Hydrogen bond(HB) strength on the Heme- myoglobin models including O2, CO and NO molecules binding to distal histidine (Heme-O2, Heme-NO and Heme-CO) in gas and solvent mediums was studied by computational methods. Calculations in the solvent were well done using the self-consistent reaction field (SCRF) and discrete methods. Quantum theory of atoms in molecules (AIM) and natural bond orbital theory (NBO) were applied to obtain the topological data and charge transfer energies, respectively. Results of the calculations clearly showed that the solvent reduced the hydrogen bond energies compared to the gas phase. Furthermore, distal histidine of the Heme models in non-polar solvents formed the strangest hydrogen bond to the diatomic molecules with respect to polar solvents. All of the HB descriptor parameters such as structural, topological, NBO and vibrational frequencies parameters suggest that the Heme-O2 has the strongest HB, which is followed by Heme-NO and Heme-CO, respectively. Totally, we obtained good correlations among Espinosa hydrogen bond energies with structural, topological, NBO and vibrational frequencies parameters in gas medium. Finally, based on the results we gained several linear equations in order to estimate of hydrogen bond energies in biological molecules.