well by the QM/MM method using the electrostatic embedding approach 16. This is as expected, because most of the protein functions are primarily achieved by the electrostatic 17-21. For example, as previous works demonstrate, the electric field that a protease exerts at the active site is one of the most important origins of its catalytic power 22-26. With the advances in computer hardware and computational methods 27-31 , a number of QM/MM molecular dynamics (MD) studies employing various implementations of the expensive (prohibitive time/computational costs) Møller-Plesset perturbation theory (MP2) have been conducted 32-43. However, it remains challenging to apply potentially highly accurate correlated ab initio QM methods (e.g., coupled clustering) in QM/MM MD simulations with a large number of QM atoms. Therefore, semi-empirical, DFT, or even Hatree-Fock (HF) methods have been employed in most QM/MM studies. However, DFT and HF methods suffer from a well-known limitation; that is, the Coulomb correlation is missing in the mean-field HF approach, which results in its inability to account for the dispersion effects, whereas many DFT-based QM methods cannot account for these effects in precise terms because the exact correlation functional is unknown 44,45. Consequently, DFT methods do not always provide correct results in QM/MM simulations 46-49 , whereas HF method can only work well in the QM/ MM simulation of specific systems (e.g., methyl-transfer reactions) 50. Great efforts have been made to account for the dispersion effects in QM methods over the past decade, with a number of empirical dispersion methods routinely used for the QM calculations 45,51-53. The inclusion of the electron correlation and dispersion effects is mandatory for QM studies related to chemical systems and various intramolecular phenomena 27,44. Investigation of the importance of these effects on the accurate description of the QM/MM interactions is a primary issue for realistic MD simulations of large or condensed systems with a QM/MM protocol. For this, first, an appropriate model system is required. Such a system should have a characteristic quantity (e.g., reaction barriers) that is easily handled by the QM/MM simulation with a small-sized QM region to facilitate the convergence of the simulation, and the characteristic quantity should be sensitive to the electrostatic interactions. It is preferable not to have dangling bonds between the QM and MM subsystems to avoid introducing unnecessary effects from the QM/MM boundary 54. The MbCO system is one of the most studied proteins for investigating ligand binding, migration or other biologically relevant processes 55-74. The spectroscopic characterization of CO has been used to explore the relationship between the dynamics, structure, and function of proteins in numerous experimental studies 63,71,73-75. The molecular migration pathway for the CO to leave the myoglobin involves a set of transition steps between certain specific cavities, including the so-called distal heme pocket (the...