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Maximum-entropy analysis of one-particle densities in atoms

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Zeitschrift für Physik D Atoms, Molecules and Clusters

Abstract

The Maximum-Entropy formalism is used to obtain approximations to the spherically averaged charge and momentum densities. The only information required is the first few radial expectation values. Analytical and numerical approximations to the central values of the densities are calculated. Moreover, the unused or unknown radial expectation values are estimated by means of the moments of these Maximum-Entropy densities. As illustration, the accuracy of these approximations are numerically studied in a Hartree-Fock framework. This method is complementary to the one which makes use of the Stieltjes-Chebyshev inequalities and leads to the least biased approximate densities compatible with the information we use.

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References

  1. Parr, R.G., Yang, W.: Density-functional theory of atoms and molecules. New York: Oxford University Press 1989

    Google Scholar 

  2. Williams, B.G. (ed.): Compton scattering: the investigation of electron momentum distributions. New York: McGraw Hill 1977

    Google Scholar 

  3. Cooper, M.J.: Rep. Prog. Phys. 48, 415 (1985)

    Article  Google Scholar 

  4. McCarthy, I.E., Weigold, E.: Phys. Rep. C 27, 275 (1976)

    Article  Google Scholar 

  5. Manninen, S.: Phys. Rev. Lett. 57, 1500 (1986)

    Article  Google Scholar 

  6. Marchetti, V., Frank, C.: Phys. Rev. Lett. 59, 1557 (1987)

    Article  Google Scholar 

  7. European Synchrotron Radiation Facility, Foundation Phase Report, Chap. V (1987)

  8. Manninen, S., Etelaniemi, V., Suortti, P.: Phys. Rev. Lett. 61, 2815 (1988)

    Article  Google Scholar 

  9. Genoud, P., Singh, A.K., Manuel, A.A., Jarlborg, T., Walker, E., Peter, M., Weller, M.: J. Phys. F 18, 1933 (1988)

    Article  Google Scholar 

  10. Cook, J.P.D., Mitroy, J., Weigold, E.: Phys. Rev. Lett. 52, 1116 (1984)

    Article  Google Scholar 

  11. Cooper, M.J., Laundy, D., Cardwell, D.A., Timms, D.N., Holt, R.S., Clark, G.: Phys. Rev. B 34, 5984 (1986)

    Article  Google Scholar 

  12. Thakkar, A.J., Simas, A.M., Smith Jr., V.H.: Mol. Phys. 41, 1153 (1980)

    Article  Google Scholar 

  13. Kato, T.: Commun. Pure Appl. Math. 10, 151 (1957)

    Article  MATH  Google Scholar 

  14. Benesch, R., Smith Jr., V.H.: In: Wave mechanics: the first fifty years. Price, W.C., Chissick, S.S., Ravensdale, T. (eds.). London: Butterworths 1973

