Some Mathematical Reasoning on the Artificial Force Induced Reaction Method

There are works of the Maeda–Morokuma group, which propose the artificial force induced reaction (AFIR) method (Maeda et al., J. Comput. Chem. 2014, 35, 166 and 2018, 39, 233). We study this important method from a theoretical point of view. The understanding of the proposers does not use the barrier breakdown point of the AFIR parameter, which usually is half of the reaction path between the minimum and the transition state which is searched for. Based on a comparison with the theory of Newton trajectories, we could better understand the method. It allows us to follow along some reaction pathways from minimum to saddle point, or vice versa. We discuss some well-known two-dimensional test surfaces where we calculate full AFIR pathways. If one has special AFIR curves at hand, one can also study the behavior of the ansatz. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc

Newton Trajectories for the tilted Frenkel‐Kontorova model

Newton trajectories are used for the Frenkel-Kontorova model of a finite chain with free-end bound- ary conditions. We optimise stationary structures, as well as barrier breakdown points for a critical tilting force were depinning of the chain happens. These special points can be obtained straight for- wardly by the tool of Newton trajectories. We explain the theory and add examples for a finite-length chain of a fixed number of 2, 3, 4, 5 and 23 particles

Comment on "reaction coordinates and pathways of mechanochemical transformations"

The adiabatic potential energy surface (PES) is a basic concept of many theoretical chemistry models. Over the past several years, the phenomena of the action of a mechanical stress over a molecular system have motivated experimental and theoretical research. In a recent article, Avdoshenko and Makarov1 describe how the concepts of an effective PES and of a reaction path (RP), or a reaction coordinate, can be used for mechanochemistry

Mechanochemistry on the müller-brown surface

Chemical processes which suffer the application of mechanical force are theoretically described by effective potential energy surface (PES). We worked out (W. Quapp, J. M. Bofill, Theor. Chem. Acc. 2016, 135, 113) that the changes due to the force for the minimums and for the saddle points can be described by Newton trajectories (NT) of the original PES. If the force is so high that the saddle point disappears into a shoulder then the mechanochemical action is fulfilled: the pulling force breaks down the reaction barrier. The point is named barrier breakdown point. Different families of NTs form corridors on the original PES which describe qualitative different actions of the force. The border regions of such corridors are governed by the valley-ridge inflection points (VRI) of the surface. Here, we discuss all this on the basis of the well-known M¿uller-Brown surface, and we describe a new kind of NT-corridor

A model for a driven Frenkel-Kontorova chain

We study a Frenkel{Kontorova (FK) model of a nite chain with free-end boundary conditions. The model has two competing potentials. Newton trajectories are an ideal tool to understand the circumstances under a driving of an FK chain by external forces. To reach the insights we calculate some stationary structures for a chain with 23 particles. We search the lowest energy saddle points for a complete minimum energy path of the chain for a movement over the full period of the on-site potential, a sliding. If an additional tilting is set, then one is interested in barrier breakdown points (BBPs) on the potential energy surface for a critical tilting force named the static frictional force. In symmetric cases, such BBPs are often valley-ridge in ection points of the potential energy surface. We explain the theory and demonstrate it with an example. We propose a model for a DC drive, as well as an AC drive, of the chain using special directional vectors of the external force

A generalized Frenkel-Kontorova model for a propagating austenite-martensite phase boundary: revisited numerically

We explain the propagating austenite-martensite phase boundary by a Frenkel-Kontorova model for a chain of meshes along a ledge of the phase transitions. We demonstrate such steps for example chains of 16 and 47 meshes. We can represent a Langevin solution which describes possible cases of a consecutive excitation of a higher phase under a low external force

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP1) along the conrotatory behavior of the end groups, as well as a 'forbidden' pathway over a saddle point of index two (SP2) along the disrotatory behavior of the end CH2 groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis-butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley-ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of 'attraction' of the different SPs. We calculate the connections of the SP2 (in its different symmetry versions) with different SPs of index one of the PES by different 'reaction pathways.' We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP2 is somewhat higher than the barrier of the conrotatory SP1, however, pathways across the slope to the SP2 open additional reaction valleys

Level sets as progressing waves: an example for wake-free waves in every dimension

The potential energy surface of a molecule can be decomposed into equipotential hypersurfaces of the level sets. It is a foliation. The main result is that the contours are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The energy seen as an additional coordinate plays the central role in this treatment. A solution of the wave equation can be a sharp front in the form of a delta distribution. We discuss a general Huygens' principle: there is no wake of the wave solution in every dimension