  The potential energy surface of the H13 proton in base cytosine of the DNA
molecules is calculated {\it ab initio} at the Gaussian98 MP2/6-311G(d,p)
level. Two potential wells are found. One corresponds to the normal cytosine,
while the other corresponds to its imino tautomer. The bindings of the proton
in these wells are stable enough against the thermo-disturbance. The motions of
the proton in these wells are oscillations around the nearest nitrogen atom
like the pendula, and may move far away from the nitrogen atom to form the
hydrogen bond with other bases. The estimated tunneling probability of the H13
proton from one well to another well shows that the life time of the proton
staying in one of these wells is about 6$\times10^2$ yr. It is too long to let
tautomers of cytosine be in thermodynamical equilibrium in a room temperature
gas phase experiment. The biological significance of these result is discussed.
