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 (|ΔE_int|) 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 ΔE_int values is the repulsive term ΔE_Pauli. 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.