Narrow Results

Reaction paths are studied with the help of diabatic potential-energy surfaces coupled in a generic external field. We show that all putative geometrical and topological features of two-dimensional (2D) potential-energy surfaces for an isomerization can be generated with a model consisting of strictly diabatic harmonic 2D wells coupled in a static (yet uniform) external field. For a large class of three-state models, we provide a phase diagram of possible topologies in the relevant parameter space for three-state models. By following the shift in diabatic electronic amplitudes (denoted by {|c_k|²}) in coherent quantum states produced in the field, we assess whether the models within each phase can produce reaction paths visiting regions of configurational space that are structurally similar to the diabatic transition state.

Persistent path homology represents an advanced mathematical approach explicitly tailored for directed systems. With its remarkable ability to characterize unbalanced or asymmetrical relationships within data, this method demonstrates great promise in qualitative analysis of the intrinsic topological features present in materials and molecules. In this work, we introduce persistent path homology at the first time for carborane analysis. Intrinsic path topological features are used to predict the stability of closo-carboranes. We qualitatively explain the connection between path topological features and properties on o-C₂B${}_{10}$H${}_{12}$, m-C₂B${}_{10}$H${}_{12}$ and p-C₂B${}_{10}$H${}_{12}$. The correlation coefficients between linear predictions based on persistent path homology and thermodynamic stability are higher than 0.95, and that for chemical stability are about 0.85. While the correlation coefficients based on nonlinear models are increased to 0.99 and 0.95, respectively. These results indicate that persistent path homology shows excellent capabilities in structural and stability analysis of multi-element cluster physics.