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Four-Component Electronic Structure Methods for Atoms

  • Chapter
Theoretical Chemistry and Physics of Heavy and Superheavy Elements

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 11))

Abstract

Four-component methods for high-accuracy atomic calculations are reviewed. The projected (or no-virtual-pair) Dirac-Coulomb-Breit Hamiltonian serves as the starting point and defines the physical framework. One-electron four-component Dirac-Fock-Breit functions, similar in spirit to Hartree-Fock orbitals in the nonrelativistic formulation, are calculated first, followed by treatment of electron correlation. Correlation methods include multiconfiguration Dirac-Fock and many-body perturbation theory or its all-order limit, the coupled cluster approach. The Fock-space CC and its extension to the intermediate Hamiltonian approach are described. Applications address mostly transition energies in various atoms. Very large basis sets, going up to l = 8, are used. High l orbitals are particularly important for transitions involving f electrons. The Breit term is required for fine-structure splittings and for f transitions. Representative applications are described, including the gold atom, with relativistic effects of 3–4 eV on transition energies; eka-gold (E111), where relativity changes the ground state from 6d 107s to 6d 97s 2; Pr3+, where the many f 2 levels are reproduced with great precision; Rf (E104), where opposite effects of relativity and correlation lead finally to a 7s 26d 2 ground state, ~0.3 eV below the 7s 26d7p predicted by MCDF; eka-lead (E114), a potential member of the “island of stability” forecast by nuclear physics, predicted to have ionization potentials higher than all other group-14 atoms except carbon; and eka-radon (E118), which has a unique property for a rare gas, positive electron affinity. Heavy anions are described, showing instances of multiple stable excited states. Finally, applications to properties other than energy are discussed.

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References

  1. Pyykkö P. Relativistic Theory of Atoms and Molecules, Vol. I, 1916–1985 (Springer-Verlag, Berlin, 1986); Vol. II 1986–1992 (Springer-Verlag, Berlin, 1993) Vol. III, 1993–1999 (Springer-Verlag, Berlin, 2000; http://www.csc.fi/lul/rtam.

    Google Scholar 

  2. See, e.g., Sucher J. in Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms, ed. Johnson W., Mohr P., and Sucher J. (American Institute of Physics, New York, 1989), p. 28.

    Google Scholar 

  3. Breit G. (1929) Phys. Rev. B34, 553;

    Google Scholar 

  4. Breit G. (1930) Phys. Rev. 36, 383;

    CAS  Google Scholar 

  5. Breit G. (1932) Phys. Rev. 39, 616.

    CAS  Google Scholar 

  6. Brown G.E. and Ravenhall D.G. (1951) Proc. Roy. Soc. A 208, 552.

    CAS  Google Scholar 

  7. Bethe H.A. and Salpeter E.E. Quantum Mechanics of One- and Two-Electron Atoms (Springer-verlag, Berlin, 1957).

    Google Scholar 

  8. Sucher J. (1980) Phys. Rev. A 22, 348; (1987) Phys. Scr. 36, 271.

    CAS  Google Scholar 

  9. Buchmüller W. and Dietz K. (1980) Z. Phys. C 5, 45.

    Google Scholar 

  10. Lindgren I. in Many-Body Methods in Quantum Chemistry, ed. Kaldor U., Lecture Notes in Chemistry Vol. 52 (Springer-Verlag, Heidelberg, 1989) p. 293;

    Google Scholar 

  11. Lindgren I. (1988) Nucl. Instrum. Methods B31, 102.

    CAS  Google Scholar 

  12. Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms, ed. Johnson W., Mohr P., and Sucher J. (American Institute of Physics, New York, 1989).

