In the present study we apply density functional theory (DFT) to calculate nonresonant X-ray emission (XE) spectra of free and chemisorbed molecules. Both ground state frozen orbital and transition potential relaxed orbital procedures are investigated for the calculation of X-ray emission energies and intensities. A code implementation of these proposals has been applied to the free and surface-adsorbed carbon monoxide, ethylene, and benzene molecules and to surface-adsorbed atomic nitrogen. The results are analyzed in comparison with experimental data and with calculations using Hartree-Fock theory. Different standard exchange-correlation functionals have been discussed. The quality of the computed DFT-level XE spectra is comparable to what is obtained using Hartree-Fock theory for intensities of the free molecules but improves, in general, the description of the spectra for the surface adsorbates. The best experimental comparison is obtained when putting the X-ray emission spectra on a common energy scale using the valence transition potentials for energies and the frozen ground state wave function for the intensities.