Reaction channels of the potential energy surface: application of Newton trajectories

The Journal of Chemical Physics

2015

Section: The Index Theoremmentioning

confidence: 97%

“…38 The approximation of asymmetric VRI points on the PES was already solved elsewhere. 29 The index theorem for NTs 22 is coupled with the manifold character of the VRIs for Newton trajectories. 5 The VRI manifold forms, together with the singular NTs, a partitioning of the configuration space.…”

Section: The Index Theoremmentioning

confidence: 99%

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

The Journal of Chemical Physics

2015

“…(It is an important property of NTs to connect stationary points with an index difference of 1, see Ref. ) The left curve of the NT 1,1 will lead to a coalescence of minimum and the SP y for a high enough pulling force at BBP 1,1 , shown below.…”

Section: Model Pes For Pulling a Linear Abc Moleculementioning

confidence: 99%

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

Quapp

Int J of Quantum Chemistry

Ribas‐Ariño

2018

Self Cite

A core idea in the context of mechanochemistry is that applying an external tensile force along a reaction coordinate should enhance the chemical reaction of interest. Here, we analyze perturbed generic molecular structures: schematic models of triatomics, ABC, and tetraatomics, AABB. They are used to demonstrate that pulling does usually not use the “reaction coordinate,” but opens new reaction pathways. Within development of these models we use the concept of Newton trajectories for a theory of mechanochemistry. However, we find cases where the theory of Newton trajectories is not applicable. For all cases, we define the curve of force‐displaced stationary points, and we discuss the importance of barrier breakdown points and valley‐ridge inflection points. The examples use Morse potentials for bonds and simple angle functions and are demonstrated by assumed real values for the potential parameters. On the basis of the systematic study of some generic models we explain a set of already observed experimental mechanochemical phenomena in specific molecular systems and we apply the results to the strength of chemical bonds.

“…Additionally, the scheme is a nice example of the index theorem for NTs. [81] ii. The upper edge is the disrot (disrotatory) subspace of the dihedrals dih35H 7 C 3 C 2 H 5 ; dih45H 8 C 4 C 1 H 6 ; dih55H 9 C 3 C 2 H 5 and dih65H 10 C 4 C 1 H 6 , and iii.…”

Section: Full Papermentioning

confidence: 99%

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

Quapp

2015

Int. J. Quantum Chem.

Self Cite

The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP 1 ) along the conrotatory behavior of the end groups, as well as a "forbidden" pathway over a saddle point of index two (SP 2 ) along the disrotatory behavior of the end CH 2 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 SP 2 (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 SP 2 is somewhat higher than the barrier of the conrotatory SP 1 , however, pathways across the slope to the SP 2 open additional reaction valleys. IntroductionMathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways.[1] With the advantage of the computer age, the subject of modelization has hugely grown in importance. In particular, over the last decades significant advances in our understanding of the world of chemistry have culminated in the development of a very large set of concepts. Some of these concepts are the potential energy surface (PES) [2][3][4] and the chemical reaction path (RP) [5] being the basic concepts for the theories of chemical dynamics and chemical transformations. The PES is a continuous function of the coordinates of the nuclei over an IR N , thus it is an N-dimensional hypersurface. It should have continuous derivatives of at least second order for our treatments. If Cartesian coordinates are used, then N53 n, however, we may also use N53 n26 nonredundant, internal coordinates for an n-atomic molecule. The PES can be seen as formally divided in catchments associated with local minima.[2] For such a picture, one has in mind steepest descent (SD) curves. The first order saddle points or transition states (TSs) are located at the deepest points of the boundary of the basins. TSs and minima correspond to stationary points of the PES. Two adjacent minima of the PES can be connected through a TS via a continuous curve in the N-dimensional coordinate space, describing the coordinates of the nuclei. The curve characterizes a RP. The concept of the RP has found a widespread use in descriptions of reaction mechanisms, which are based on geometrical rearrangements of the atoms comprising a given chemical system. [6] Mor...