Chondroitin sulfate (CS) is one of several glycosaminoglycans that are major components of proteoglycans. A linear polymer consisting of repeats of the disaccharide -4G1cA beta-3GalNAc beta 1-, CS undergoes differential sulfation resulting in five unique sulfation patterns. Because of the dimer repeat, the CS glycosidic "backbone" has two distinct sets of conformational degrees of freedom defined by pairs of dihedral angles: (phi(1), psi(1)) about the beta 1-3 glycosidic linkage and (phi(2), psi(2)) about the beta(1)-4 glycosidic linkage. Differential sulfation and the possibility of cation binding, combined with the conformational flexibility and biological diversity of CS, complicate experimental efforts to understand CS three-dimensional structures at atomic resolution. Therefore, all-atom explicit-solvent molecular dynamics simulations with Adaptive Biasing Force sampling of the CS backbone were applied to obtain high-resolution, high-precision free energies of CS disaccharides as a function of all possible backbone geometries. All 10 disaccharides (beta 1-3 vs beta 1-4 linkage x five different sulfation patterns) were studied; additionally, ion effects were investigated by considering each disaccharide in the presence of either neutralizing sodium or calcium cations. GlcA beta-3GalNAc disaccharides have a single, broad, thermodynamically important free-energy minimum, whereas GalNAc beta-4G1cA disaccharides have two such minima. Calcium cations but not sodium cations bind to the disaccharides, and binding is primarily to the GlcA-COO- moiety as opposed to sulfate groups. This binding alters the glycan backbone thermodynamics in instances where a calcium cation bound to -COO- can act to bridge and stabilize an interaction with an adjacent sulfate group, whereas, in the absence of this cation, the proximity of a sulfate group to -COO- results in two like charges being both desolvated and placed adjacent to each other and is found to be destabilizing. In addition to providing information on sulfation and cation effects, the present results can be applied to building models of CS polymers and as a point of comparison in studies of CS polymer backbone dynamics and thermodynamics.