Mass-weighted Cartesian coordinates steepest descent reaction paths

The MEP is defined as the path of steepest descent in mass-weighted Cartesian coordinates. This is also called intrinsic reaction coordinate (IRC). In reality, we know that many other paths close to the IRC path would also lead to a reaction and the percentage of the time each path is taken could be described by the Boltzmann distribution. 

The actual path mapped out by the MEP on the PES is dependent on coordinate system. However, changes in coordinate system do not alter the nature of the stationary points on the PES (i.e. minima, TSs, etc.). One coordinate system, mass-weighted Cartesian coordinates (see Section 10.2.3), is especially significant for reaction dynamics, and the MEP in this coordinate system is known as the intrinsic reaction coordinate (IRC) [162]. In this section, we use the terms MEP, IRC, steepest descent path, and reaction path synonymously. 

The dynamics of a reaction complex is connected with the intrinsic reaction coordinate (IRC) or, better, intrinsic reaction path (IRC path), which is simply the steepest descent path expressed in mass-weighted Cartesian coordinates. The IRC path was first used by Eliason and Hirschfelder, and later investigated in great detail by Fukui and co-workers. ... 

By following the steepest descent path we change the coordinates of all the N atoms of the system. If the atoms were moving infinitely slowly the path would be mapped out by the classical equations of motion. However, the displacement of the atoms should not be mass dependent. This can be avoided by introducing mass-weighted coordinates in a similar manner to what is done in the normal mode treatment of vibrational motion. We therefore introduce the socalled intrinsic reaction path (IRP) [19]. The IRP is defined as the steepest descent path in mass-weighted coordinates. Thus we have the mass weighted cartesian position coordinates and notation, such that... 

The mass-weighted path of steepest descent in Cartesian coordinates has been termed the "intrinsic reaction coordinate" [13]. In the past, it was used by a number of scientists [14] to describe some kind of reaction dynamics. Since then, the path has been analyzed, particularly by Fukui et al. [13,15,16]. At present, it is well-accepted, and its calculation is, for instance, implemented in the GAUSSIAN program package [17], using a procedure established by Schlegel [18]. In the coordinate space, diis path... 

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