For the title complexes we discuss the results of DFT calculations for (i) the molecular and electronic structures, (ii) the rotational barriers of the carbenes around the Fe=C-carb bond (Delta E-rot), and (iii) the binding energies of the carbenes (D-e). Where available, the calculated properties of the Fe=C-carb bonds are compared with previous theoretical and experimental data of some prototypical carbene complexes classified as Fischer- or Schrock-type compounds. It is shown that the rotational barriers of the carbenes, the Fe-C-carb bond distances and bond strengths are sensitive to the carbene substituents and to the ligands L attached to iron. For complexes with given L the values of Delta E-rot diminish in the order: CH2 > CF2 > CMe2 and an inverse ordering is obtained for the decrease of the Fe=C-carb bond distance. The Delta E-rot of dimethyl-carbene are close to those of Fischer-type compounds, while Delta E-rot of methylidene approach values typical for Schrock-type carbenes. The replacement of the CO ligand by poorer pi-acceptor ligand increases the values of Delta E-rot in the order: CO < PH3 < dhpe < PPh3 and diminishes the Fe-C-carb bond distance in the same order. The binding energies (D-e) of the carbenes are larger than the first dissociation energy of CO from the pentacarbonyliron complex. For complexes with given L, except one, the D-e values decrease in the order: CH2 > CMe2 > CF2. The properties of the investigated compounds are traced back to the character of the Fe -> C-carb pi-backbonding interactions and their competitions with the Fe - L and R - C-carb pi-interactions. It is also shown that the PH3 ligand can only be considered with caution as a good model for the PPh3 ligand in computational studies.