原子扩展Kohn-Sham基态的数值研究
A numerical study of the extended Kohn-Sham ground states of atoms
摘要：
本文考虑了圆柱对称外势作用下的扩展Kohn-Sham模型。详细介绍了模型的变分近似和离散空间的构造，以及求解离散化Kohn-Sham方程的算法。利用该程序，我们计算了简化的Hartree-Fock（rHF）模型和扩展的Kohn-Sham X $α$模型中周期表前四行所有原子的占据和未占据能级.这些结果使我们能够测试数值上的原子rHF和Kohn-Sham哈密顿在我们以前的理论工作中使用的密度泛函微扰理论和赝势的负谱的假设。有趣的是，我们观察到的偶然简并之间的s和d壳层或p和d壳层在费米能级的一些原子。我们还考虑了原子受均匀电场作用的情况。对于不同大小的电场，我们计算了Dirichlet边界条件下的碳原子密度的响应，我们检查，在小电场的限制，与一阶密度泛函微扰理论得到的结果一致。
英文摘要：
In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed together with the algorithm to solve the discretized Kohn-Sham equations used in our code. Using this code, we compute the occupied and unoccupied energy levels of all the atoms of the first four rows of the periodic table for the reduced Hartree-Fock (rHF) and the extended Kohn-Sham X$α$ models. These results allow us to test numerically the assumptions on the negative spectra of atomic rHF and Kohn-Sham Hamiltonians used in our previous theoretical works on density functional perturbation theory and pseudopotentials. Interestingly, we observe accidental degeneracies between s and d shells or between p and d shells at the Fermi level of some atoms. We also consider the case of an atom subjected to a uniform electric-field. For various magnitudes of the electric field, we compute the response of the density of the carbon atom confined in a large ball with Dirichlet boundary conditions, and we check that, in the limit of small electric fields, the results agree with the ones obtained with first-order density functional perturbation theory.
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