  We calculate the effective trigonal crystal field Delta which splits the t2g
levels of effective models for NaxCoO2 as the local symmetry around a Co ion is
reduced from Oh to D3d. To this end we solve numerically a CoO6 cluster
containing a Co ion with all 3d states and their interactions included, and its
six nearest-neighbor O atoms, with the geometry of the system, in which the
CoO6 octahedron is compressed along a C3 axis. We obtain Delta near 130 meV,
with the sign that agrees with previous quantum chemistry calculations, but
disagrees with first-principles results in the local density approximation
(LDA). We find that Delta is very sensitive to a Coulomb parameter which
controls the Hund coupling and charge distribution among the d orbitals. The
origin of the discrepancy with LDA results is discussed.
