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.