    Google Scholar 

  13. Mittleman M. (1971) Phys. Rev. A 4, 893;

    Google Scholar 

  14. Mittleman M. (1972) Phys. Rev. A 5, 2395;

    Google Scholar 

  15. Mittleman M. (1981) Phys. Rev. A 24, 1167.

    CAS  Google Scholar 

  16. Davydov A.S., Quantum Mechanics (NEO Press, Peaks Island, Maine, 1966) chap. vIII.

    Google Scholar 

  17. Kim Y.-K. (1967) Phys. Rev. 154, 17.

    CAS  Google Scholar 

  18. Kagawa T. (1975) Phys. Rev. A 12, 2245;

    CAS  Google Scholar 

  19. Kagawa T. (1980) Phys. Rev. A 22, 2340.

    CAS  Google Scholar 

  20. Johnson W.R. and Sapirstein J. (1986) Phys. Rev. Lett. 57, 1126;

    Google Scholar 

  21. Johnson W.R., Idrees M., and Sapirstein J., (1987) Phys. Rev. A 35, 3218;

    CAS  Google Scholar 

  22. Blundell S.A., Johnson W.R., Liu Z.W., and Sapirstein J. (1989) Phys. Rev. A 39, 3768;

    CAS  Google Scholar 

  23. Johnson W.R., Blundell S.A., and Sapirstein J. (1988) Phys. Rev. A 37, 307; (1988) Phys. Rev. A 37, 2764; (1990) Phys. Rev. A 41, 1689.

    CAS  Google Scholar 

  24. Quiney H.M., Grant I.P., and Wilson S. (1987) J. Phys. B 20 1413;

    CAS  Google Scholar 

  25. Quiney H.M., Grant I.P., and Wilson S. (1987) Phys. Scr. 36, 460;

    CAS  Google Scholar 

  26. Quiney H.M., Grant I.P., and Wilson S. in Many-Body Methods inQuanturm Chemistry, ed. Kaldor U., Lecture Notes in Chemistry Vol. 52 (Springer-Verlag, Heidelberg, 1989);

    Google Scholar 

  27. Quiney H.M., Grant I.P., and Wilson S. (1990) J. Phys. B 23, L271;

    CAS  Google Scholar 

  28. Grant I.P. and Quiney H.M., Adv. Atom. Molec. Phys. 23, 37 (1988).

    Google Scholar 

  29. Ishikawa Y., Binning R.C., and Sekino H. (1989) Chem. Phys. Lett. 160, 206;

    CAS  Google Scholar 

  30. Ishikawa Y. (1990) Phys. Rev. A 42, 1142;

    CAS  Google Scholar 

  31. Ishikawa Y. (1990) Chem. Phys. Lett. 166, 321;

    CAS  Google Scholar 

  32. Ishikawa Y. and Quiney H.M. (1993) Phys. Rev. A 47, 1732;

    CAS  Google Scholar 

  33. Ishikawa Y. and Koc K. (1994) Phys. Rev. A 50, 4733.

    CAS  Google Scholar 

  34. Johnson W. R. and Soff G. (1985) At. Data Nucl. Data Tables 33, 405.

    CAS  Google Scholar 

  35. Visscher L. and Dyall K. G. (1997) At. Data Nucl. Data Tables 67, 207.

    CAS  Google Scholar 

  36. Desclaux J.-P. (1975) Comput. Phys. Commun. 9, 31.

    Google Scholar 

  37. Grant I.P., McKenzie B.J., Norrington P.H., Mayers D.F., and Pyper N.C. (1980) Comput. Phys. Commun. 21, 207.

    CAS  Google Scholar 

  38. Ishikawa Y. and Kaldor U., in Computational Chemistry: Review of Current Trends, ed. Leszczynski J. (World Scientific, Singapore, 1996), vol. I, p. 1.

