Abstract

An extrapolation method based on a screening approximation, applied to available initial values of polarizability for low stages of ionization, is used to obtain dipole and quadrupole polarizabilities for more highly ionized members of many isoelectronic sequences. It is suggested that the derived screening constants xL and limiting ratios FL may have significant physical meaning, especially the latter which may have an interpretation in terms of hydrogenic polarizabilities.

© 1979 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Edlen, in Handb. Phys. 27, 80 (1964).
  2. A. Dalgarno, “Atomic Polarizabilities and Shielding Factors,” Adv. Phys. 11, 281–315 (1962).
    [Crossref]
  3. A. L. Stewart, “The Properties of the Helium Atom and the Two-Electron Systems,” Adv. Phys. 12, 299–353 (1963).
    [Crossref]
  4. L. P. Bokacheva and N. P. Borisova, “An Additive-Orbital Scheme for Calculating the Polarizabilities of Atoms and Molecules,” J. Struct. Chem. 16, 344–350 (1975).
    [Crossref]
  5. S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
    [Crossref]
  6. R. F. Stewart and B. C. Webster, “Calculation of Atomic Polarizabilities by Finite-Difference Methods,” J. Chem.Soc. Farad, Trans. II 69, 1685–1690 (1973).
    [Crossref]
  7. P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
    [Crossref]
  8. R. F. Stewart, “Static Polarizabilities of the Ne, Mg and Ar Isoelectronic Sequences,” Mol. Phys. 29, 787–791 (1975).
    [Crossref]
  9. A. Dalgarno and H. A. J. Mclntyre, “The Polarizabilities and Shielding Factors of the Beryllium Sequence,” Proc. Phys. Soc. 85, 47–50 (1965).
    [Crossref]
  10. S. A. Adelman and A. Szabo, “Coulomb Approximation for Multipole Polarizabilities and Dispersion Forces; Analytic Static Polarizabilities of Ground and Excited State Atoms,” J. Chem. Phys. 58, 687–696 (1973).
    [Crossref]
  11. W. Witschel and J. Haars, “Multipole Polarizibilities from Hartree-Fock Densities by Statistical Perturbation Theory, a Semiempirical Approach,” Z. Naturforsch. 30A, 876–882 (1975).
  12. M. R. Flannery and A. L. Stewart, “The Dipole Polarizability of Members of the Lithium Sequence,” Proc. Phys. Soc. 82, 188–191 (1963).
    [Crossref]
  13. M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).
  14. I. Shimamura, “Method of Green’s Function for Polarizabilities and Mean Excitation Energies of Ground- and Excited-State Hydrogen-Like Atoms,” J. Phys. Soc. Jpn. 40, 239–249 (1976).
    [Crossref]
  15. J. Lahiri and A. Mukherji, “Self-Consistent Perturbation. II. Calculation of Quadrupole Polarizability and Shielding Factor,” Phys. Rev. 141, 428–430 (1966).
    [Crossref]
  16. A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
    [Crossref]
  17. A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
    [Crossref]

1977 (1)

A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
[Crossref]

1976 (1)

I. Shimamura, “Method of Green’s Function for Polarizabilities and Mean Excitation Energies of Ground- and Excited-State Hydrogen-Like Atoms,” J. Phys. Soc. Jpn. 40, 239–249 (1976).
[Crossref]

1975 (3)

W. Witschel and J. Haars, “Multipole Polarizibilities from Hartree-Fock Densities by Statistical Perturbation Theory, a Semiempirical Approach,” Z. Naturforsch. 30A, 876–882 (1975).

L. P. Bokacheva and N. P. Borisova, “An Additive-Orbital Scheme for Calculating the Polarizabilities of Atoms and Molecules,” J. Struct. Chem. 16, 344–350 (1975).
[Crossref]

R. F. Stewart, “Static Polarizabilities of the Ne, Mg and Ar Isoelectronic Sequences,” Mol. Phys. 29, 787–791 (1975).
[Crossref]

1974 (1)

A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
[Crossref]

1973 (2)

S. A. Adelman and A. Szabo, “Coulomb Approximation for Multipole Polarizabilities and Dispersion Forces; Analytic Static Polarizabilities of Ground and Excited State Atoms,” J. Chem. Phys. 58, 687–696 (1973).
[Crossref]

R. F. Stewart and B. C. Webster, “Calculation of Atomic Polarizabilities by Finite-Difference Methods,” J. Chem.Soc. Farad, Trans. II 69, 1685–1690 (1973).
[Crossref]

1971 (1)

S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
[Crossref]

1969 (1)

M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).

