The stability against fragmentation and possible relaxation of the lowest e
xcited states of the Na5F4 cluster (representative of cubic non stoechiomet
ric clusters with an excess sodium atom, also called sodium-tail) is invest
igated by means of one-electron pseudopotential calculations with particula
r reference to photoabsorption processes from the ground state. Whereas the
equilibrium configuration of the ground state has C-3v symmetry, the doubl
y degenerate 1(2)E excited state is affected by a conical intersection and
a Jahn-Teller effect associated with the rotation of the sodium tail around
the C-3-axis. This yields a "Mexican hat" topology for the lowest sheet wi
th three equivalent C-s minima. Alternatively the 2(2)A(1) State has a mini
mum retaining the C-3v symmetry. The dissociation paths of the cluster alon
g the C-3-axis into respectively Na4F4 + Na and Na4F3 + NaF are also invest
igated. Among the former paths, the excited states are found adiabatically
stable with respect to the products. However in the Al symmetry, fragmentat
ion into NaF exhibits an interesting avoided crossing between configuration
s correlated respectively with Na4F3+ + NaF- and Na4F3 + NaF. Such interact
ion, similar to the well-known charge exchange processes in elementary mole
cules might induce non adiabatic predissociation of the 22A1 state. This me
chanism is invoked to explain the differences between R2PI and depletion sp
ectra, correlated with the dissociation or relaxation of the excited states
.