We construct an isothermal-isobaric partition function of glass-forming polymeric liquids by separating the local minima of the potential energy hypersurface from the anharmonic vibrations about these packings. The partition function is evaluated by a maximum term method. A suitable approximation to the partition function below a temperature T2 is required since the maximum term approach is not valid in this range of temperatures. We obtained the following results : (a) The density of states including thermodynamic quantities such as entropy and heat capacity reveal an Ehrenfest second-order transition at T2; (b) T2 < T2,c where T2,c is the temperature of the transition when considering only configurational contributions; (c) if the density of states at the minimum energy is finite, then T2,c does not vanish; (d) the stability conditions [Eqs. (17)-(20)] necessary to derive (b); (e) the discontinuity of various thermo-dynamic quantities such as heat capacity, thermal expansion coefficient and compressibility at T2.