Visualization of the Intrinsic Reaction Coordinate and Global Reaction Route Map by Classical Multidimensional Scaling

Abstract

A classical multidimensional scaling (CMDS) method is employed to visualize an intrinsic reaction coordinate (IRC) and a global reaction route map consisting of the equilibrium minima and transition state structures connected by the IRC network. As demonstrations, the method was applied to the IRCs of the intramolecular proton transfer in malonaldehyde and the S2 reaction of OH + CHF → CHOH + F, which are both well described by two principal coordinates. Next, the method was applied to the global reaction route map of the Au cluster; the resulting map shows appropriate positions of five minima and 14 transition states in a reduced 2- or 3-dimensional coordinate space successfully.

Visualization of the Dynamics Effect: Projection of on-the-Fly Trajectories to the Subspace Spanned by the Static Reaction Path Network

“…2, positions of reactant (R), transition state (TS), highly-curvature points (A, B), and product (P) are also shown where the region around B shows a high curvature but the region around A shows a calm curvature because of a reduction of the dimension. As discussed in our previous study, 18 PCo1 correlates with an O-C-F bond angle (related to Froaming) while PCo2 correlates with a C-F interatomic distance (related to C-F dissociation). Following our previously proposed method, 12 we calculated distance functions for all the points along the trajectories from the reference structures, R, TS, A, B, and P, and plotted those as a function of time.…”

“…In order to discuss in more detail which modes are excited through the curvature of IRC, it is useful to project the reaction path curvature vector to the vibrational modes orthogonal to IRC, 3 or converting it to an internal coordinate representation in a scheme of unified reaction valley approach (URVA). In the same way as our previous study, 18 the CMDS method was employed to visualize the IRC path for OH -+ CH3F → [CH3OH…F]in a reduced dimension. In the present computations, 101 geometries along the IRC were picked up, and the distance matrix D was generated for these reference geometries with the ij-th element dij defined in Eq.…”

Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices

“…5-7) for 500 steps of 1 fs and propagated in the product direction. As was observed in most of the trajectories calculated by Tsutsumi et al, 42 aer dissociating, the uoride ion did not orbit the resultant methanol and hydrogen bond with the hydroxide group, but rather dissociated completely and did not re-associate for the duration of the trajectory (500 fs). As can be seen in Fig.…”

“…Only 10% of MD trajectories conducted by Tsutsumi et al showed the uoride ion hydrogen bonding with the resultant methanol, while the other 90% had the uoride dissociating from the system completely. 42 In this system, with squared interatomic distances as input to PCA, PC1 accounted for 78.7% of the variance, PC2 for 14.5%, and PC3 for 4.9% (Fig. 6c, below).…”

“…The rst two, "malonaldehyde" and "S N 2", are prototypical test systems that have been previously used by Tsutsumi et al to illustrate their dimensionality reduction approach. 41,42 The third is a simple torsional rotation of N 2 O-appended acrylonitrile. The last example is the opening of substituted cyclopropylidene to generate chiral allenes.…”