The formulation and implementation of analytic energy gradients for periodic density functional calculations with STO/NAO Bloch basis set

Analytic energy gradients with respect to atomic coordinates for systems with translational invariance are formulated within the framework of Kohn-Sham Density Functional Theory. The energy gradients are implemented in the BAND program for periodic DFT calculations which directly employs a Bloch basis set made up of Slater-type (STOs) and numeric atomic orbitals (NAOs). The details of our implementation are described including the use of symmetry in the reciprocal and direct spaces, as well as the application of the frozen core approximation