the vertical singlet-tripler energy gap and the spin potential (the first derivative of the total energy with respect to the number of unpaired electrons), and the inclusion of the spin hardness (the second derivative of the total energy with respect to the number of unpaired electrons) improves this relationship considerably. It is also shown that the geometrical relaxation accompanying the adiabatic excitation in the halocarbenes is constant.