A systematic first-principles study is performed to investigate the 20-electron transition metal complexes (C5H5)2TM(E1E2)2 (TM = Cr, Mo, W; E1E2 = CO, N2, BF). The bond dissociation energy (De) based on (C5H5)2TM(E1E2)2 → (C5H5)2TM(E1E2) + E1E2 indicates much lower thermodynamic stability of (C5H5)2TM(N2)2 because of poor binding ability of N2 ligands. For the thermodynamic stable (C5H5)2TM(E1E2)2 complexes (TM = Cr, Mo, W; E1E2 = CO, BF), their 20-electron nature is derived from their occupied nonbonding molecular orbital mainly donated by ligands. Furthermore, charge transfer from TMs to the C5H5 ligands is revealed by the atoms in molecules (AIM) theory, leading to the positive charges of the TM atoms. On the other hand, the nature of the TM-E1 bond has been thoroughly analyzed by the energy decomposition analysis (EDA) method. The absolute value of interaction energies (|ΔEint|) between (C5H5)2TM(E1E2) and E1E2 has the same trend as the corresponding bond dissociation energy and Wiberg bond orders of TM-E1 bonds, following the order W > Mo > Cr with same ligands and BF > CO with same TM. Additionally, the largest contribution to the ΔEint values is the repulsive term ΔEPauli. Similar contributions from covalent and electrostatic terms to the TM-E1 bonds were found, which can be described as the classic dative bond with nearly same σ and π contributions. The stronger σ donations and π backdonations in (C5H5)2TM(BF)2 than in (C5H5)2TM(CO)2 indicate much more stability of (C5H5)2TM(BF)2.