We have calculated the frequency-dependent exact exchange (EXX) kernel of time-dependent (TD) density functional theory employing our recently proposed computational method based on cubic splines. With this kernel we have calculated the linear density response function and obtained static polarizabilites, van der Waals coefficients and correlation energies for all spherical spin compensated atoms up to Argon. Some discrete excitation energies have also been calculated for Be and Ne. As might be expected, the results of the TDEXX approximation are close to those of TD Hartree-Fock theory. In addition, correlation energies obtained by integrating over the strength of the Coulomb interaction turn out to be highly accurate.
Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation
Variety of scenarios of the magnetic exchange response in topological insulators
本文用相对论k.p理论研究了磁交换场对三维层状拓扑绝缘体带隙区能带结构的影响。对于垂直于层（沿$z$）的场，我们揭示了带隙边缘对磁化的响应的新颖的非常规方案。价态和导电态的修改被认为是在其$Γ$ -点自旋$s^z$和总角动量$J^z$的原子网站上的状态被本地化。实际情况取决于$s^z$和$J^z$是否具有相同或相反的符号。特别地，价态的相反符号和导电态的相同符号在Bi $_2$ Te $_3$中引起非常规响应-在体晶体和超薄膜中，这从根本上将这种拓扑绝缘体与Bi $_2$ Se $_3$区分开来，其中两种状态具有相同的符号.为了更深入地了解具有反向和非反向零场能带结构的绝缘体中的不同情况，从第一性原理出发构建了最小四带三阶k.p模型。在这个模型中，我们分析了绝缘体的场致能带结构，并确定了出现在磁相的外尔节点，并根据情况表现不同。我们用陈数$\mathcal{C}$表征了改进的能带结构的拓扑结构，发现非常规响应伴随着大的陈数$\mathcal{C}=\pm3$。
