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The distinction  between a transition state and a transition structure. Strictly speaking, a transition state is a thermodynamic concept, the species an ensemble of which are in a kind of equilibrium with the reactants in Eyring's1 transition- state theory. Since equilibrium constants are determined by free energy differences, the transition state, within the strict use of the term, is a free energy maximum along the reaction coordinate (in so far as a single species can be considered representative of the ensemble). This species is also often (but not always) also called an activated complex. A transition structure, in strict usage, is the saddle point on a theo- retically calculated  PES. Normally such a surface is drawn through a set of points each of which represents the enthalpy of a molecular species at a certain geometry; recall that free energy differs from enthalpy by temperature times entropy. The
transition structure is thus a saddle point on an enthalpy surface. However, the energy of each of the calculated points does not normally include the vibrational energy, and even at OK a molecule has such energy (ZPE). The usual calculated PES is thus a hypothetical, physically unrealistic surface in that it neglects vibrational energy, but it should qualitatively, and even semiquantitatively, resemble the vibrationally-corrected one since in considering relative enthalpies ZPEs at least roughly cancel. In accurate work ZPEs are calculated for stationary points and added to the "frozen-nuclei" energy of the species at the bottom of the reaction coordinate curve
in an attempt to give improved relative energies which represent enthalpy differences at OK (and thus, at this temperature where entropy is zero, free energy differences also). It is also possible to calculate enthalpy and entropy differences, and thus free energy differences, at, say, room temperature. Many chemists do not routinely distinguish between two terms, and in this book the commoner term, transition state, is used. Unless indicated otherwise, it will mean a calculated geometry, the saddle point on a hypothetical vibrational-energy-free PES. ----from
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