I am trying to study the shifts in the Fermi level of a graphene - ssDNA hydrid system, depending on the identity of the ssDNA. The structures are obtained from a classical MD simulation, and cannot be geometry optimized. I ran two distinct calculations: one at the $\Gamma$ point and other one at a Kpoint mesh of 10x10x1. From the PDoS plots, what I observe is that the Fermi of the system is dominated by the contributions from graphene (which is expected). However, I also find that the HOMO of the ssDNA molecule lies very close to the Fermi of the system. When I am trying to compare my results to this paper (Figure 3 to be exact), I see that they get an appreciable difference in the HOMO levels of the nucleobases. The interactions between the ssDNA and the graphene surface would be largely non-covalent interactions such as $\pi$-stacking. This leads to my question: How accurate are DFTB+ calculations for these systems?
The DNA-graphene interaction is only weak when there is no considerable charge transfer between them. Now you have many aryl radicals in your graphene, and aryl radicals are electron-deficient radicals. This means that the Fermi level of the system is probably low, and it is not very surprising if it is comparable to or even lower than the HOMO of the DNA (in the latter case you'll see considerable charge transfer between them).
The paper you cited didn't introduce defects in the graphene, so naturally their Fermi level is closer to the Fermi levels of typical conjugated organic molecules (remember that graphene is nothing but an infinitely large polycyclic aromatic hydrocarbon). As a result, the HOMO of DNA is significantly lower than the Fermi level in their system.
PS: I may have said this before, but I would like to reiterate that having so many aryl radical defects in graphene is extremely unlikely in realistic settings. The aryl radicals will recombine, react with water/oxygen/solvent, or otherwise restructure themselves long before you can experimentally put your ssDNA into the hole. It is a common mistake to assume that all defects are formed by simply removing or replacing a few atoms, while neglecting the (potentially huge and extremely rapid) structural rearrangement after you made the removal or replacement, not to mention that it may be experimentally impossible to carry out that removal or replacement in the first place. Moreover, even if some of the aryl radicals survive till you could put the ssDNA into the hole, the radicals will immediately undergo hydrogen abstraction and/or radical addition reactions with the ssDNA, so that the ssDNA will soon be not a DNA anymore.