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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4738-4744 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4641-4643 
    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.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 381-386 
    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.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 6895-6900 
    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.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 2174-2174 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 21 (1971), S. 127-142 
    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.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 51-65 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The identification of the stage of ionization for various kinds of one-center electron repulsion integrals, occurring when nonbonding or lone-pair electrons are considered explicitly as well as π-electrons, is discussed for conjugated organic molecules containing heteroatoms N. It is concluded that the value for the negative ions should be used for (πCπC | πCπC) in all the states but for (πNπN | πNπN) only in the π-π states. In the n-π states, the appropriate value of (πNπN | πNπN) is that of the neutral atom if the molecule contains only one N atom. If more than one N atom is involved in the molecule, some weighted mean of the values for the negative ion and for the neutral atom should be used. The value for the neutral atom is most adequate for one-center repulsion integrals other than the (ππ | ππ) type in both the π-π and the n-π states. The method of determining these integrals is also discussed. It is concluded that they are to be determined from the consideration of appropriate electron-transfer reactions except for exchange integrals. The exchange integrals are shown to have to be determined from the Slater-Condon parameters derived from the analysis of the experimental atomic energy levels. Illustrative calculations are given for the lower singlet levels of the formaldehyde, pyrazine, pyridine, and the p-benzoquinone molecule. It is found that the calculated energies of the n-π transitions become much too low unless the (ππ | ππ) values of the heteroatoms in the molecule are chosen differently in the n-π states and in the π-π states as pointed out theoretically in this article.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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  • 8
    Publication Date: 1992-08-01
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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  • 9
    Publication Date: 1970-03-15
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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  • 10
    Publication Date: 1980-06-01
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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