Decay properties of spatial molecular orbitals

Using properties of the Fourier transform we prove that if a Hartree–Fock molecular spatial orbital is in L1(R3), then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary and short. Our result implies that occupied orbitals with positive eigenvalues will decay t...

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Main Author: Richard A. Zalik
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Results in Applied Mathematics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2590037425000044
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author Richard A. Zalik
author_facet Richard A. Zalik
author_sort Richard A. Zalik
collection DOAJ
description Using properties of the Fourier transform we prove that if a Hartree–Fock molecular spatial orbital is in L1(R3), then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary and short. Our result implies that occupied orbitals with positive eigenvalues will decay to zero provided they are in L1.
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issn 2590-0374
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publishDate 2025-02-01
publisher Elsevier
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series Results in Applied Mathematics
spelling doaj-art-d10ead2973ad4ab19f7a56724397b2c12025-08-20T02:56:51ZengElsevierResults in Applied Mathematics2590-03742025-02-012510054010.1016/j.rinam.2025.100540Decay properties of spatial molecular orbitalsRichard A. Zalik0Department of Mathematics and Statistics, Auburn University, Auburn, Al. 36849–5310, United States of AmericaUsing properties of the Fourier transform we prove that if a Hartree–Fock molecular spatial orbital is in L1(R3), then it decays to zero as its argument diverges to infinity. The proof is rigorous, elementary and short. Our result implies that occupied orbitals with positive eigenvalues will decay to zero provided they are in L1.http://www.sciencedirect.com/science/article/pii/S2590037425000044Laplace operatorFourier transformConvolutionOrbitalDivided difference
spellingShingle Richard A. Zalik
Decay properties of spatial molecular orbitals
Results in Applied Mathematics
Laplace operator
Fourier transform
Convolution
Orbital
Divided difference
title Decay properties of spatial molecular orbitals
title_full Decay properties of spatial molecular orbitals
title_fullStr Decay properties of spatial molecular orbitals
title_full_unstemmed Decay properties of spatial molecular orbitals
title_short Decay properties of spatial molecular orbitals
title_sort decay properties of spatial molecular orbitals
topic Laplace operator
Fourier transform
Convolution
Orbital
Divided difference
url http://www.sciencedirect.com/science/article/pii/S2590037425000044
work_keys_str_mv AT richardazalik decaypropertiesofspatialmolecularorbitals