General formulation of the variational cellular method for molecules and crystals

A variational form of the cellular method is proposed as a new model to solve the one-electron Schrödinger equation for molecules and crystals. The model keeps such good features of the traditional cellular method as the arbitrary partition of space, and eliminates its main drawback, the slow convergence of the cellular expansion series. With the aid of a criterion of precision on the trial wave functions, we discuss the possibilities offered by the method for more accurate calculations of the electronic structures of molecules and solids. As an example of the accuracy and fast convergence of the model, computation of the energy spectrum of the molecular hydrogen ion ${\mathrm{H}}_2^{+}$ is presented.