Yüksek dereceli sonlu elemanlar yöntemi tabanlı Kohn-Sham yoğunluk fonksiyonel kuramı çerçevesinde varyasyonel tutarlı kuvvetlerle geometri eniyilemesi

Variationally consistent atomic forces are computed for Kohn-Sham density functional theory (DFT) solved via a higher order finite element (FEM) framework. Force expressions are derived for pseudopotential and all-electron settings in a unified structure. Generalized gradient approximations are additionally addressed together with nonlinear core correction in the same pseudopotential setting. Classical Lagrange basis functions are used as well as non-uniform rational B-spline (NURBS) basis in isogeometric analysis concept. Calculated forces have been shown to be variationally consistent with energies. Reference force values have been generated through Kohn-Sham DFT software packages and accuracy of forces is verified. Finally, geometry optimizations have been conducted. For this purpose, several optimization algorithms are tested for their robustness, computational cost and ease of implementation. Fast inertial relaxation engine (FIRE) algorithm is eventually chosen as the optimization algorithm. Variationally consistent forces allow conducting geometry optimization even at coarse meshes, finding the energy minima of any particular setup. Optimized ground state ge- ometries have also been compared with those obtained from reference software packages, showing very close agreement with values reported in literature.