On the Definition of a Reaction Path RP

Most of the literature that has been accumulated over the years on this important problem has been collected in several excellent surveys.It is beyond the scope of this section to repeat all the references we focus our interest on a number of recent developments of this field. Further literature can be found in the following chapters. 

Let us first explain a number of terms which are important for the further considerations (for similar attempts see for instance Ref.13) The energy profile over such an RP defines a mountain path (relief path, Fig.l) which leads over a highest energy point, the saddle. The saddle point (SP) of primary chemical interest has only one direction of negative curvature in the energy profile (Figs. 1,2). Therefore, it is called a SP of index 1 on the PES (cf. the table in Sect. 2.3 in the literature one can also find the term SP of first order). 

Such a saddle point defines the so-called transition structure which may be used as the structure of the corresponding transition state when using the conventional transition state theory. In conventional TST, this point of the PES defines the atomic configurations of the transition state and is subject to a statistical treatment, in order to determine thermodynamic quantities. However, the coordinates of the transition state may, but need not, agree with this transition structure. An identification of the transition structure with the geometry of the transition state is mostly possible or at least a good initial approximation, but in certain cases (gas phase results) not sufficient (cf.Sect. 1.4). 

The term transition state must be reserved for denoting the energy states as well as the structure of the energy maximum along a free energy (enthalpy) path (SP on a free enthalpy surface) at the actual temperature. 

For the RP the term reaction coordinate (RC) is also frequently used. It originates from the very beginning of the transition state theory where it was used to characterize the motion over the saddle point. Today, the term RC instead of RP is mostly used when the RP is represented by a straight-line axis in the usual E vs RP diagrams. 

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