Valley-Ridge inflection points

B3.5.7.3 BIFURCATION OF THE REACTION PATH AND VALLEY-RIDGE INFLECTION POINTS... 

The geometrical properties of the PES in the vicinity of a transition state mean that the steepest descent path down from the transition state (also generally calculated in mass-weighted coordinates, and called the intrinsic reaction coordinate or IRC) will usually lead only to a single reactant in one direction and a single product (or intermediate) in the other. However, a transition state can sometimes be shared by more than one reactant and/or product. One of these cases arises when the PES possesses a so-called valley-ridge inflection point (VRI). °... 

The general shape of the PES for this reaction is given in Figure 8.17. Note that the MEP proceeds from TS 63 to 62, and the MEP does not bifurcate. There is, however, a ridge that some trajectories may cross, allowing for trajectories to go from 63 to 64. This behavior is similar to that of a valley ridge inflection point, but there is no VRl on the MEP in this case. 

Sheppard, A.N., Acevedo, O. Multidimensional exploration of valley-ridge inflection points on potential energy surfaces. J. Am. Chem. Soc. 2009,131, 2530 40. 

If we set /c(x,y) = 0, we obtain a flank line starting in the valley-ridge-inflection point (VRI) at (0,0) where, per definition, the curvature of the contour line is zero. Its equation is... 

Hirsch, M. Quapp, W. Heidrich, D. The set of valley-ridge inflection points on the potential energy surface of water. Phys. Chem. Chem. Phys. 1999, 1, 5291-5299. 

Figure 1 A model potential energy surface illustrating minima, transition structures, second-order saddle points, a valley-ridge inflection point, and reaction paths (Reproduced from Ref, 2a, with permission from World Scientific Publishing)...

---