  The leading electronic interactions governing the local physics of the CE
phase of half-doped manganites are extracted from correlated ab initio
calculations performed on an embedded cluster. The electronic structure of the
low-energy states is dominated by double exchange configurations and
O-2$p_{\sigma}$ to Mn-3d charge transfer configurations. The model spectra of
both a purely magnetic non-symmetric Heisenberg Hamiltonian involving a
magnetic oxygen and two non-symmetric double exchange models are compared to
the \textit{ab initio} one. While a satisfactory agreement between the
Heisenberg spectrum and the calculated one is obtained, the best description is
provided by a double exchange model involving excited non-Hund atomic states.
This refined model not only perfectly reproduces the spectrum of the embedded
cluster in the crystal geometry, but also gives a full description of the local
double-well potential energy curve of the ground state (resulting from the
interaction of the charge localized electronic configurations) and the local
potential energy curves of all excited states ruled by the double exchange
mechanism.
