The self-assembly behavior of gemini (dimeric or twin-tail) dicarboxylate disodium surfactants is studied using molecular dynamics simulations. A united atom model is employed for the surfactants with fully atomistic counterions and water. This gemini architecture, in which two single tailed surfactants are joined through a flexible hydrophobic linker, has been shown to exhibit concentration-dependent aqueous self-assembly into lyotropic phases including hexagonal, gyroid, and lamellar morphologies. Our simulations reproduce the experimentally observed phases at similar amphiphile concentrations in water, including the unusual ability of these surfactants to form gyroid phases over unprecedentedly large amphiphile concentration windows. We demonstrate quantitative agreement between the predicted and experimentally observed domain spacings of these nanostructured materials. Through careful conformation analyses of the surfactant molecules, we show that the gyroid phase is electrostatically stabilized related to the lamellar phase. By starting with a lamellar phase, we show that use of a bulkier N(CH3) 4+ counterion in place of Na+ drives the formation of a gyroid phase. Decreasing the charge on the surfactant headgroups by carboxylate protonation decreases the degree of order in the lamellar phase. Using our models, we show that the translational diffusion of water and the Na+ counterions is decreased by several orders of magnitude over the studied concentration range, and we attribute these effects to strong correlations between the mobile species and the surfactant headgroups.