  Recently the oxygen-reconstructed tantalum surface Ta(001)-p(3$\times$3)-O
has experienced considerable attention due its use as a potential platform for
Majorana physics in adatom chains. Experimental studies using scanning
tunneling microscopy and spectroscopy found rich atomic and electronic
structures already for the clean Ta(001)-O surface, which we combine here with
$ab~initio$ methods. We discover two metastable superstructures at the root of
the different topographic patterns, discuss its emergence during annealing, and
identify the electronic properties. The latter is determined as the sole origin
for the contrast reversal seen at positive bias. The observed effects are
essentially connected to the two distinct oxygen states appearing on the
surface in different geometries. The second superstructure was found in
simulations by introducing oxygen vacancies, what was also observed in tantalum
pentoxide systems. Additionally we study the charge distribution on the
oxidized surface and underline its importance for the adsorption process of
polarizable atoms and molecules.
