截断基组格林函数多重散射理论：一种增广KKR形式
Green's function multiple-scattering theory with a truncated basis set: An Augmented-KKR formalism
摘要：
Korringa-Kohn-Rostoker（KKR）格林函数，多重散射理论是一种有效的以点为中心的电子结构技术，用于解决$N$散射体的组装。波函数在每个散射中心上以球面波为基础展开，并索引到最大轨道和方位角数$L_{max}=(l,m)_{max}$，而确定光谱特性的散射矩阵在相移$δ_{l>l_{tr}}$可忽略不计的$L_{tr}=(l,m)_{tr}$处截断。历史上，$L_{max}$被设置为等于$L_{tr}$ ;然而，更适当的程序保留了$L_{max}>L_{tr}$的自由电子和单位点贡献，其中$δ_{l>l_{tr}}$被设置为零[Zhang和Butler，Phys. Rev. B { \bf 46}，7433]。我们提出了一个数值高效和准确的\emph{augmented} -KKR格林函数形式主义，解决了KKR长期方程矩阵求逆[ $\mathcal{R}^3$过程与秩$N(l_{tr}+1)^2$ ]，并包括高阶$L$贡献通过线性代数[ $\mathcal{R}^2$过程与秩$N(l_{max}+1)^2$ ]。增广KKR产生适当规范化的波函数，数值上更便宜的基集收敛，和总电荷密度和电子计数，同意劳埃德公式。对于面心立方铜，体心立方铁和L $1_0$ CoPt，我们提出的形式主义和数值结果的准确性和收敛的总能量，费米能量，和磁矩与$L_{max}$为一个给定的$L_{tr}$。
英文摘要：
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number $L_{max}=(l,m)_{max}$, while scattering matrices, which determine spectral properties, are truncated at $L_{tr}=(l,m)_{tr}$ where phase shifts $δ_{l>l_{tr}}$ are negligible. Historically, $L_{max}$ is set equal to $L_{tr}$; however, a more proper procedure retains free-electron and single-site contributions for $L_{max}>L_{tr}$ with $δ_{l>l_{tr}}$ set to zero [Zhang and Butler, Phys. Rev. B {\bf 46}, 7433]. We present a numerically efficient and accurate \emph{augmented}-KKR Green's function formalism that solves the KKR secular equations by matrix inversion [$\mathcal{R}^3$ process with rank $N(l_{tr}+1)^2$] and includes higher-order $L$ contributions via linear algebra [$\mathcal{R}^2$ process with rank $N(l_{max}+1)^2$]. Augmented-KKR yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. For fcc Cu, bcc Fe and L$1_0$ CoPt, we present the formalism and numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus $L_{max}$ for a given $L_{tr}$.
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