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  • 1
    Electronic Resource
    Electronic Resource
    Relativistic effect on total energies for determination of correlation energies of atoms from their experimental total energies (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4738-4744 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Relativistic effect Erel upon the total electronic energy of an atom is discussed with particular reference to obtaining the nonrelativistic total energy Eexact from the experimental total energy. Numerical values of this effect obtained by various authors by different nonempirical methods are compared for neutral atoms of rare-gas elements. It is shown that methods either of a Hartree–Fock-type or of a Dirac–Hartree–Fock-type give much the same Erel value for He through Ar. It is pointed out that Erel calculated with Hartree–Fock wave functions is not adequate for use in obtaining Eexact from the experimental total energy and that the Erel value calculated with wave functions including electron correlation should work well, although an actual demonstration can be done only for two-electron systems for lack of data. A semiempirical formula is therefore proposed, which is useful for least-squares fit of experimental total energies of isoelectronic series of atoms to extract nonrelativistic total energies along with the relativistic effect. From nonrelativistic energies thus derived, semiempirical values of correlation energies of atoms are obtained. The results thus obtained are in reasonable agreement with correlation energies derived by Clementi along somewhat different lines. The power series expansion in Z of the fitted formula for the He series shows that numerical values of expansion coefficients agree reasonably well with the corresponding values obtained by accurate relativistic and nonrelativistic Z expansion-type calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456763
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  • 2
    Electronic Resource
    Electronic Resource
    Effect of the Lamb shift upon ionization potentials or excitation energies of atoms and ions (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4641-4643 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The effect of the Lamb shift upon the ionization potential of the He-like atoms in their ground states is analyzed. It is shown that the Lamb shift of the ground state of the He-like atom tends to twice the same quantity of the H-like atom of the same Z in its ground state when Z→∞. From this observation, it is supposed that the Lamb shift of a given state of an atom or an ion with more than one electron is made up of the one-electron contributions, which can be calculated with the well known formulas for the radiative corrections to the energy levels of one-electron atoms by introducing the concept of the effective nuclear charge. To confirm this supposition, it is shown that the radiative corrections for the energy levels of the 2 1,3S states of the He atom as well as for the fine structure splittings of the 2 3P and 3 3P states of the He atom can be understood along the same line. It is finally concluded that the effect of the Lamb shift upon the ionization potential or the excitation energy may have to be considered only if a 1s electron is involved either in the ionization or in the excitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452826
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  • 3
    Electronic Resource
    Electronic Resource
    Relation between the Z−1 type expansion of the total energy of isoelectronic atoms and the many-electron theory on the electron correlation by Sinanoglu (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 381-386 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By applying the economical formula for the total energies of isoelectronic atoms presented by the present authors [J. Chem. Phys. 84, 6895 (1986)] to both the nonrelativistic exact energy and the Hartree–Fock energy, an expression of the Z−1 expansion type for the correlation energy is obtained for isoelectronic series involving the first-row atoms. Based upon the expression obtained, the following conclusions are derived on the relation between the Z−1 type expansion theory and Sinanoglu's many-electron theory (MET): (i) the Z2 term has nothing to do with the electron correlation; (ii) the term proportional to Z represents the internal correlation energy Eint in MET, at least when Z is large in comparison with the number of electrons N; (iii) the constant term in the Z−1 type expansion is the limiting value of the sum of the semi-internal and the all-external correlation energy (EF+Eu) when Z→∞ and its values for the ground-state atoms show a systematic trend when plotted against N; (iv) the sum of the Z−1 and the higher order terms in Z−1 represents the Z dependence of EF+Eu, although its small amount is attributable to a part of Eint when Z−N(approximately-less-than)1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453583
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  • 4
    Electronic Resource
    Electronic Resource
