The graphics processing units (GPUs), or graphics cards, are processors that were originally designed to perform dedicated tasks to the computer graphics operations. However, NVIDIA has developed an extension of the C language for programming GPUs, called CUDA (Compute Unified Device Architecture). This allowed the use of GPUs, in High Performance Computing, for processing generic data. The physical systems studied by quantum mechanics have dimensions close to atomic scale, such as molecules, atoms, protons and electrons. The Density Functional Theory (DFT) is one of the most used interactive methods to find an approximated solution to the Schrödinger equation. However, the calculations in DFT are computationally intensive because of the exchange and correlation electronic integrals, integrals to calculate the Hartree energy and electrons kinetic energy, which requires greater computational effort as the number of electrons present in the simulation increases. This research aimed to study the DFT calculations and identify parts of the algorithm that, if changed, experience performance benefits from execution in GPU. Thus, computationally intensive DFT functions of the SIESTA method (Spanish Initiative for Electronic Simulations with Thousands of Atoms) were parallelized and used to calculate the physical properties of nanotubes and fullerenes. It was found that the implementation of SIESTA parallel version on the GPU is able to achieve gains in performance, in individual functions, of one or even two orders of magnitude, making it promising employment of GPUs to speed up the processing of Density Functional Theory.