  We present a new approach to computing multiplets for core spectroscopies,
whereby the crystal field is constructed explicitly from the positions and
charges of surrounding atoms. The simplicity of the input allows the
consideration of crystal fields of any symmetry, and in particular facilitates
the study of spectroscopic effects arising from low symmetry environments. The
interplay between polarization directions and crystal field can also be
conveniently investigated. The determination of the multiplets proceeds from a
Dirac density functional atomic calculation, followed by the exact
diagonalization of the Coulomb, spin-orbit and crystal field interactions for
the electrons in the open shells. The eigenstates are then used to simulate
X-ray Absorption Spectroscopy and Resonant Inelastic X-ray Scattering spectra.
In examples ranging from high symmetry down to low symmetry environment,
comparisons with experiments are done with unadjusted model parameters as well
as with semi-empirically optimized ones. Furthermore, predictions for the RIXS
of low-temperature MnO and for Dy in a molecular complex are proposed.
