Automatic Differentiation of the Energy within Self-consistent Tight-Binding Methods

We present and implement the calculation of analytical n-order geometric derivatives of the energy obtained within the framework of the density functional based tight binding approach. The use of automatic differentiation techniques allows a unique implementation for the calculation of derivatives up to any order providing that the computational facilities are sufficient. As first applications, the derivatives are used to build an analytical potential energy surface around the optimized geometry of acetylene. We also discuss the relevant anharmonic contributions that have to be considered when building such an analytical potential energy surface for acetylene, ethylene, ethane, benzene, and naphtalene.