采用基于变分优化正交化连带Laguerre 基函数的准确对角化方法计算了无支撑单层MoS2 中A 型激子的能量和波函数. 介电屏蔽效应破坏了SO(3)对称性导致激子能量以反常的轨道角动量顺序出现. 该方法利用连带Laguerre 多项式构造了既满足束缚态又满足连续态的正交基函数集， 并推导了哈密顿量矩阵元的解析表达式. 收敛速度不仅与基函数的数量有关， 而且与变分参数的大小有关. 在变分优化下， 收敛速度非常快， 表明了该方法的可靠性. 采用正交化连带Laguerre 基矢可大大减小基函数的数量和计算量. 我们计算的激子本征能量即使是在很少的基函数下也与文献中的结果非常吻合. 变分优化二维正交归一化连带Laguerre 基矢适用于二维材料中激子和原子物理的精确描述.

The exaction energies and wave functions in a freestanding monolayer MoS2 are calculated

by an ex- act diagonalization method based on a variationally optimized

orthogonalized associated Laguerre basis. The dielectric screening effect breaks the SO(3)

symmetry， which leads to the fact the exaction energies appear in an a-

nomalous energy ordering of the orbital angular momentum. The method uses associated

Laguerre polynomials to

construct orthogonal basis functions that satisfy both bound and continuum states

automatically and the analytical expressions for the matrix elements of the Hamiltonian are derived. The rate of convergence depends

not only on the number of basis functions but also on the variational parameter. In the case of

variational optimization， the conver- gences are surprisingly fast and show the reliability of

the method. Using the orthogonalized associated Laguerre ba-sis can reduce considerably the basis size and computational cost. Our calculated

eigenenergies with even a small number of basis functions are in excellent agreement with the

results available in the literature. The variationally op- timized orthogonalized associated

Laguerre basis is proven to be suitable for the accurate description of exaction in

two-dimensional materials and atomic physics.