The role of depth and flatness of a potential energy surface in chemical reaction dynamics (Q2220892)

The study of some qualitative properties of chemical reactions is here carried out via Hamiltonian bifurcation theory, in the cases of one and two degrees of freedom. The focus is on the geometry of the potential energy surface which describes how the potential energy depends on the coordinates. The two quantities used for mirroring the geometry of the ``potential energy landscape'' are depth and flatness. The former is the difference in potential energy between the saddle and the evolving center point at the bottom of the well, the latter is given by the average of the gradient norm of the potential energy. From the chemical viewpoint, depth and flatness are expected to heavily influence the reaction behavior, and, to investigate this, the effect on four particular quantities is calculated. The first one of these is the ratio of the bottleneck width and the well width. In the case of one degree of freedom, e.g., with phase space coordinates \(x\) and \(p_x\), a given energy (i.e., a single value of the Hamiltonian) singles out a particular orbit which is symmetric w.r.t. the \(x\)-axis. It shows a ``bottleneck'' where \(\vert p_x \vert\) has a local minimum. The bottleneck width then is the difference between the two values of \(p_x\) at that minimum. The well width is the difference between the two values of \(p_x\), where \(\vert p_x \vert\) has a local maximum. The second quantity calculated is a certain reaction probability. The third one, the gap time, refers to crossing times w.r.t. the so-called dividing surface. The fourth and final one is the directional flux through the dividing surface in the case of two degrees of freedom.