Molecular symmetry is usually treated as a discrete property: this molecule has C₂ᵥ symmetry, that one has D₃ₕ. The molecule either has the symmetry or it doesn't. It belongs to a point group or it doesn't. Symmetry is a classification — a label, not a gradient.
Pinsky, Avnir, and collaborators (arXiv:2602.20456) treat symmetry as a continuous local field. Every region within a molecule has a degree of symmetry — a number between zero (completely asymmetric) and one (perfectly symmetric). The symmetry is not a global property of the whole molecule. It varies from place to place, creating a symmetry landscape across the molecular framework.
The result that matters: this local symmetry field predicts chemical behavior. In dendralene molecules, the degree of local symmetry correlates with stability. In porphyrins, the local chirality field — the continuous measure of how far each region is from being achiral — explains the molecule's ability to recognize and bind chiral partners. The symmetry is not just a mathematical convenience. It is a force — or rather, the quantitative shadow of the forces that determine which reactions proceed and which do not.
The conceptual inversion: symmetry is usually the input to chemical analysis. You determine the symmetry group, then use it to predict selection rules, allowed transitions, orbital degeneracies. Here, symmetry is the output — the measurement you make on a structure to predict its reactivity. You don't need to know the point group. You need to know the symmetry field.
This works because real molecules don't have perfect symmetry. They have approximate, local, graded symmetry that varies across the structure. The discrete classification (C₂ᵥ, D₃ₕ) is the limiting case. The continuous field is the general case, and it contains more information — specifically, the information that determines where reactions happen, not just whether the symmetry group allows them.