Convolution representation of the relation between total electron density and that of s states in closed-shell atoms
Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expresse...
Ausführliche Beschreibung
Gespeichert in:
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E-Artikel |
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| Erschienen: |
1987 |
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| Umfang: |
Online-Ressource 5 |
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| Reproduktion: |
APS Digital Backfile Archive 1893-2003 |
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| Übergeordnetes Werk: |
Enthalten in: Physical review / A - College Park, Md., 1970, 35(1987), 2, Seite 491-495 |
| Übergeordnetes Werk: |
volume:35 ; year:1987 ; number:2 ; pages:491-495 ; extent:5 |
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| 520 | |a Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. | ||
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(DE-627)NLEJ248523678 (DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668 DE-627 ger DE-627 rakwb Convolution representation of the relation between total electron density and that of s states in closed-shell atoms 1987 Online-Ressource 5 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. APS Digital Backfile Archive 1893-2003 Pucci, R. oth Enthalten in Physical review / A College Park, Md., 1970 35(1987), 2, Seite 491-495 Online-Ressource (DE-627)NLEJ248237853 (DE-600)1472694-4 1094-1622 nnns volume:35 year:1987 number:2 pages:491-495 extent:5 https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 35 1987 2 491-495 5 |
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(DE-627)NLEJ248523678 (DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668 DE-627 ger DE-627 rakwb Convolution representation of the relation between total electron density and that of s states in closed-shell atoms 1987 Online-Ressource 5 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. APS Digital Backfile Archive 1893-2003 Pucci, R. oth Enthalten in Physical review / A College Park, Md., 1970 35(1987), 2, Seite 491-495 Online-Ressource (DE-627)NLEJ248237853 (DE-600)1472694-4 1094-1622 nnns volume:35 year:1987 number:2 pages:491-495 extent:5 https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 35 1987 2 491-495 5 |
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(DE-627)NLEJ248523678 (DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668 DE-627 ger DE-627 rakwb Convolution representation of the relation between total electron density and that of s states in closed-shell atoms 1987 Online-Ressource 5 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. APS Digital Backfile Archive 1893-2003 Pucci, R. oth Enthalten in Physical review / A College Park, Md., 1970 35(1987), 2, Seite 491-495 Online-Ressource (DE-627)NLEJ248237853 (DE-600)1472694-4 1094-1622 nnns volume:35 year:1987 number:2 pages:491-495 extent:5 https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 35 1987 2 491-495 5 |
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(DE-627)NLEJ248523678 (DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668 DE-627 ger DE-627 rakwb Convolution representation of the relation between total electron density and that of s states in closed-shell atoms 1987 Online-Ressource 5 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. APS Digital Backfile Archive 1893-2003 Pucci, R. oth Enthalten in Physical review / A College Park, Md., 1970 35(1987), 2, Seite 491-495 Online-Ressource (DE-627)NLEJ248237853 (DE-600)1472694-4 1094-1622 nnns volume:35 year:1987 number:2 pages:491-495 extent:5 https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 35 1987 2 491-495 5 |
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(DE-627)NLEJ248523678 (DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668 DE-627 ger DE-627 rakwb Convolution representation of the relation between total electron density and that of s states in closed-shell atoms 1987 Online-Ressource 5 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. APS Digital Backfile Archive 1893-2003 Pucci, R. oth Enthalten in Physical review / A College Park, Md., 1970 35(1987), 2, Seite 491-495 Online-Ressource (DE-627)NLEJ248237853 (DE-600)1472694-4 1094-1622 nnns volume:35 year:1987 number:2 pages:491-495 extent:5 https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668 Verlag Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-APS GBV_NL_ARTICLE AR 35 1987 2 491-495 5 |
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convolution representation of the relation between total electron density and that of s states in closed-shell atoms |
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Convolution representation of the relation between total electron density and that of s states in closed-shell atoms |
| abstract |
Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. |
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Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. |
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Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ248523678</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231114095531.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231114s1987 xx |||||o 00| ||und c</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ248523678</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-601)aps:affcbcdc6738f7d07f662a69a9c9caaf5aa0b668</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Convolution representation of the relation between total electron density and that of s states in closed-shell atoms</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">5</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ρs(r), we have explored for closed-shell atoms a convolution relation between ρs(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and fs(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ρs(r)∝r-4ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ∂2ρ/∂r2 evaluated at the nucleus.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">APS Digital Backfile Archive 1893-2003</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pucci, R.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Physical review / A</subfield><subfield code="d">College Park, Md., 1970</subfield><subfield code="g">35(1987), 2, Seite 491-495</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ248237853</subfield><subfield code="w">(DE-600)1472694-4</subfield><subfield code="x">1094-1622</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:35</subfield><subfield code="g">year:1987</subfield><subfield code="g">number:2</subfield><subfield code="g">pages:491-495</subfield><subfield code="g">extent:5</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/aps%3Aaffcbcdc6738f7d07f662a69a9c9caaf5aa0b668</subfield><subfield code="x">Verlag</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-APS</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">35</subfield><subfield code="j">1987</subfield><subfield code="e">2</subfield><subfield code="h">491-495</subfield><subfield code="g">5</subfield></datafield></record></collection>
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