An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis

Abstract

The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.

Toward a theory of mechanochemistry: Simple models from the very beginnings

“…Our main point, and interest, is the understanding of the direction of a given external force, which decides which reaction valley on the PES is used for an induced reaction. To establish the relevance of our former works we go back here to the early beginnings of the pulling of very small molecular models. The model ansatz of Equations and allows to theoretically treat the influence of an external force, f , on the PES of a molecule.…”

“…Jakobs and Sijbesma demonstrated that this principle also holds for coordination bonds like ruthenium(II)‐NHC. This fact can be related to the existence of optimal BBPs whose effects are enhanced by this type of complexes. Note that we did not discuss here how fast the force is applied, because we treat only static properties of the effective PES.…”

“…The kind of points is also discussed elsewhere . An algorithm to locate optimal BBPs has been recently proposed . Note that a bond will actually break before the BBP due to finite temperature effects or by the zero point energy of the corresponding bond.…”

“…However, the barrier “last” to overcome below the BBP will be elusive, see below sections 5 and 9. Conversely to the calculation of the BBP of a given PES, there are proposals to use pulling experiments to reconstruct a one‐dimensional section of the PES in the pulling direction . However, there are also mental reservations against the possibility of such an ansatz …”

“…Note that coupled degrees of freedom of the PES, but under a fixed force direction, are treated elsewhere …”