  Several time domain fluorescence Stokes shift (TDFSS) experiments have
reported a slow power law decay in the hydration dynamics of a DNA molecule.
Such a power law has neither been observed in computer simulations nor in some
other TDFSS experiments. Here we observe that a slow decay may originate from
collective ion contribution because in experiments DNA is immersed in a buffer
solution, and also from groove bound water and lastly from DNA dynamics itself.
In this work we first express the solvation time correlation function in terms
of dynamic structure factors of the solution. We use mode coupling theory to
calculate analytically the time dependence of collective ionic contribution. A
power law decay in seen to originate from an interplay between long range
probe-ion direct correlation function and ion-ion dynamic structure factor.
Although the power law decay is reminiscent of Debye-Falkenhagen effect yet
solvation dynamics is dominated by ion atmosphere relaxation times at longer
length scales (small wave number) than in electrolyte friction. We further
discuss why this power law may not originate from water motions which have been
computed by molecular dynamics simulations. Lastly, we propose several
experiments to check the prediction of the present theoretical work.