    Z dependence of the total energy and the electrostatic potential at the nucleus for the isoelectronic atoms with particular reference to the two-electron atoms in their ground state (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 6895-6900 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Equations expressing the total energy E and the electrostatic potential at the nucleus V0,A for an isoelectronic series of atoms as functions of atomic number Z have been examined. Based upon the Z−α expansion of Fröman and Hall, it has been found that equations E=(1/2)LZ2+KZ+W2+W'3(Z−α)−1 +W4(Z−α)−2 and V0,A=LZ+K−W'3(Z−α)−2 −2W4(Z−α)−3 work very well in the sense that they can form the basis of constructing very accurate empirical formulas for E(Z) and V0,A (Z) by fitting these equations to the Thakkar–Smith data for the He–like atoms including H−. Superiority of our approach over Gorunganthu and Bonham's approach based upon the Taylor series expansion is pointed out. Relevance of our formulas with the results of the Z−1 perturbation calculations has been pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450694
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  • 5
    Electronic Resource
    Electronic Resource
    Erratum: Relativistic effect on total energies for determination of correlation energies of atoms from their experimental total energies [J. Chem. Phys. 91, 4738 (1989)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 2174-2174 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463993
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  • 6
    Electronic Resource
    Electronic Resource
    On the evaluation of the energies of hybridized valence states (1972)
    Springer
    Theoretical chemistry accounts 25 (1972), S. 248-253 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Das Verfahren zur Berechnung der Energie von Valenzzuständen, wie es von Öpik für den Fall hybridizierter Orbitale erweitert wurde, wird bezüglich der Behandlung von Nichtdiagonalelementen kritisiert. Es wird gezeigt, daß solche Terme, die der Wechselwirkung von Multipletts gleicher Symmetrie, aber verschiedener Konfiguration entsprechen, nur bei verhältnismäßig groben Rechnungen vernachlässigt werden dürfen. Anhand eines Beispiels wird gezeigt, daß sie bei größeren Ansprüchen an die Genauigkeit eingeschlossen werden sollten.
    Notes: Abstract The method of evaluation of the valence-state energy from the observed term values, as proposed originally by Moffitt [1] for unhybridized valence state and extended by Öpik [3] to the hybridized one, is critically reviewed. It is shown for the hybridized valence states that off-diagonal terms, corresponding to interactions among multiplets of the same symmetry arising from different configurations participating in the hybridized valence state, must also be considered in addition to the diagonal terms considered in Öpik's method. Actual procedure of doing this is given. A numerical example given shows that the improvement of Öpik's method proposed here may be ignored in a crude theory but is worth considering in order that the accurate value of the valence-state energy be obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527291
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  • 7
    Electronic Resource
    Electronic Resource
    Convenient formulas for evaluation of the hybridized valence states involving thes - p hybrid orbitals and their applications to the atoms and the ions of carbon, nitrogen, and oxygen (1973)
    Springer
    Theoretical chemistry accounts 30 (1973), S. 129-136 
    Details
    ISSN: 1432-2234
    Keywords: Hybridized valence state energy formulas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Formulas to calculate the energies of the hybridized valence states are given. The formulas cover any of the hybridized valence states, so far as the valence orbitals involved ares-p hybrids, and are useful in the sense that they give essentially the same results as those obtained with the modified Öpik method [1] quickly. The prescriptions and the numerical data for the actual evaluation of the hybridized valence-state energies are also given with particular reference to the atoms and the ions of carbon, nitrogen, and oxygen. In Appendix, addenda and corrigenda of the previous paper [1] are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01209760
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  • 8
    Electronic Resource
    Electronic Resource
    The valence orbital ionization potential of the first transition-metal atoms and ions (1970)
    Springer
    Theoretical chemistry accounts 18 (1970), S. 208-222 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Mit den Anno-Teruya-Werten für die durchschnittliche Energie der Konfigurationen und den experimentellen Ionisationspotentialen werden für Atome und Ionen der Konfigurationen 3d α4s α p γ die 3d-, 4s- und 4p-VOIPs bestimmt. Mangels verfügbarer Daten werden nicht alle Konfigurationen dieses Typs behandelt. Sofern Daten verfügbar sind, wird den VOIPs einer isoelektronischen Reihe eine in der Kernladungszahl Z quadratische Gleichung angepa\t: VOIP=A 0+A 1 Z+A 2 Z 2. Dies aus dieser Gleichung gewonnenen RegelmÄ\igkeiten in den Koeffizienten A 0, A 1 und A 2 werden mit der einfachen Slaterformel für die Gesamtenergie eines Atoms als Abschirmeffekte der inneren Elektronen erklÄrt.
