A real-space non-periodic computational framework is developed for Kohn-Sham density functional theory (DFT). The electronic structure calculation framework is based on the finite element method (FEM) where the underlying basis is chosen as non-uniform rational B-splines (NURBS) which display continuous higher-order derivatives. The framework is formulated within a unified presentation that can simultaneously address both all-electron and pseudopotential settings in radial and three-dimensional cases. The canonical Kohn-Sham equation and the Poisson equation are discretized on different meshes in order to ensure that the underlying variational structural of Kohn-Sham DFT is preserved within the weak formulation of FEM. The discrete generalized eigenvalue problem emanating from the Kohn-Sham equation is solved efficiently based on the Chebyshev-filtered subspace iteration method. Numerical investigations in the radial case demonstrate all-electron and local pseudopotential capabilities on single atoms. In the three-dimensional case, all-electron and nonlocal pseudopotential computations on single atoms and small molecules are followed by local and nonlocal pseudopotential studies on larger systems. At all stages, special care is taken to demonstrate optimal convergence rates towards the ground state energy with chemical accuracy. Comparisons with classical Lagrange basis sets indicate the significantly higher per-degree-of-freedom accuracy displayed by NURBS. Specifically, cubic NURBS discretizations can offer a faster route to a prescribed accuracy than even sixth-order Lagrange discretizations on comparable meshes, thereby indicating considerable efficiency gains which are possible with these higher-order basis sets within effective numerical implementations.

针对Kohn-Sham密度泛函理论（DFT），开发了一种实空间非周期性计算框架。电子结构计算框架基于有限元方法（FEM），在该方法中，基础被选为显示连续高阶导数的非均匀有理B样条（NURBS）。该框架是在统一的表示形式中制定的，可以同时解决径向和三维情况下的全电子和伪电势设置。规范的Kohn-Sham方程和Poisson方程在不同的网格上离散化，以确保在有限元法的弱公式内保留Kohn-Sham DFT的底层变异结构。基于Chebyshev滤波子空间迭代方法，有效地解决了Kohn-Sham方程产生的离散广义特征值问题。径向情况下的数值研究表明了单个原子上的全电子和局部伪势能。在三维情况下，对单个原子和小分子的全电子和非局部伪电位计算之后，对大型系统进行局部和非局部伪电位研究。在所有阶段，都应特别注意以化学精度证明朝基态能量的最佳收敛速度。与经典Lagrange基集的比较表明，NURBS显示的每自由度精度明显更高。特别，