Browsing by Author "Karaca, Kaan"
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Item Open Access Geometry optimization with variationally consistent forces using higher-order finite element methods in Kohn-Sham density functional theory calculations(2021-09) Karaca, KaanVariationally consistent atomic forces are computed for Kohn-Sham density func-tional 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 ad-dressed together with nonlinear core correction in the same pseudopotential set-ting. 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, compu-tational cost and ease of implementation. Fast inertial relaxation engine (FIRE) algorithm is eventually chosen as the optimization algorithm. Variationally con-sistent 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.Item Restricted Türkiye'nin ilk nükleer reaktörü: TR-1(Bilkent University, 2020) Peker, Dilşad Simay; Kırmacı, Selin; Karaca, Kaan; Lomlu, RanaTürkiye'nin ilk reaktörü olan TR-1 hakkında olan bu araştırma yazısı TR-1'in açılma kararından başlayarak kuruluş süresini, aktif yıllarındaki çalışmalarını ve kapanış sürecini sosyal, siyasi ve ekonomik olarak detaylı bir şekilde incelemektedir. Bu süreçlerde karşılaşılan problemlere, halkın bakış açısına, kapanış nedenlerine ve Türkiye'nin gelişimine katkısına da değinen bu yazı TR-1'den sonra nükleer alanında yapılan çalışmaları da anlamak için bir ışık tutmaktadır.Item Open Access Variationally consistent Hellmann–Feynman forces in the finite element formulation of Kohn–Sham density functional theory(Elsevier, 2023-01-01) Karaca, Kaan; Temizer, İlkerHellmann–Feynman forces are derived within the numerical framework of the finite element method for density functional theory in the Kohn–Sham formalism. The variational consistency of the force expressions in all-electron and pseudopotential settings are carefully examined, with a particular focus on the implications arising from different representations for interaction terms that are associated with electrostatics. Numerical investigations in nonperiodic systems which range from diatomic molecules to carbon allotropes demonstrate the systematic convergence that is offered by the finite element framework, not only for energy and force but also for geometric configuration and molecular statics parameters. A range of higher-order discretizations employing fixed meshes are invoked within these examples based on classical finite elements as well as on isogeometric analysis. Overall, this work contributes to recent advances which demonstrate the viability of the finite element method for carrying out ab initio molecular dynamics.