Minimizing the Kohn–Sham total energy for periodic systems

We describe how a previously developed constrained minimization algorithm can be adapted to minimize the total energy of a periodic atomistic system under the Kohn–Sham density functional theory framework. The algorithm uses the Bloch theorem to reduce the complexity of the calculation by working with a number of unit cells separately. We present the Bloch theorem in terms of linear algebra, and point out its implication on the spectral property of the Kohn–Sham Hamiltonian.