  The bandgap constitutes a challenging problem in density functional theory
(DFT) methodologies. It is known that the energy gap values calculated by
common DFT approaches are underestimated. The bandgap was also found to be
related to the derivative discontinuity (DD) of the exchange-correlation
potential in the Kohn-Sham formulation of DFT. Several reports have shown that
DD appears as a step on the potential curve. The step structure is a mandatory
structure for aligning the KS energy levels in the ionization potentials in a
dissociated molecule in both fragments and is a function of electron
localisation. Reproducing the step in the DFT framework gives the charge
transfer process and the correct energy gap and describes the source of
dissociation. This step phenomenon has not yet been studied in the non-additive
kinetic potential $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$, a key quantity
used in embedding theories. While $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$
is known to be difficult to approximate, in this work, we explain how an
accurate energy gap can be produced from the analytically inverted
$v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$, even if we use the input densities
calculated by the local and semi-local functionals. We used the precisely
calculated $v^{\text{NAD}}[\rho_A,\rho_B](\textbf{r})$ reported in our previous
publication [Phys. Rev. A 106, 042812 (2022)] to produce the energy gap for
some model systems and report in this work the promising accuracy of our
results through the comparison with the results obtained from one of the most
accurate calculations, OEP theory with the KLI local approximation.
