Convergence and reliability of the Rehr-Albers formalism in multiple-scattering calculations of photoelectron diffraction
Convergence and reliability of the Rehr-Albers formalism in multiple-scattering calculations of photoelectron diffraction
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DOI：
10.1103/physrevb.58.13121
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发表时间：
1998-11-15
影响因子：
3.7
通讯作者：
Fadley, CS
中科院分区：
文献类型：
--
作者：
Chen, Y;de Abajo, FJG;Fadley, CS
基于展开级数的Rehr-Albers （RA）可分离格林函数形式已经成功地加速了光电子衍射模拟的多重散射簇计算，特别是在其二阶版本中。本文通过与精确的基于聚类的形式进行比较，从计算速度、多次散射阶数上的收敛性、近似阶数上的收敛性和聚类大小上探讨了这种形式的性能。我们发现二阶RA近似[由（6x6）散射矩阵表征]对于许多情况都是足够的，特别是当发生光发射的初始状态为s或p型时。对于最一般和定量的应用，对于d个初始状态[三阶，即（10x10）矩阵]和f个初始状态[四阶，即（15x15）矩阵]，RA的高阶版本可能是必要的。然而，当电子波沿着多重散射路径进行时，所需的RA阶数会降低，这可以与选择性和自动切断弱贡献矩阵元素和路径一起利用，以产生至少一个数量级的计算机时间节省，而不会造成明显的精度损失。对于大多数需要5%衍射强度精度的问题来说，大约100个原子的簇大小应该足够了。在将具有可变几何的二阶理论与作为虚拟“实验”的精确理论进行比较时，可以看到对结构的卓越敏感性。因此，我们对Rehr-Albers形式的实现代表了一种精确模拟光电子衍射的通用、定量和有效的方法。[s0163 - 1829(98) 04943 - 1]。
The Rehr-Albers (RA) separable Green's-function formalism, which is based on an expansion series, has been successful in speeding up multiple-scattering cluster calculations for photoelectron diffraction simulations, particularly in its second-order version. The performance of this formalism is explored here in terms of computational speed, convergence over orders of multiple scattering, over orders of approximation, and over cluster size, by comparison with exact cluster-based formalisms. It is found that the second-order RA approximation [characterized by (6x6) scattering matrices] is adequate for many situations, particularly if the initial state from which photoemission occurs is of s or p type. For the most general and quantitative applications, higher-order versions of RA may become necessary for d initial states [third-order, i.e., (10x 10) matrices] and f initial states [fourth-order, i.e., (15x15) matrices]. However, the required RA order decreases as an electron wave proceeds along a multiple-scattering path, and this can be exploited, together with the selective and automated cutoff of weakly contributing matrix elements and paths, to yield computer time savings of at least an order of magnitude with no significant loss of accuracy. Cluster sizes of up to approximately 100 atoms should be sufficient for most problems that require about 5% accuracy in diffracted intensities. Excellent sensitivity to structure is seen in comparisons of second-order theory with variable geometry to exact theory as a fictitious "experiment." Our implementation of the Rehr-Albers formalism thus represents a versatile, quantitative, and efficient method for the accurate simulation of photoelectron diffraction. [S0163-1829(98)04943-1].