The potential energy surface of H(13) proton in base cytosine of the DNA molecules is calculated at the Gaussian 98 MP2/6-311G(d,p) level. Two potential wells are found. One corresponds to the normal cytosine, while the other corresponds to its trans-imino tautomer. The estimated tunneling probability of the H(13) proton from one well to another well shows that the life time of the proton staying in one of these wells is about 600 yrs. It is too long to let tautomers of cytosine be in thermodynamical equilibrium in a room temperature gas phase experiment.