9.7.1 Overview

The concept of a reaction path is chemically intuitive (a pathway from reactants to products) yet somewhat theoretically ambiguous because most mathematical definitions depend upon the chosen coordinate system. Stationary points on a potential energy surface are independent of this choice, but the path connecting them is not, and there exist various mathematical definitions of a “reaction path”. Q-Chem uses the intrinsic reaction coordinate (IRC) definition, as originally defined by Fukui, ³⁸⁶ Fukui K.
J. Phys. Chem.
(1970), 74, pp. 4161. Link which has come to be a fairly standard choice in quantum chemistry. The IRC is essentially sequence of small, steepest-descent paths going downhill from the transition state.

The reaction path is most unlikely to be a straight line and so by taking a finite step length along the direction of the gradient you will leave the “true” reaction path. A series of small steepest descent steps will zig-zag along the actual reaction path (a behavior known as “stitching”). Ishida et al. ⁵⁷⁸ Ishida K., Morokuma K., Komornicki A.
J. Chem. Phys.
(1977), 66, pp. 215. Link developed a predictor-corrector algorithm, involving a second gradient calculation after the initial steepest-descent step, followed by a line search along the gradient bisector to get back on the path, and this algorithm was subsequently improved by Schmidt et al.. ¹¹³³ Schmidt M. W., Gordon M. S., Dupuis M.
J. Am. Chem. Soc.
(1985), 107, pp. 2585. Link This is the method that Q-Chem adopts. It cannot be used for the first downhill step from the transition state, since the gradient is zero, so instead a step is taken along the Hessian mode whose frequency is imaginary.

The reaction path can be defined and followed in $Z$-matrix coordinates, Cartesian coordinates or mass-weighted Cartesian coordinates. The latter represents the “true” IRC as defined by Fukui. ³⁸⁶ Fukui K.
J. Phys. Chem.
(1970), 74, pp. 4161. Link If the rationale for following the reaction path is simply to determine which local minima are connected by a given transition state, which, is arguably the major use of IRC algorithms, then the choice of coordinates is irrelevant. In order to use the IRC code, the transition state geometry and the exact Hessian must be available. These must be computed via two prior calculations, with JOBTYPE = TS (transition structure search) and JOBTYPE = FREQ (Hessian calculation), respectively. Job control variables and examples appear below.

An IRC calculation is invoked by setting JOBTYPE = RPATH in the $rem section, and additional $rem variables are described below. IRC calculations may benefit from the methods discussed in Section 9.3 for obtaining good initial guesses for transition-state structures. The final pathway (in both forward and backward directions) is printed at the end of the Q-Chem output file as a sequence of Cartesian-coordinate geometries representing steps along the pathway. The format for this output is a standard one that is readable, for example, by the Visual Molecular Dynamics (VMD) program.^{W. Humphrey, A. Dalke, and K. Schulten (1996), 15}