1966 (2)

J. Lahiri and A. Mukherji, “Self-Consistent Perturbation. II. Calculation of Quadrupole Polarizability and Shielding Factor,” Phys. Rev. 141, 428–430 (1966).
[Crossref]

P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
[Crossref]

1965 (1)

A. Dalgarno and H. A. J. Mclntyre, “The Polarizabilities and Shielding Factors of the Beryllium Sequence,” Proc. Phys. Soc. 85, 47–50 (1965).
[Crossref]

1964 (1)

B. Edlen, in Handb. Phys. 27, 80 (1964).

1963 (2)

A. L. Stewart, “The Properties of the Helium Atom and the Two-Electron Systems,” Adv. Phys. 12, 299–353 (1963).
[Crossref]

M. R. Flannery and A. L. Stewart, “The Dipole Polarizability of Members of the Lithium Sequence,” Proc. Phys. Soc. 82, 188–191 (1963).
[Crossref]

1962 (1)

A. Dalgarno, “Atomic Polarizabilities and Shielding Factors,” Adv. Phys. 11, 281–315 (1962).
[Crossref]

Adamov, M. N.

M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).

Adelman, S. A.

S. A. Adelman and A. Szabo, “Coulomb Approximation for Multipole Polarizabilities and Dispersion Forces; Analytic Static Polarizabilities of Ground and Excited State Atoms,” J. Chem. Phys. 58, 687–696 (1973).
[Crossref]

Balmakov, M. D.

M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).

Bhattacharya, A. K.

A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
[Crossref]

Bokacheva, L. P.

L. P. Bokacheva and N. P. Borisova, “An Additive-Orbital Scheme for Calculating the Polarizabilities of Atoms and Molecules,” J. Struct. Chem. 16, 344–350 (1975).
[Crossref]

Borisova, N. P.

L. P. Bokacheva and N. P. Borisova, “An Additive-Orbital Scheme for Calculating the Polarizabilities of Atoms and Molecules,” J. Struct. Chem. 16, 344–350 (1975).
[Crossref]

Dalgarno, A.

A. Dalgarno and H. A. J. Mclntyre, “The Polarizabilities and Shielding Factors of the Beryllium Sequence,” Proc. Phys. Soc. 85, 47–50 (1965).
[Crossref]

A. Dalgarno, “Atomic Polarizabilities and Shielding Factors,” Adv. Phys. 11, 281–315 (1962).
[Crossref]

Edlen, B.

B. Edlen, in Handb. Phys. 27, 80 (1964).

Flannery, M. R.

M. R. Flannery and A. L. Stewart, “The Dipole Polarizability of Members of the Lithium Sequence,” Proc. Phys. Soc. 82, 188–191 (1963).
[Crossref]

Fraga, S.

S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
[Crossref]

Gupta, A.

A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
[Crossref]

Haars, J.

W. Witschel and J. Haars, “Multipole Polarizibilities from Hartree-Fock Densities by Statistical Perturbation Theory, a Semiempirical Approach,” Z. Naturforsch. 30A, 876–882 (1975).

Hibbert, A.

A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
[Crossref]

Hurst, R. P.

P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
[Crossref]

Karplus, M.

P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
[Crossref]

Lahiri, J.

J. Lahiri and A. Mukherji, “Self-Consistent Perturbation. II. Calculation of Quadrupole Polarizability and Shielding Factor,” Phys. Rev. 141, 428–430 (1966).
[Crossref]

Lan, Vo Ky

A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
[Crossref]

Langhoff, P. W.

P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
[Crossref]

Le Dourneuf, M.

A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
[Crossref]

Lo, B. W. N.

S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
[Crossref]

Mclntyre, H. A. J.

A. Dalgarno and H. A. J. Mclntyre, “The Polarizabilities and Shielding Factors of the Beryllium Sequence,” Proc. Phys. Soc. 85, 47–50 (1965).
[Crossref]

Mukherjee, P. K.

A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
[Crossref]

Mukherji, A.

J. Lahiri and A. Mukherji, “Self-Consistent Perturbation. II. Calculation of Quadrupole Polarizability and Shielding Factor,” Phys. Rev. 141, 428–430 (1966).
[Crossref]

Rebane, T. K.

