Dynamics of an A-DNA homopolymer crystal with sodium ions: A Green-function approach

We apply lattice dynamics to calculate the vibrational modes of a perfect A-DNA homopolymer crystal with sodium ions. A Green-function method is used to reduce the dimension of the matrix to be diagonalized. We concentrate on the biologically significant crystal modes with frequencies less than 100 wave numbers. 94% of the crystal modes were likely to be located in this frequency range. Characteristics of the crystal modes are analyzed. We find that the interhelical modes dominate in the frequency range 25–30 ${\mathrm{cm}}^{\mathrm{-}1}$ and the intrahelical modes dominate for frequencies greater than 80 ${\mathrm{cm}}^{\mathrm{-}1}$. The infrared absorption peaks at 35, 50, and 83 ${\mathrm{cm}}^{\mathrm{-}1}$ in our model. The former two bands are not counterion dependent and the latter one is. Our Raman scattering spectrum peaks around 30 ${\mathrm{cm}}^{\mathrm{-}1}$ and it is strongly counterion dependent. The counterion-dependency trend of this band is the same as that of the experimental 25-${\mathrm{cm}}^{\mathrm{-}1}$ feature, extrapolated to 0 relative humidity, observed in both DNA and RNA crystals. The characteristics of the experimental Raman scattering features at 25 and 35 ${\mathrm{cm}}^{\mathrm{-}1}$ are consistent with our results.