Efficient hybrid and screened hybrid density functional calculations of carbon and silicon nanostructures electronic properties

Hybrid functionals combine Density Functional Theory (DFT) with a fraction of Fock exchange. Screened hybrid functionals use a screened Fock exchange instead. In recent years, those methods became more popular as they yield results that are in better agreement with experiment for various physical properties. However, the calculation of Fock exchange can be computationally intensive for large systems. In this paper, we demonstrate the use of an efficient real-space approach that is based on projection schemes and an FFT based Poisson solver, for large atomistic systems. We apply this approach for silicon quantum dots and graphene nanoribbons and show the size dependence of physical properties such as the band gap and ionization potential. Finally, we show how those calculations can be further accelerated through the use of Graphical Processing Units (GPUs).