M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).

Saxena, K. M. S.

S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
[Crossref]

Shimamura, I.

I. Shimamura, “Method of Green’s Function for Polarizabilities and Mean Excitation Energies of Ground- and Excited-State Hydrogen-Like Atoms,” J. Phys. Soc. Jpn. 40, 239–249 (1976).
[Crossref]

Stewart, A. L.

M. R. Flannery and A. L. Stewart, “The Dipole Polarizability of Members of the Lithium Sequence,” Proc. Phys. Soc. 82, 188–191 (1963).
[Crossref]

A. L. Stewart, “The Properties of the Helium Atom and the Two-Electron Systems,” Adv. Phys. 12, 299–353 (1963).
[Crossref]

Stewart, R. F.

R. F. Stewart, “Static Polarizabilities of the Ne, Mg and Ar Isoelectronic Sequences,” Mol. Phys. 29, 787–791 (1975).
[Crossref]

R. F. Stewart and B. C. Webster, “Calculation of Atomic Polarizabilities by Finite-Difference Methods,” J. Chem.Soc. Farad, Trans. II 69, 1685–1690 (1973).
[Crossref]

Szabo, A.

S. A. Adelman and A. Szabo, “Coulomb Approximation for Multipole Polarizabilities and Dispersion Forces; Analytic Static Polarizabilities of Ground and Excited State Atoms,” J. Chem. Phys. 58, 687–696 (1973).
[Crossref]

Webster, B. C.

R. F. Stewart and B. C. Webster, “Calculation of Atomic Polarizabilities by Finite-Difference Methods,” J. Chem.Soc. Farad, Trans. II 69, 1685–1690 (1973).
[Crossref]

Witschel, W.

W. Witschel and J. Haars, “Multipole Polarizibilities from Hartree-Fock Densities by Statistical Perturbation Theory, a Semiempirical Approach,” Z. Naturforsch. 30A, 876–882 (1975).

Adv. Phys. (2)

A. Dalgarno, “Atomic Polarizabilities and Shielding Factors,” Adv. Phys. 11, 281–315 (1962).
[Crossref]

A. L. Stewart, “The Properties of the Helium Atom and the Two-Electron Systems,” Adv. Phys. 12, 299–353 (1963).
[Crossref]

Atomic Data (1)

S. Fraga, K. M. S. Saxena, and B. W. N. Lo, “Hartree-Fock Values of Energies, Interaction Constants, and Atomic Properties for the Groundstates of the Negative Ions, Neutral Atoms, and First Four Positive Ions from Helium to Krypton,” Atomic Data 3, 323–359 (1971).
[Crossref]

Handb. Phys. (1)

B. Edlen, in Handb. Phys. 27, 80 (1964).

Int. J. Quant. Chem. (1)

A. Gupta, A. K. Bhattacharya, and P. K. Mukherjee, “Coupled Hartree-Fock Calculation of Static Dipole Polarizabilities and Shielding Factors of Open Shell Systems,” Int. J. Quant. Chem. 8, 97–105 (1974).
[Crossref]

J. Chem. Phys. (1)

S. A. Adelman and A. Szabo, “Coulomb Approximation for Multipole Polarizabilities and Dispersion Forces; Analytic Static Polarizabilities of Ground and Excited State Atoms,” J. Chem. Phys. 58, 687–696 (1973).
[Crossref]

J. Chem.Phys. (1)

P. W. Langhoff, M. Karplus, and R. P. Hurst, “Approximations to Hartree-Fock Perturbation Theory,” J. Chem.Phys. 44, 505–514 (1966).
[Crossref]

J. Chem.Soc. Farad, Trans. II (1)

R. F. Stewart and B. C. Webster, “Calculation of Atomic Polarizabilities by Finite-Difference Methods,” J. Chem.Soc. Farad, Trans. II 69, 1685–1690 (1973).
[Crossref]

J. Phys. B: Atom Molec. Phys. (1)

A. Hibbert, M. Le Dourneuf, and Vo Ky Lan, “Atomic Polarizabilities and Polarized Pseudo-States in the Multiconfigurational Approach II. First Row Atoms and Ions,” J. Phys. B: Atom Molec. Phys. 10, 1015–1025 (1977).
[Crossref]

