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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| Language: | English |
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Elsevier
2025-02-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000044 |
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| _version_ | 1850037442912976896 |
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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. |
| format | Article |
| id | doaj-art-d10ead2973ad4ab19f7a56724397b2c1 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| 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 |