Determinacy

A simple topology-based model for predicting the activation barriers of reactive processes at 0 K

“…Luckily, ELF topography accurately captures the complexities of this surface. For example, an exposure factor constitutes a suitable visual measure of the persistency 6,34–37 of a critical point (CP). Furthermore, this topological concept is an adequate metric for exploring the structural stability of CP 4,6,38–42 and, in general, the system molecular graph.…”

Revisiting the bonding evolution theory: a fresh perspective on the ammonia pyramidal inversion and bond dissociations in ethane and borazane

“…A CP is termed degenerate if the |Δ H | evaluated at this point yields a zero value. 44,46,47 CT is a robust mathematical program that succeeded in describing all distinct changes in the geometric shape of (generic) parametric families triggered by the creation/annihilation of CPs through seven unfoldings constrained to have four parameters at most. One-state-variable unfoldings are called cuspoids, and their common characteristic is to have only one null eigenvalue.…”

“…These unfoldings are parametric polynomials of degree equal to or greater than 3, which accurately approximate the ELF shape in the locality of a topographical bifurcation if some requirements are met. 44–46 Each function describes one of the seven types of degeneracy exhibited by ELF critical points (CPs). A CP is said to be degenerate if evaluating the determinant of the Hessian matrix yields 0; otherwise, it is called hyperbolic.…”

“…A CP is said to be degenerate if evaluating the determinant of the Hessian matrix yields 0; otherwise, it is called hyperbolic. 44,46,47 The collection of the hyperbolic (Morse-type) CPs and the gradient lines connecting them is called a topographic map or phase-space portrait. 48–53 Abrupt changes in such a space comprising both the type and number of CPs are frequently referred to as topological bifurcations.…”

Abstracts and Their Mysterious In-Betweens: Attuning to the Lacuna of Scholarly Communications

“…“The unexpectedness is because the conditions surrounding the event change slowly and continuously. Nevertheless, a sudden discontinuity—a radical jump—occurs, overthrowing the existing order” (Castrigiano & Hayes, 1993/2018, p. xii). When this happens, one form can give way to another in the midst of catastrophic change, and what emerges has the capacity to exceed the sum of its parts.…”