In this work, we model the zero-bias conductance for the four different DNA strands that were used in conductance measurement experiment [A. K. Mahapatro, K. J. Jeong, G. U. Lee, and D. B. Janes, Nanotechnology 18, 195202 (2007)]. Our approach consists of three elements: (i) ab initio calculations of DNA, (ii) Greens function approach for transport calculations, and (iii) the use of two parameters to determine the decoherence rates. We first study the role of the backbone. We find that the backbone can alter the coherent transmission significantly at some energy points by interacting with the bases, though the overall shape of the transmission stays similar for the two cases. More importantly, we find that the coherent electrical conductance is tremendously smaller than what the experiments measure. We consider DNA strands under a variety of different experimental conditions and show that even in the most ideal cases, the calculated coherent conductance is much smaller than the experimental conductance. To understand the reasons for this, we carefully look at the effect of decoherence. By including decoherence, we show that our model can rationalize the measured conductance of the four strands, both qualitatively and quantitatively. We find that the effect of decoherence on G:C base pairs is crucial in getting agreement with the experiments. However, the decoherence on G:C base pairs alone does not explain the experimental conductance in strands containing a number of A:T base pairs. Including decoherence on A:T base pairs is also essential. By fitting the experimental trends and magnitudes in the conductance of the four different DNA molecules, we estimate for the first time that the deocherence rate is 6 meV for G:C and 1.5 meV for A:T base pairs.
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