Chirp-wave expansion of the electron wavefunctions in atoms
The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp c...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2014
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8760
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8760
- Palabra clave:
- Chirp basis set
Chirp expansion of wavefunctions
Chirp series
Fractional Fourier transform
Local gauge transformation
Basis sets
Chirp series
Electron wavefunctions
Fractional Fourier series
Fractional Fourier transforms
Gauge transformation
Infinite numbers
Natural oscillation
Atoms
Fourier series
Electrons
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Chirp-wave expansion of the electron wavefunctions in atoms |
| title |
Chirp-wave expansion of the electron wavefunctions in atoms |
| spellingShingle |
Chirp-wave expansion of the electron wavefunctions in atoms Chirp basis set Chirp expansion of wavefunctions Chirp series Fractional Fourier transform Local gauge transformation Basis sets Chirp series Electron wavefunctions Fractional Fourier series Fractional Fourier transforms Gauge transformation Infinite numbers Natural oscillation Atoms Fourier series Electrons |
| title_short |
Chirp-wave expansion of the electron wavefunctions in atoms |
| title_full |
Chirp-wave expansion of the electron wavefunctions in atoms |
| title_fullStr |
Chirp-wave expansion of the electron wavefunctions in atoms |
| title_full_unstemmed |
Chirp-wave expansion of the electron wavefunctions in atoms |
| title_sort |
Chirp-wave expansion of the electron wavefunctions in atoms |
| dc.subject.keywords.none.fl_str_mv |
Chirp basis set Chirp expansion of wavefunctions Chirp series Fractional Fourier transform Local gauge transformation Basis sets Chirp series Electron wavefunctions Fractional Fourier series Fractional Fourier transforms Gauge transformation Infinite numbers Natural oscillation Atoms Fourier series Electrons |
| topic |
Chirp basis set Chirp expansion of wavefunctions Chirp series Fractional Fourier transform Local gauge transformation Basis sets Chirp series Electron wavefunctions Fractional Fourier series Fractional Fourier transforms Gauge transformation Infinite numbers Natural oscillation Atoms Fourier series Electrons |
| description |
The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves. © 2013 Elsevier B.V. All rights reserved. |
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2014 |
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2014 |
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2019-11-06T19:05:19Z |
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2019-11-06T19:05:19Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Artículo |
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publishedVersion |
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Journal of Computational and Applied Mathematics; Vol. 263, pp. 218-224 |
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0377-0427 |
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https://hdl.handle.net/20.500.12585/8760 |
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10.1016/j.cam.2013.12.016 |
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Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.none.fl_str_mv |
Repositorio UTB |
| identifier_str_mv |
Journal of Computational and Applied Mathematics; Vol. 263, pp. 218-224 0377-0427 10.1016/j.cam.2013.12.016 Universidad Tecnológica de Bolívar Repositorio UTB |
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https://hdl.handle.net/20.500.12585/8760 |
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eng |
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eng |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional |
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openAccess |
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Recurso electrónico |
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application/pdf |
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2019-11-06T19:05:19Z2019-11-06T19:05:19Z2014Journal of Computational and Applied Mathematics; Vol. 263, pp. 218-2240377-0427https://hdl.handle.net/20.500.12585/876010.1016/j.cam.2013.12.016Universidad Tecnológica de BolívarRepositorio UTBThe description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves. © 2013 Elsevier B.V. All rights reserved.Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIASRecurso electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2https://www2.scopus.com/inward/record.uri?eid=2-s2.0-84891682706&doi=10.1016%2fj.cam.2013.12.016&partnerID=40&md5=4e245cd1d56a7acb5a11936aedf47cd7Scopus 35094573000Scopus 56270896900Chirp-wave expansion of the electron wavefunctions in atomsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Chirp basis setChirp expansion of wavefunctionsChirp seriesFractional Fourier transformLocal gauge transformationBasis setsChirp seriesElectron wavefunctionsFractional Fourier seriesFractional Fourier transformsGauge transformationInfinite numbersNatural oscillationAtomsFourier seriesElectronsTorres, E.Torres, R.Bloch, F., Über die quantenmechanik der elektronen in kristallgittern (1928) Z. Phys., 52, pp. 555-600Slater, J.C., Wave functions in a periodic potential (1937) Phys. Rev., 51, pp. 846-851Herring, C., A new method for calculating wave functions in crystals (1940) Phys. Rev., 57, pp. 1169-1177Phillips, J.C., Kleinman, L., New method for calculating wave functions in crystals and molecules (1959) Phys. Rev., 116, pp. 287-294Kohanoff, J., (2006) Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods, , Cambridge University PressGygi, F., Adaptive Riemannian metric for plane-wave electronic-structure calculations (1992) Europhys. Lett., 19 (7), p. 617Namias, V., The fractional order Fourier transform and its application to quantum mechanics (1980) J. Inst. Math. Appl., 25, pp. 241-265McBride, A.C., Kerr, F.H., On namias's fractional Fourier transforms (1987) IMA J. Appl. Math., 39 (2), pp. 159-175Ozaktas, H.M., Barshan, B., Mendlovic, D., Onural, L., Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms (1994) J. Opt. Soc. Amer. A, 11 (2), pp. 547-559Pei, S.-C., Yeh, M.-H., Luo, T.-L., Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform (1999) IEEE Trans. Signal Process., 47 (10), pp. 2883-2888Pauli, W., Relativistic field theories of elementary particles (1941) Rev. Modern Phys., 13, pp. 203-232Kohn, W., Sham, L.J., Self-consistent equations including exchange and correlation effects (1965) Phys. Rev., 140, pp. 1133-A1138Vosko, S.H., Wilk, L., Nusair, M., Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis (1980) Can. J. Phys., 58 (8), pp. 1200-1211Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A., Joannopoulos, J.D., Iterative minimization techniques for ab initio total-energy calculations: Molecular dynamics and conjugate gradients (1992) Rev. Modern Phys., 64, pp. 1045-1097http://purl.org/coar/resource_type/c_6501ORIGINALDOI10_1016j_cam_2013_12_016.pdfapplication/pdf687201https://repositorio.utb.edu.co/bitstream/20.500.12585/8760/1/DOI10_1016j_cam_2013_12_016.pdfac45952000f449ee631821ec58e880e0MD51TEXTDOI10_1016j_cam_2013_12_016.pdf.txtDOI10_1016j_cam_2013_12_016.pdf.txtExtracted texttext/plain18993https://repositorio.utb.edu.co/bitstream/20.500.12585/8760/4/DOI10_1016j_cam_2013_12_016.pdf.txt7d658fbc7dbdc31cd58595c734b11979MD54THUMBNAILDOI10_1016j_cam_2013_12_016.pdf.jpgDOI10_1016j_cam_2013_12_016.pdf.jpgGenerated Thumbnailimage/jpeg94029https://repositorio.utb.edu.co/bitstream/20.500.12585/8760/5/DOI10_1016j_cam_2013_12_016.pdf.jpge1a38684f2532088db9816459740945cMD5520.500.12585/8760oai:repositorio.utb.edu.co:20.500.12585/87602020-10-23 04:48:42.923Repositorio Institucional UTBrepositorioutb@utb.edu.co |