    Abstract: Résumé Les potentiels d'ionisation des orbitales de valence (VOIP) 3d, 4s et 4p sont déterminés pour les atomes et les ions de configuration électronique 3d α4s α p γ en utilisant les valeurs de Anno-Teruya des énergies moyennes des configurations et les potentiels d'ionisation expérimentaux. Par suite d'absence de données toutes les configurations de ce type ne sont pas étudiées. Dans la mesure des données existantes, une relation quadratique en fonction du numéro atomique Z est ajustée pour les VOIP d'une série isoélectronique: VOIP=A 0+A 1 Z+A 2 Z 2. Les coefficients A 0, A 1 et A 2 ainsi obtenus sont analysés à la lumière des expressions simples de Slater pour l'énergie totale d'un atome avec l'idée d'un effet d'écran dû aux électrons internes.
    Notes: Abstract The 3d, 4s and 4p valence orbital ionization potentials (VOIP) are determined for the atoms and the ions with the electron configuration 3d α4s α p γ, using the Anno-Teruya values of the average energies of the configurations and the experimental ionization potentials. Not all the configurations of this type are treated for lack of the data. As far as the data are available, a quadratic equation in terms of the atomic number Z is fitted to the VOIP's of an isoelectronic series: VOIP=A 0+A 1 Z+A 2 Z 2. The coefficients A 0's, A 1's and A 2's thus obtained are analysed in the light of Slater's simple expression for the total energy of an atom with the idea of screening effect due to inner electrons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527335
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  • 9
    Electronic Resource
    Electronic Resource
    Valence orbital ionization potentials of 1s 22s m2p n atoms and ions (1970)
    Springer
    Theoretical chemistry accounts 18 (1970), S. 223-234 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Unter Benutzung der Anno-Teruya-Werte für die durchschnittliche Energie der Konfigurationen werden systematisch für Atome und Ionen der Konfiguration 1s 22s m 2p n die 2s- und 2p-VOIP's bestimmt. Alle FÄlle mit den nach dem Pauli-Prinzip möglichen Werten für m und n werden behandelt. Das 2s- oder 2p-VOIP eines besonderen Ions ist beinahe unabhÄngig von der Elektronenkonfiguration. Nach der Methode der kleinsten quadratischen Abweichung werden die VOIP's einer isoelektronischen Serie mit Hilfe einer in Z (Z=Kernladungszahl) quadratischen Gleichung bestimmt: VOIP=A 0 +A 1 Z+A 2 Z 2. Die Koeffizienten A 0,A1 und A 2 zeigen untereinander für verschiedene isoelektronische Serien bemerkenswerte RegelmÄ\igkeiten, die mit der einfachen Slaterformel für die Gesamtenergie eines Atoms oder Ions als Abschirmeffekte der inneren Elektronen erklÄrt werden können. Durch die Untersuchung dieser RegelmÄ\igkeiten konnten verschiedene Abschirmkonstanten bestimmt werden.
    Abstract: Résumé Les potentiels d'ionisation des orbitales de valence (VOIP) 2s et 2p sont systématiquement déterminés pour les atomes et les ions de configuration 1s 22s m2p n, en utilisant les valeurs de Anno-Teruya pour les énergies moyennes des configurations. Tous les cas possibles d'après le principe de Pauli sont traités. Le VOIP 2s ou 2p d'un ion donné avec une configuration de ce type est presque indépendant de la configuration électronique. Une relation quadratique en fonction du numéro atomique Z est ajustée pour les VOIP d'une série isoélectronique par la méthode des moindres carrés: VOIP=A 0+A 1 Z +A 2 Z 2. Des régularités remarquables se manifestent pour A 0, A 1, A 2 dans différentes séries isoélectroniques; ceci peut Être expliqué à l'aide des expressions simples de Slater pour l'énergie totale d'un atome (ou d'un ion) avec l'idée d'un effet d'écran dğ aux électrons internes. Différentes constantes d'écran ont été déterminées par l'analyse de ces régularités.
