The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that characterizes the Green's function within a local solution representation. This paper studies various approximations of the SPM, under the condition that an appropriate reference is used for perturbation. In particular, we justify the convergence of the SPM approximations with respect to the size of scattering region and the length of scattering path, which are the central numerical parameters to achieve a linear-scaling MST method. We present numerical experiments on several typical systems to support the theory.

翻译：多重散射理论（MST）是一种格林函数方法，已广泛应用于晶体无序系统的电子结构计算。MST方法的核心特性是散射路径矩阵（SPM），该矩阵在局域解表示中刻画了格林函数的性质。本文在选用适当参考系进行微扰的条件下，系统研究了SPM的多种近似方法。特别地，我们论证了SPM近似关于散射区域尺寸和散射路径长度的收敛性——这两个参数正是实现线性标度MST方法的关键数值参数。通过对若干典型体系的数值实验，我们为理论分析提供了实证支持。