Sickle cell disease is a genetic disorder associated with a single mutation (Glu-β6 → Val-β6) in the β chains of hemoglobin, causing the polymerization of deoxygenated sickle cell hemoglobin (deoxy-HbS). The deoxy-HbS binding free energy was recently studied through molecular simulations, and a value of −14 ± 1 kcal mol^–1 was found. Here, we studied the binding free energy of normal adult hemoglobin (deoxy-HbA), which does not polymerize at normal physiological conditions, with the aim of elucidating the importance of the presence of Val-β6 and of the absence of Glu-β6 on the aggregation of deoxy-HbS. A binding free energy of −4.4 ± 0.5 kcal mol^–1 was found from a one-dimensional potential of mean force. Hydrophobic interactions are shown to represent less than 20% of the interactions in the contact interface, and despite similarly strong hydrogen-bonded ion pairs (i.e., salt bridges) and water bridged electrostatic interactions are found for deoxy-HbA and deoxy-HbS, a large repulsive potential energy is associated with Glu-β6, whereas a mild attractive potential energy is connected with Val-β6. Interestingly, Asp-β73 switches from forming a major electrostatic repulsive pair with Glu-β6 in deoxy-HbA, to forming a major attractive residue pair with Val-β6 in deoxy-HbS, consistent with the view that damping of electrostatic repulsions involving Glu-β6, namely, those associated with Asp-β73, could be responsible for the polymerization of deoxy-HbA at high potassium phosphate concentrations. Solvation analysis shows that functional groups forming salt bridges and water bridged interactions preserve a nearly intact first hydration sphere, avoiding a complete dewetting free energy penalty. These results support the view that the absence of Glu-β6 is more important than the presence of Val-β6, and that although hydrophobic effects, associated with the Val-β6 dehydration and interaction with the hydrophobic pocket in the neighbor tetramer, are important, electrostatic interactions are dominant, opposite to a picture where HbS association is driven by hydrophobic interactions.