Density functional theory (DFT) is a powerful method for probing chemical and material properties and guiding the design of novel materials from first principles. However, the computational demands of large-scale and/or long-time DFT calculations can be challenging. To address this limitation, this thesis employs the approximate DFT method, density functional tight-binding (DFTB), as an alternative approach to DFT. The first part of the thesis demonstrates the accuracy and reliability of DFT methods in describing the electronic structure and properties of chemical and material systems. In the second part of the thesis, we transition from DFT to analyze the accuracy and efficiency of DFTB in performing large-scale electronic structure calculations. To achieve this goal, we have interfaced DFTB with the cluster approach to statistical mechanics (CASM) program, which allows for the efficient calculation of formation energies and convex hull. Furthermore, we have extended the DFTB approach to perform long-timescale metadynamics calculations on biochemical systems with the help of GPUs. GPU-enabled DFTB allows for an efficient and accurate description of the free energy surfaces and provides valuable insight into the transition pathways. In summary, this thesis aims to accelerate ab initio computations by enabling accurate and efficient prediction of material and chemical properties with DFTB. GPU-enhanced DFTB is a powerful tool for exploring the electronic and thermodynamic properties of complex materials, chemical, and biochemical systems, with potential applications in materials science, physics, and chemistry.