  We report one algorithm for simulating oxygen $K$-edge RIXS for weakly
correlated systems, using maximally localized Wannier functions as the basis
set. The $N$-electron wavefunction is formulated using the single Slater
determinant, and the many-body effect is treated explicitly at the dipole
matrix element level. The simulated result of oxygen $K$-edge RIXS for solid
state Li$_2$CO$_3$ matches well with the experimental data. Besides being
efficient and reasonably accurate, this algorithm also shows potential to
extent to more complex RIXS problems.
