Π-electrons in a Single Strand of Dna: a Phenomenological Approach

We revisit the problem of the electronic properties of a single strand of DNA, formulating the Hückel approximation for π-electrons in both the sugar-phosphate backbone chain and the π-stacking of nitrogenous bases in a single strand of DNA where the nitrogenous bases are adenine (A), guanine (G), cytosine (C) and thymine (T), respectively. We calculate the electronic band structure of π-electrons: (i) in the single nitrogenous base molecules such as A, G, C and T, (ii) in the single sugar-phosphate molecule, (iii) in the single nucleotide systems such as A, G, C, T with the single sugar-phosphate group, and (iv) in the system of a single strand of DNA with an infinite repetition of a nucleotide such as A, G, C and T, respectively. We find the following: In the case of (i), there is an energy gap between the energy levels for the HOMO and LUMO in the nitrogenous base. This guarantees the semiconducting character of the bases as a mother material. In the case of (ii), there are the HOMO localized at the oxygen site with a double bond and the LUMO localized around the phosphorus atom, which have a quite large energy gap. In the case of (iii), the energy levels for the HOMO and LUMO of the nitrogenous base remain almost the same as those of the nucleotide, while those of the sugar-phosphate group remain the same as well. The HOMO of the sugar-phosphate group exists right below the HOMO of the nitrogenous base. Therefore, comparing the energy levels for the HOMOs of the nitrogenous base group with those of the sugar-phosphate group, the nitrogenous base group behaves as a donor while the sugar-phosphate group behaves as an acceptor. In the case of (iv), there are energy bands and band gaps for the extended states in the nitrogenous base group and the sugar-phosphate group as well as the discrete levels for the localized states at the phosphate site in the spectrum. There is a transition from semiconductor to semimetal as the π-electron hopping between the nitrogenous bases of nucleotide is increased. The details of the above will be discussed in the present paper. Thus, we show the powerfulness of the Hückel theory in the study of DNA as well, although this theory is, at the first glance, oversimplified and purely phenomenological.