  Environmental two-level systems (TLS) have been identified as significant
decoherence sources in Josephson junction (JJ) based circuits. For such quantum
devices to be functional, the removal or control of the TLS is a necessity.
Understanding the microscopic origins of the 'strongly coupled' TLS type is one
current path of investigation to that end. The delocalized oxygen model
suggests the atomic position of an oxygen atom is spatially delocalized in the
oxide forming the JJ barrier. In this report we extend this model from its
previous 2+1D construction to a complete 3D description using a Wick-rotated
time-dependent Schrodinger equation to solve for time-independent solutions in
three dimensions. We compute experimentally observable parameters for phase
qubits and compare the results to the 2+1D framework. We devise a Voronoi
classification scheme to investigate oxygen atoms delocalizing within strained
and non-strained crystalline lattices, as well as realistic atomic positions a
JJ amorphous tunnel barrier constructed in previous density functional studies.