    Notes: Abstract The 2s and 2p valence orbital ionization potentials (VOIP) are determined systematically for atoms and ions with configurations 1s 22s m2p n , using the Anno-Teruya values of the average energies of the configurations. All the cases with possible values of m and n, in conformity with the Pauli principle, are treated. The 2s or 2p VOIP of a particular ion with the configuration of this type is almost independent of the electron configuration. The VOIP's of an isoelectronic series are fitted to a quadratic equation in terms of atomic number Z: VOIP=A 0+A 1 Z+A 2 Z 2, by a least-squares method. There are remarkable regularities among A 0's, A 1's or A 2's, for different isoelectronic series, which may be explained by Slater's simple expression for the total energy of an atom (or ion) with the idea of screening effect due to inner electrons. Various screening constants have been determined from the analysis of such regularities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527336
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  • 10
    Electronic Resource
    Electronic Resource
    Systematic determination of the Slater-Condon parameters of atoms and ions with 1s 2 2s m 2p n configurations (1971)
    Springer
    Theoretical chemistry accounts 21 (1971), S. 127-142 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Semiempirische Werte der Slater-Parameter F 2(2p,2p) und G 1(2s, 2p) wurden für die Atome und Ionen mit der Elektronenkonfiguration 1s 22s m2p n aus den experimentellen atomaren Energietermen bestimmt. Insbesondere wurden die Parameter bestimmt, die für semiempirische Berechnungen der Elektronenstruktur von Molekülen benötigt werden. Die Berechnung ergibt weiterhin Werte von E av, der Durchschnittsenergie der Konfigurationen der genannten Atome. Die vorliegende Arbeit geht auch auf die Bestimmung des semiempirischen bzw. effektiven Wertes von F 0 aus ΔE einer geeigneten Elektronenübertragungsreaktion ein, die auf die Arbeit von Anno [15] zurückgeht. Die semiempirischen Werte der Slater-Parameter sowie der ΔE und E av zeigen annähernd lineare Abhängigkeit von der Atomnummer Z innerhalb isoelektronischer Reihen. Aus dem Gesamtverhalten der genannten Kurven wird geschlossen, daβ die Zuordnung der atomaren Energieterme von Na5+(1s 22p 4) falsch sein dürfte.
    Abstract: Résumé Détermination à partir des niveaux d'énergie atomiques expérimentaux des valeurs semi-empiriques des paramètres de Slater F 2(2p, 2p) et G 1(2s, 2p) pour les atomes et les ions ayant les configurations 1s 22s m2p n. On a fait particulièrement attention d'obtenir les valeurs des paramètres à utiliser pour des calculs moléculaires semi-empiriques. Le calcul a aussi fourni les énergies moyennes des configurations de ces atomes. On évoque aussi le calcul de la valeur semi-empirique ou effective de F 0 à partir du ΔE d'une réaction appropriée de transfert électronique, selon une idée de Anno [15]. Les valeurs semiempiriques des paramètres de Slater, ainsi que celles des ΔE et E moy, montrent une dépendance presque linéaire au nombre atomique Z à travers les séries isoélectroniques. A partir des tendances générales des lignes de corrélation, on remarque que l'attribution des niveaux d'énergie atomiques de Na5+(1s 22p 4) doit être fausse.
    Notes: Abstract Semiempirical values of the Slater parameters F 2(2p,2p) and G 1(2s, 2p) have been determined for the atoms and ions with the electron configurations 1s 22s m2p n from the experimental atomic energy levels. Particular attention has been paid to get the values of the parameters to be used for semiempirical calculations on molecular electronic structure. The calculation has also yielded E av's, the average energies of configurations of these atoms. Evaluation of the semiempirical or effective value of F 0 from ΔE of an appropriate electron-transfer reaction, based on the idea presented by Anno [15], is also referred to in the present paper. The semiempirical values of the Slater parameters as well as those of ΔE's and E av's show almost linear dependence upon atomic number Z through isoelectronic series. From the overall tendency of the correlation lines, it is pointed out that the assignment of atomic energy levels of Na5+ (1s 22p 4) must be wrong.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00530210
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