  An efficient method of interpretation of the crystal field effect in
non-metallic f-electron systems, the {\it enhanced angular overlap model}
(EAOM), is presented. The method is established on the ground of perturbation
expansion of the effective Hamiltonian for localized electrons and first
principles calculations related to available experimental data. Series of
actinide compounds, $An$O$_2$, oxychalcogenides, $An$O$X$ and dichalcogenides
U$X_2$ where $X$ = S, Se, Te and $An$ = U, Np serve as a probe of effectiveness
of the proposed method. An idea is to enhance the usual angular overlap model
with {\it ab initio} calculations of those contributions to the crystal field
potential, which cannot be represented by the usual angular overlap model
(AOM). The enhancement leads to an improved fitting and makes the approach
intrinsically coherent. In addition, the {\it ab initio} calculations of the
main, AOM-consistent part of the crystal field potential allows one to fix the
material-specific relations for the EAOM parameters in the effective
Hamiltonian. In consequence, the electronic structure interpretation based on
EAOM can be extended to the systems of the lowest point symmetries or/and
deficient experimental data. Several examples illustrating the promising
capabilities of EAOM are given.
