Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.