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July 26, 2026SIAM Journal on Applied Mathematics

The Geometry of the Hückel/Tight-Binding Method for Modeling Molecular Systems

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Authors

MBMarisol Bermúdez‐MontañaEEErnesto Estrada

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Overview

Geometric reformulation of Hückel method links molecular properties to algebraic graph theory, suggesting advances in modeling techniques.

Key Points

  • This research aims to integrate geometric reformulation into the Hückel and tight-binding methods for enhanced molecular modeling.
  • Developed a geometric framework using algebraic graph theory and statistical mechanics.
  • Extended classical concepts of charge density and bond order to include bond orbital energies.
  • Constructed geometric descriptors like internodal distances and node angles to analyze molecular properties.
  • New geometric descriptors correlate with chemical properties such as bond lengths and reactivity.
  • Utilized analytical results from linear and cyclic polyenes and polycyclic aromatic hydrocarbons to support findings.
  • Suggested pathways to integrate HMO/TB methods with ab initio methods and machine learning techniques.

Cite This Study

Bermúdez‐Montaña et al. (2026) studied this question.

synapsesocial.com/papers/6a65a84ed3aea3239cd78b9fhttps://doi.org/10.1137/25m1791883
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Also Consider

Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Simplified LCAO Method for the Periodic Potential Problem1954 · 5,216 citations
  2. 2A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology2000 · 573 citations
  3. 3Electronic coarse graining: Predictive atomistic modeling of condensed matter2019 · 20 citations