Metal ions and intrinsically disordered peptides amyloid-β40 and amyloid-β42 are at the center of Alzheimer´s disease pathology. Divalent copper ion binds to amyloid-β40 and amyloid-β42 peptides with varying coordination chemistries. Experiments face challenges in the measurements of divalent copper ion bound monomeric amyloid-β40 and amyloid-β42 in an aqueous solution medium because of fast conformational changes, rapid aggregation processes and solvent effects. Theoretical studies complement experiments and provide insights at the atomic and molecular levels with dynamics. However, until recently, potential functions for simulating divalent copper ion bound amyloid-β40 and amyloid-β42 peptides with varying coordination chemistries were lacking. Using new potential functions that were developed for divalent copper centers, Cu(II), including three histidine residues and an oxygen-ligated amino acid residue, the structures and thermodynamic properties of Cu(II)-bound amyloid-β40 and amyloid-β42 peptides in an aqueous solution medium were studied. For these purposes, extensive first principles calculations and replica exchange molecular dynamics simulations were conducted. In this study, the secondary and tertiary structural properties, conformational Gibbs free energy values, potential of mean force surfaces, salt bridges and aggregation propensities of aqueous Cu(II)-bound amyloid-β40 and amyloid-β42 peptides are presented. Different than previous findings in the literature, results clearly show that the coordination chemistry variations impact the structural and thermodynamic properties of divalent Cu(II) bound amyloid-β alloforms in water. Specificities about these differences are revealed in this study at the atomic level with dynamics. Results presented herein are the first to offer a comparison of the monomeric Cu(II)-bound amyloid-β40 and amyloid-β42 peptides with varying coordination chemistries using bonded model potential functions.