J. Phys. Soc. Jpn. (1)

I. Shimamura, “Method of Green’s Function for Polarizabilities and Mean Excitation Energies of Ground- and Excited-State Hydrogen-Like Atoms,” J. Phys. Soc. Jpn. 40, 239–249 (1976).
[Crossref]

J. Struct. Chem. (1)

L. P. Bokacheva and N. P. Borisova, “An Additive-Orbital Scheme for Calculating the Polarizabilities of Atoms and Molecules,” J. Struct. Chem. 16, 344–350 (1975).
[Crossref]

Mol. Phys. (1)

R. F. Stewart, “Static Polarizabilities of the Ne, Mg and Ar Isoelectronic Sequences,” Mol. Phys. 29, 787–791 (1975).
[Crossref]

Opt. Spectr. (1)

M. N. Adamov, M. D. Balmakov, and T. K. Rebane, “Calculation of the Optical Polarizability of the Hydrogen Atom in the 2s and 2p States,” Opt. Spectr. 27, 100–101 (1969).

Phys. Rev. (1)

J. Lahiri and A. Mukherji, “Self-Consistent Perturbation. II. Calculation of Quadrupole Polarizability and Shielding Factor,” Phys. Rev. 141, 428–430 (1966).
[Crossref]

Proc. Phys. Soc. (2)

M. R. Flannery and A. L. Stewart, “The Dipole Polarizability of Members of the Lithium Sequence,” Proc. Phys. Soc. 82, 188–191 (1963).
[Crossref]

A. Dalgarno and H. A. J. Mclntyre, “The Polarizabilities and Shielding Factors of the Beryllium Sequence,” Proc. Phys. Soc. 85, 47–50 (1965).
[Crossref]

Z. Naturforsch. (1)

W. Witschel and J. Haars, “Multipole Polarizibilities from Hartree-Fock Densities by Statistical Perturbation Theory, a Semiempirical Approach,” Z. Naturforsch. 30A, 876–882 (1975).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

FIG. 1
FIG. 1

Variation of ionic dipole polarizabilities α1(N,Z) with number N of electrons, for some representative nuclear charges Z. Solid points, previously available values; open circles, present values. The solid lines are loci of the quantities 1 (1,Z), discussed in the text.

FIG. 2
FIG. 2

Dependence on Z of the ratios RL(N,Z) = αL(N,Z)/L(1,Z), for the helium sequence (N = 2) and the neon sequence (N = 10).

Tables (5)

Tables Icon

TABLE I Comparison of present extrapolation with available values of polarizability (units a 0 3)

Tables Icon

TABLE II Dipole polarizabilitiesaα1(N,Z) for ions of nuclear atomic number Z and N electrons

Tables Icon

TABLE IIIa Quadrupole polarizabilities α2(N,Z) (units a 0 5)

Tables Icon

TABLE IIIb Quadrupole polarizabilities α2(N,Z) (units a 0 5)

Tables Icon

TABLE IV Comparison of some publisheda dipole polarizability values

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

α L ( 1 , Z ) = ( 2 L + 2 ) ! ( L + 2 ) 2 2 L + 1 L ( L + 1 ) Z ( 2 L + 2 ) .
α 1 ( 2 , Z ) = 9 ( Z 0.359375 ) 4 ,
α 2 ( 2 , Z ) = 30 ( Z 0.450564 ) 6 .
k L ( 2 , Z ) = ( 2 L + 2 ) ln ( 1 0.360 + 0.090 ( L 1 ) Z )
α L ( 2 , Z ) = 2 α L ( 1 , Z ) exp [ k L ( 2 , Z ) ] .
R 1 F 1 , R 2 F 2 where F 1 , F 2 1 .
R L F L ( 1 x L ( 10 ) Z ) ( 2 L + 2 ) F L exp [ k L ( 10 , Z ) ]
k L ( 10 , Z ) = ( 2 L + 2 ) ln ( 1 x L ( 10 ) Z ) .
ln R L = ln F L + ( 2 L + 2 ) r = 1 5 1 r ( x L Z ) r .
( 2 L + 2 ) r = 1 5 x L r [ 1 r ( 1 Z b r 1 Z a r ) ] + ln ( R L ( 10 , Z a ) R L ( 10 , Z b ) ) = 0 .
α L ( 10 , Z ) = 10 α L ( 1 , Z ) F L exp [ ( 2 L + 2 ) r = 1 5 ( x L r / r Z r ) ] .