This thesis consists of two parts. In the first part, the properties of excess electrons in water clusters are studied via a hybrid quantum and classical mechanics method. The existence of the solvated electron in water was experimentally demonstrated long ago, and it is among the most interesting charged species. However, a satisfactory characterization of the water clusters has always been a challenge. In our simulation, we treat a region of the cluster nearest to the centroid of the excess electron distribution quantum mechanically, while the rest of the water molecules are treated classically. The binding energies of a localized excess electron are calculated in clusters with sizes ranging from 16 to 300. The density distributions of the excess electrons verify the existence of both surface localization mode and interior localization model. We studied the energetically favored localization modes depending on the sizes of the clusters and the transition point. In the second part, the energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field, and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin of the four electrons and the ensuing spin degeneracies. These six states appear to cross at a single value of the magnetic field, with the crossing point becoming sharper for larger interdot distances. As the strength of the Coulomb repulsion increases, the six states tend to become degenerate and a well defined energy gap separates them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule. Using the spin-resolved pair-correlation functions, one can map the EXD many-body wave functions onto the spin functions associated with the four localized electrons. The ability to determine associated spin functions enables investigations concerning entanglement properties of the system of four electrons.