Exploring the structural interplay of ligands with uranyl can provide important knowledge for technology advances in uranium extraction from seawater. However, obtaining such chemical information is not an easy endeavor experimentally. From a plethora of computational methods, this work provides both microscopic insights and free-energy profiles of the binding between uranyl and deprotonated glutardiamidoxime (H2B) for which experimental structural information is not available, despite H2B being an important model ligand with an open-chain conformation for understanding aqueous uranium extraction chemistry. In our molecular dynamics (MD) simulations, we explicitly accounted for the water solvent as well as the Na+ and Cl- ions. We found that hydrogen bonding plays a critical role in dictating the binding configurations of B2- and HB- with uranyl. Simulated free energies of sequential ligand binding to form UO2B, [UO2B2]2-, and [UO2(HB)B]- show very good agreement with the experimental values, lending support to our structural insights. The potential of mean force simulations showed the common feature of an important intermediate state where one end of the ligand binds to uranyl while the other end is solvated in water. Bringing the loose end of the ligand to bind with uranyl has a free-energy barrier of 15-25 kJ/mol. The present work shows that the combined simulation approach can reveal key structural and thermodynamic insights toward a better understanding of aqueous complexation chemistry for uranium extraction from the sea.