Browsing by Subject "Kohn-Sham density functional theory"

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Open Access
Geometry optimization with variationally consistent forces using higher-order finite element methods in Kohn-Sham density functional theory calculations
(2021-09) Karaca, Kaan
Variationally 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.
Open Access
Hybrid finite element / multipole expansion method for atomic Kohn-Sham density functional theory calculations
(Elsevier, 2023-05) Yalçın, Mehmet A.; Temizer, İlker
A numerical framework is developed for aspherical atomic Kohn-Sham density functional theory calculations. The framework invokes higher-order finite elements as a radial discretization in combination with a multipole expansion for controlling the spherical resolution. Both all-electron and nonlocal pseudopotential calculations are addressed in a unified setting. The overall approach is validated through a range of numerical examples which demonstrate the systematic convergence of the radial and spherical discretizations as well as the outstanding accuracy that can be efficiently obtained in the presence of strong aspherical external fields. Overall, the presented approach offers a route to adaptive local enrichment for electronic structure calculation in the context of the finite element method.