The Transition State as a Symmetry Point in the Morphology of the Electron Density
Year: 2026
Type: preprint
Abstract: We show that the transition state is a structural feature of the electron density, corresponding to a symmetry point in its evolving morphology. This symmetry arises in the directional organization of charge within charge-transfer pathways linking reacting fragments and can be quantified using scale-invariant descriptors derived from the Hessian of the density at bond critical points. The difference in directionalities defines a natural morphological parameter, η , whose evolution tracks the redistribution of density along a reaction coordinate. Within a low-order expansion in , the energy is expressed in terms of a bias, h , and a stiffness, β , that together determine the stationary point of the system. In the symmetric limit ( h ≈ 0), this stationary point occurs at η = 0, corresponding to equal directional organization toward competing centers. When h ≠ 0, the stationary point shifts away from symmetry, reflecting a bias in the density’s reorganization. We demonstrate this behavior in a series of morphologically simple atom-transfer reactions, including oxygen transfer, hydrogen-atom transfer in heme systems, and proton transfer. In the neutral atom-transfer cases, the transition state coincides with the symmetry condition η = 0, while in proton transfer it shifts in accordance with the predicted bias. These results provide a structural interpretation of the transition state in terms of the morphology of the electron density and establish a low-dimensional framework for chemical reactivity in which electrostatic effects act through two distinct channels: variations in electrostatic potential primarily modulate β , while electric fields alter h , particularly in reactions involving charged intermediates.
Source: ChemRxiv
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166529708