Large isotope effects have been observed in various kinds of hydrogen bonded ferro / antiferroelectrics. In clariflying their origin, themodynamic properties of the hydrogen bond are of essential importance. Two numerical methods are applied to analyze the model for isolated hydrogen bond at finite temperatures and the results of excited energy levels of proton or deuteron are examined. It is found that the second excited state is not far enough from the first excited state to be neglected discussing themodynamic properties of hydrogen especially in their ordered states.