Economics-inspired molecular reactivity descriptors from atom-resolved reactivity inequality
5 affiliations
- 1Department of Chemistry, Faculty of Natural, Mathematical, and Engineering Sciences
- 2King’s College London
- 3Grupo de Modelización y Diseño Molecular, Departamento de Química Orgánica, Facultad de Ciencias
- 4Universidad de Granada
- 5Vrije Universiteit Brussel (VUB, Pleinlaan 2, Brussels, Belgium, 1050
Abstract
Reactivity descriptors in conceptual density functional theory (DFT) usually belong to one of two broad families. Global descriptors give one value per molecule, which is easy to compare between molecules but says nothing about which parts of the molecule are more reactive. Local descriptors show how reactivity varies within a molecule and point to its most reactive atoms, but their dimension changes from one molecule to the next, which makes them hard to compare. Mapping global reactivity onto atoms is well established; the reverse, compressing a local reactivity map into a few informative numbers, is not. Economics has long faced the equivalent problem of summarising how wealth is shared across a population. Here we borrow its solution, the Gini coefficient, and apply it to the atom-condensed dual descriptor. The positive and negative parts of the dual descriptor give two Gini reactivity descriptors, Gp and Gn, that measure how unevenly the response to nucleophilic and to electrophilic attack is spread across a molecule. Tested on three controlled series of substituted carbonyls, conjugated ketones and conjugated amines, Gp and Gn behave as chemically sensible measures. They separate inductive from conjugative perturbations, respond differently to electronwithdrawing and electron-donating groups, and trace a shift from localised to delocalised response as conjugation grows. The two descriptors carry distinct mechanistic information and are promising compact features for data-driven chemistry. More broadly, this work shows that tools developed to measure inequality in societies can quantify how reactivity is shared within a molecule, and that crossing disciplinary boundaries can open new ways of reading electronic structure.
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BibTeX
@misc{pai2026economicsinspired,
title = {{Economics-inspired molecular reactivity descriptors from atom-resolved reactivity inequality}},
author = {Surya Darshan Pai and Isaac Vidal-Daza and Frank De Proft and Francisco J. Martin-Martinez},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009455/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009455/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Economics-inspired molecular reactivity descriptors from atom-resolved reactivity inequality
AU - Surya Darshan Pai
AU - Isaac Vidal-Daza
AU - Frank De Proft
AU - Francisco J. Martin-Martinez
PY - 2026
DA - 2026/09/24
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009455/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009455/v1
AB - Reactivity descriptors in conceptual density functional theory (DFT) usually belong to one of two broad families. Global descriptors give one value per molecule, which is easy to compare between molecules but says nothing about which parts of the molecule are more reactive. Local descriptors show how reactivity varies within a molecule and point to its most reactive atoms, but their dimension changes from one molecule to the next, which makes them hard to compare. Mapping global reactivity onto atoms is well established; the reverse, compressing a local reactivity map into a few informative numbers, is not. Economics has long faced the equivalent problem of summarising how wealth is shared across a population. Here we borrow its solution, the Gini coefficient, and apply it to the atom-condensed dual descriptor. The positive and negative parts of the dual descriptor give two Gini reactivity descriptors, Gp and Gn, that measure how unevenly the response to nucleophilic and to electrophilic attack is spread across a molecule. Tested on three controlled series of substituted carbonyls, conjugated ketones and conjugated amines, Gp and Gn behave as chemically sensible measures. They separate inductive from conjugative perturbations, respond differently to electronwithdrawing and electron-donating groups, and trace a shift from localised to delocalised response as conjugation grows. The two descriptors carry distinct mechanistic information and are promising compact features for data-driven chemistry. More broadly, this work shows that tools developed to measure inequality in societies can quantify how reactivity is shared within a molecule, and that crossing disciplinary boundaries can open new ways of reading electronic structure.
ER -