  15. Hoffman-Ostenhof, M., Hoffman-Ostenhof, T.: Phys. Rev. A 16, 1782 (1977)

    Article  MathSciNet  Google Scholar 

  16. Thakkar, A.J.: J. Chem. Phys. 86, 5060 (1987)

    Article  Google Scholar 

  17. Sperber, G.: Int. J. Quantum Chem. 5, 189 (1971)

    Article  Google Scholar 

  18. Gadre, S.R., Gejji, S.P.: J. Chem. Phys. 80, 1175 (1984)

    Article  Google Scholar 

  19. Gadre, S.R., Chakravorty, S.J., Pathak, R.K.: J. Chem. Phys. 78, 4581 (1983)

    Article  Google Scholar 

  20. Galvez, F.J.: Phys. Rev. A 39, 501 (1989)

    Article  Google Scholar 

  21. Angulo, J.C., Dehesa, J.S., Galvez, F.J.: Phys. Rev. A 42, 4069 (1990); erratum Phys. Rev. A 43, 641 (1991)

    Article  Google Scholar 

  22. Angulo, J.C., Dehesa, J.S.: Phys. Rev. A 44, 1516 (1991)

    Article  Google Scholar 

  23. Westgate, W.M., Simas, A.M., Smith Jr., V.H.: J. Chem. Phys. 83, 4054 (1985)

    Article  Google Scholar 

  24. Kryachko, E.S., Koga, T.: J. Chem. Phys. 91, 1108 (1989)

    Article  Google Scholar 

  25. Sears, S.B., Gadre, S.R.: J. Chem. Phys. 75, 4626 (1981)

    Article  Google Scholar 

  26. Sears, S.B., Matcha, R.L.: J. Chem. Phys. 74, 589 (1981)

    Article  MathSciNet  Google Scholar 

  27. King, F.W.: J. Chem. Phys. 80, 4371 (1984)

    Article  Google Scholar 

  28. Yue, W., Janmin, L.: Phys. Scr. 30, 414 (1984)

    Article  Google Scholar 

  29. Antolin, J., Zarzo, A., Angulo, J.C.: Phys. Rev. A 48, 4149 (1993)

    Article  Google Scholar 

  30. Angulo, J.C., Antolin, J. Zarzo, A.: Z. Phys. D 28, 269 (1993)

    Article  Google Scholar 

  31. Zarzo, A., Angulo, J.C., Antolin, J.: J. Phys. B 26, 4663 (1993)

    Article  Google Scholar 

  32. Fraga, S., Malli, G.: Many electron systems: properties and interactions. Philadelphia: Saunders 1968

    Google Scholar 

  33. Bonham, R.A., Lee, J.S., Kennerly, R., St. John, W.: Adv. Quantum Chem. 11, 1 (1978)

    Article  Google Scholar 

  34. Pucci, R., March, N.H.: J. Chem. Phys. 76, 4089 (1982)

    Article  Google Scholar 

  35. King, F.W.: Phys. Rev. A 38, 6017 (1988)

    Article  Google Scholar 

  36. Porras, I., Galvez, F.J.: Phys. Rev. A 41, 4052 (1990)

    Article  Google Scholar 

  37. Defranceschi, M., Berthier, G.: J. Phys. France 51, 2791 (1990)

    Article  Google Scholar 

  38. Epstein, I.R.: Phys. Rev. A 8, 160 (1973)

    Article  Google Scholar 

  39. Manninen, S.: Phys. Rev. Lett. 59, 1557 (1987)

    Article  Google Scholar 

  40. Angulo, J.C., Dehesa, J.S., Galvez, F.J.: Z. Phys. D 18, 127 (1991)

    Article  Google Scholar 

  41. Corcoran, C.T., Langhoff, P.W.: J. Math. Phys. 18, 651 (1977)

    Article  MathSciNet  Google Scholar 

  42. Landau, H.J.: Bull. Am. Math. Soc. 16, 47 (1987)

    Article  MATH  Google Scholar 

  43. Ciulli, S., Mounsif, M., Gorman, N., Spearman, T.D.: J. Math. Phys. 32, 1717 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  44. Jaynes, E.T.: Phys. Rev. 106, 620 (1957) and 108, 171 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  45. Skilling, J., Bryan, R.K.: Mon. Not. R. Astr. Soc. 211, 111 (1984)

    MATH  Google Scholar 

  46. Liu, D.M., Wong, E.K.: Phys. Rep. 193, 41 (1990)

    Article  MathSciNet  Google Scholar 

  47. Antolin, J.: Phys. Rev. D 43, 1532 (1991)

    Article  Google Scholar 

  48. Koga, T.: Theor. Chim. Acta (Berlin) 64, 249 (1984)

    Article  Google Scholar 

  49. Antolin, J., Zarzo, A., Angulo, J.C.: Phys. Rev. A 50, 240 (1994)

    Article  Google Scholar 

  50. Angulo, J.C., Yafiez, R.J., Antolin, J., Zarzo, A.: Int. J. Quantum Chem. 56, 747 (1995)

    Article  Google Scholar 

  51. Corcoran, C.T., Langhoff, P.W.: Chem. Phys. Lett. 41, 609 (1976)

    Article  Google Scholar 

  52. Haydock, R. Heine, V., Kelly, M.: J. Phys. C 5, 2845 (1972)

    Article  Google Scholar 

  53. Frontini, M., Gautschi, V., Milovanovic, G.V.: Numer. Math. 50, 503 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  54. Escalas, E., Viano, G.A.: J. Math. Phys. 34, 5781 (1993)

    Article  MathSciNet  Google Scholar 

  55. Antolin, J.: J. Math. Phys. 31, 791 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  56. Leasenburg, M.J., Mead, L.R.: J. Math. Phys. 34, 6009 (1993)

    Article  MathSciNet  Google Scholar 

  57. Csiszar, I. Ann. Probab. 3, 146 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  58. Dowson, D.C., Wragg, A.: IEEE Trans. Inf. Theory IT-19, 689 (1973)

    Article  MathSciNet  Google Scholar 

  59. Tagliani, A., Frontini, M.: Private communication

  60. Clementi, E., Roetti, C.: At. Data Nucl. Data Tables 14, 177 (1974)

    Article  Google Scholar 

  61. McLean, A.D., McLean, R.S.: At. Data Nucl. Data Tables 26, 197 (1981)

    Article  Google Scholar 

  62. Kociszewski, A.: J. Phys. A 19, L823 (1986)

    Article  MATH  Google Scholar 

  63. Taghani, A.: J. Math. Phys. 34, 326 (1993)

    Article  MathSciNet  Google Scholar 

  64. Frontini, M., Taghani, A.: Entropy convergence in Stieltjes and Hamburger moment problem. Milano: Politecnico di Milano 1995 (Preprint)

    Google Scholar 

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Author notes

  1. A. Zarzo

    Present address: Departamento de Matemática Aplicada, ETS Ingenieros Industriales, Universidad Politecnica de Madrid, E-28006 Madrid, Spain

  2. J.C. Angulo

    Present address: Departamento de Física Moderna, Facultad de Ciencias, Universidad de Granada, E-18071, Granada, Spain

  3. R.J. Yáñez

    Present address: Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, E-18071, Granada, Spain

Authors and Affiliations

  1. 'Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain

    A. Zarzo, J.C. Angulo & R.J. Yáñez

  2. Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, E-50009, Zaragoza, Spain

    J. Antolín

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  1. A. Zarzo
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  2. J.C. Angulo
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  3. J. Antolín
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  4. R.J. Yáñez
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Zarzo, A., Angulo, J., Antolín, J. et al. Maximum-entropy analysis of one-particle densities in atoms. Z Phys D - Atoms, Molecules and Clusters 37, 295–299 (1996). https://doi.org/10.1007/s004600050043

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  • DOI: https://doi.org/10.1007/s004600050043

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