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This paper develops a “magnetic Hückel” extension of the Hückel molecular orbital method by incorporating an external magnetic field via the Peierls substitution, yielding a complex-weighted hopping Hamiltonian on a hydrogen-depleted molecular graph. Under standard Hückel assumptions, the resulting operator is shown to coincide with the Hermitian adjacency matrix of the graph, providing a physical interpretation that allows flux-dependent observables to be computed from its spectrum. The authors apply the framework to polycyclic aromatic hydrocarbons and report that molecular topology strongly governs magnetic response, with linearly fused systems showing regular oscillations in orbital magnetization and other architectures showing more complex spectral rearrangements. A key limitation they note is that the derivations rely on standard Hückel assumptions for the π-electron system. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
We introduce a magnetic extension of the Hückel molecular orbital (HMO) method in which the effect of an external magnetic field is incorporated through the Peierls substitution. In this formulation, the π -electron Hamiltonian of a conjugated molecule becomes a complex-weighted hopping operator defined on the hydrogen-depleted molecular graph. Under the standard Hückel assumptions, this operator coincides with the Hermitian adjacency matrix of the graph, providing a physical realization of Hermitian adjacency operators within molecular electronic structure theory. The magnetic-HMO framework enables the calculation of flux-dependent electronic observables such as bond currents, ring currents, orbital magnetization, and orbital susceptibility directly from the spectrum of the magnetic adjacency matrix. Applications to polycyclic aromatic hydrocarbons show that the magnetic response of π -electron systems is strongly controlled by molecular topology. In particular, linearly fused systems exhibit regular flux-dependent oscillations in the orbital magnetization, whereas nonlinear and extended molecules display more complex spectral rearrangements associated with multiple conjugation pathways. MSC (2020): 05C50; 92E10; 81Q10; 05C90.
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MAGNETIC HÜCKEL THEORY: FRAMEWORK FOR THE HERMITIAN ADJACENCY MATRIX OF GRAPHS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 16 February 2026 V1 Latest version Share on MAGNETIC HÜCKEL THEORY: FRAMEWORK FOR THE HERMITIAN ADJACENCY MATRIX OF GRAPHS Author : Ernesto Estrada [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177122000.00740543/v1 143 views 91 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We introduce a magnetic extension of the Hückel molecular orbital (HMO) method in which the effect of an external magnetic field is incorporated through the Peierls substitution. In this formulation, the π -electron Hamiltonian of a conjugated molecule becomes a complex-weighted hopping operator defined on the hydrogen-depleted molecular graph. Under the standard Hückel assumptions, this operator coincides with the Hermitian adjacency matrix of the graph, providing a physical realization of Hermitian adjacency operators within molecular electronic structure theory. The magnetic-HMO framework enables the calculation of flux-dependent electronic observables such as bond currents, ring currents, orbital magnetization, and orbital susceptibility directly from the spectrum of the magnetic adjacency matrix. Applications to polycyclic aromatic hydrocarbons show that the magnetic response of π -electron systems is strongly controlled by molecular topology. In particular, linearly fused systems exhibit regular flux-dependent oscillations in the orbital magnetization, whereas nonlinear and extended molecules display more complex spectral rearrangements associated with multiple conjugation pathways. MSC (2020): 05C50; 92E10; 81Q10; 05C90. Supplementary Material File (manuscript_magnetic_tight-binding_mmas.pdf) Download 3.21 MB Information & Authors Information Version history V1 Version 1 16 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords flux-dependent hamiltonians hermitian graph operators magnetic adjacency matrix peierls substitution Authors Affiliations Ernesto Estrada [email protected] Instituto de Fisica Interdisciplinar y Sistemas Complejos View all articles by this author Metrics & Citations Metrics Article Usage 143 views 91 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Ernesto Estrada. MAGNETIC HÜCKEL THEORY: FRAMEWORK FOR THE HERMITIAN ADJACENCY MATRIX OF GRAPHS. Authorea . 16 February 2026. DOI: https://doi.org/10.22541/au.177122000.00740543/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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