  We present a density functional theory (DFT) calculation in the generalized
gradient approximation to study the possibility for the existence of
Jahn-Teller (JT) or pseudo Jahn-Teller (PJT) type local distortions in the
La-Ba-Cu-O superconducting system. We performed the calculation and
correspondingly group theory classification of the electronic ground state of
the CuO${_{6}}^{-10}$ elongated octahedra cluster, immersed in a background
simulating the superconductor. Part of the motivation to do this study is that
the origin of the apical deformation of the CuO${_{6}}^{-10}$ cluster is not
due to a pure JT effect, having therefore a non {\it a priori} condition to
remove the degeneracy of the electronic ground state of the parent regular
octahedron. We present a comparative analysis of the symmetry classified
electron spectrum with previously reported results using unrestricted
Hartree-Fock calculations (UHF). Both the DFT and UHF calculations produced a
non degenerate electronic ground state, not having therefore the necessary
condition for a pure JT effect. However, the appearance of a degenerate E$_{g}$
state near to the highest occupied molecular orbital in the DFT calculation,
suggests the possibility for a PJT effect responsible for a local distortion of
the oxidized CuO$_{6}^{-9}$ cluster.
