Fractal Properties in Electronic Spectra of GA Sequences of Human DNA

In this work, we report the eigenenergies spectra for GA sequences present on human chromosome 7, obtained from an entirely atomistic Extended Huckel single-strand DNA model. For GA sequences ranging from 10 to 330 nucleotides (10,739 atoms) in steps of 10 nucleotides cumulatively, the density of states presented a beautiful and clear trend in the form of larger conductance in the region of [ \(-20\) $-20$ , \(-10\) $-10$ ] eV, like a digital signature, while the sequence length is increased. From a fractal analysis point of view, both level spacing and cumulative level spacing distribution of the energy spectra presented one kind of random Cantor set fractal behavior, including a devil’s staircase for their energy spectra. Besides this, a more accurate \(f(\alpha )\) $f(\alpha )$ analysis has confirmed that these spectra are multifractal.