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 scattering length of reference, which are the central numerical parameters to achieve a linear scaling method with MST. We also present some 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，广泛应用于晶体无序系统的电子结构计算。MST方法的关键特性是散射路径矩阵（SPM），该矩阵在局部解表示中表征格林函数。本文研究了在采用适当参考进行微扰条件下SPM的各种近似。具体而言，我们论证了SPM近似关于散射区域大小及参考散射长度的收敛性——这两个参数是实现MST线性标度方法的核心数值参数。我们还选取若干典型系统进行数值实验，以验证该理论的有效性。