  The zero point kinetic energy of protons in water is large on the scale of
chemical interaction energies(29 Kj/mol in bulk room temperature water). Its
value depends upon the structure of the hydrogen bond network, and can change
as the network is confined or as water interacts with surfaces. These changes
have been observed to be large on a chemical scale for water confined in carbon
nanotubes and in the pores of xerogel, and may play a fundamental, and
neglected, role in biological processes involving confined water. We measure
the average momentum distribution of the protons in salmon Na-DNA using Deep
Inelastic Neutron Scattering, for a weakly hydrated (6w/bp) and a dehydrated
fiber sample. This permits the determination of the change in total kinetic
energy of the system per water molecule removed from the DNA and placed in the
bulk liquid. This energy is equal, within errors, to the measured enthalpy for
the same process, demonstrating that changes in the zero point motion of the
protons, arising from changes in structure as water molecules are incorporated
in the DNA, are a significant factor in the energetics of the transition from
the A to B phase with hydration, in this case, providing the entire binding
energy of the water molecules to the DNA. The shape of the momentum
distribution in the dehydrated phase is consistent with coherent delocalization
of some of the protons in a double well potential, with a separation of the
wells of .2 Angstroms.
