The set of valley–ridge inflection points on the potential energy surface of water

How does a reaction path branching take place? A classification of bifurcation events

“…There was a speculation on the meaning of VRI for high overtones using the example H 2 O [18]. However, it seems that it is to reject by the experimental assigns of high local modes of water.…”

Newton Trajectories in the Curvilinear Metric of Internal Coordinates

“…where m is the step number [9,10,25,29,32]. A m is the adjoint matrix of the Hessian and g m is the gradient at point x m .…”

“…It is an uncertainty of the RP definition, how a reaction path ascends to the SP. We use here the distinguished or driven coordinate method [7] in the modern form of RGF [8][9][10][11][12][13].…”

Comment on “Exploring the potential energy landscape of the Thomson problem via Newton homotopies” [J. Chem. Phys. 142, 194113 (2015)]

“…We note that there exists a long list of theoretical developments, 4-7,9-13,19-30 as well as of applications of NTs in Chemistry. [31][32][33][34][35][36][37][38] We can, on the other hand, start with the simplest definition of an NT that the gradient lies in a fixed 1-dimensional subspace 18 or that the gradient of the PES along the curve always points into a given direction:…”

“…Pieces of the manifold of VRI points were already often found on the PES of small molecules. A successful search is reported of VRI regions for the molecules H 2 O, 31 . 38 The approximation of asymmetric VRI points on the PES was already solved elsewhere.…”