    Google Scholar 

  39. Kaldor U. and Eliav E. (1998) Adv. Quantum Chem. 31, 313.

    CAS  Google Scholar 

  40. Lee Y.-S. and McLean A.D. (1982) J. Chem. Phys. 76, 735.

    CAS  Google Scholar 

  41. Aerts P.J.C. and Nieuwpoort W.C. (1985) Chem. Phys. Lett. 113, 165; ibid. 125, 83 (1986).

    CAS  Google Scholar 

  42. Stanton R. E. and Havriliak S. (1984) J. Chem. Phys. 81, 1910.

    CAS  Google Scholar 

  43. Ishikawa Y., Baretty R., and Binning R.C. (1985) Intern. J. Quan-tum Chem. Symp. 19, 285;

    CAS  Google Scholar 

  44. Ishikawa Y. and Sekino H. (1990) Chem. Phys. Lett. 165, 243.

    CAS  Google Scholar 

  45. Ishikawa Y., Binning R.C., and Sando K.M. (1983) Chem. Phys. Lett. 101, 111;

    CAS  Google Scholar 

  46. Ishikawa Y., Binning R.C., and Sando K.M. (1984) Chem. Phys. Lett. 105, 189;

    CAS  Google Scholar 

  47. Ishikawa Y., Binning R.C., and Sando K.M. (1985) Chem. Phys. Lett. 117, 444;

    CAS  Google Scholar 

  48. Ishikawa Y., Baretty R., and Binning R.C. (1985) Chem. Phys. Lett. 121, 130;

    CAS  Google Scholar 

  49. Ishikawa Y. and Quiney H.M. (1987) Intern. J. Quantum Chem. Symp. 21, 523.

    CAS  Google Scholar 

  50. Smith F. C. and Johnson W. R. (1967) Phys. Rev. 160, 136.

    CAS  Google Scholar 

  51. Desclaux J. P. (1973) At. Data Nucl. Data Tables 12, 311.

    CAS  Google Scholar 

  52. Fricke B., Greiner W., and Waber J. T. (1977) Theor. Chim. Acta 21, 235.

    Google Scholar 

  53. Fricke B. and Soff G. (1977) At. Data Nucl. Data Tables 19, 83.

    CAS  Google Scholar 

  54. Lu C. C., Carlson T. A., Malik F. B., Tucker T. C., and Nestor C. W. (1971) At. Data 3, 1.

    CAS  Google Scholar 

  55. Mann J. B. and Waber J. T. (1970) J. Chem. Phys. 53, 2397.

    CAS  Google Scholar 

  56. Grant I. P. (1970) Adv. Phys. 19, 747;

    CAS  Google Scholar 

  57. Grant I.P. and Quiney H.M. (1988) Adv. At. Mol. Phys. 23, 37.

    Google Scholar 

  58. Dyall K. G., Grant I. P., Johnson C. T., Parpia F. A., and Plummer E. P. (1989) Comput. Phys. Commun. 55, 425.

    CAS  Google Scholar 

  59. Parpia F. A., Froese-Fischer C., and Grant I. P. (1996) Comput. Phys. Commun. 94, 249.

    CAS  Google Scholar 

  60. Rodrigues G. C., Ourdane M. A., Bieroń J., Indelicato P., and Lindroth E. (2000) Phys. Rev. A 63, 012510.

    Google Scholar 

  61. Vilkas M. J., Koc K., and Ishikawa Y. (1997) Chem. Phys. Lett. 280, 167;

    CAS  Google Scholar 

  62. Vilkas M. J., Ishikawa Y., and Koc K. (1998) Phys. Rev. E 58, 5096;

    CAS  Google Scholar 

  63. Vilkas M. J., Ishikawa Y., and Koc K. (1998) Intern. J. Quantum Chem. 70, 813.

    CAS  Google Scholar 

  64. Sapirstein J. (1998) Rev. Mod. Phys. 70, 55.

    CAS  Google Scholar 

  65. Vilkas M. J., Ishikawa Y., and Koc K. (1999) Phys. Rev. A 60, 2808;

    CAS  Google Scholar 

  66. Ishikawa Y., Vilkas M. J., and Koc M. (2000) Intern. J. Quantum Chem. 77, 433.

    CAS  Google Scholar 

  67. Coester F. (1958) Nucl. Phys. 7, 421;

    Google Scholar 

  68. Coester F. and Kümmel H. (1960) Nucl. Phys. 17, 477.

    CAS  Google Scholar 

  69. Čížek J. (1969) Adv. Chem. Phys. 14, 35.

    Google Scholar 

  70. Bartlett R. J. (1991) Theor. Chim. Acta 80, 71.

    CAS  Google Scholar 

  71. Salomonson S., Lindgren I., and Mårtensson A.-M (1980) Phys. Scr. 21, 351;

    CAS  Google Scholar 

  72. Lindgren I. and Morrison J., Atomic Many-Body Theory, 2nd ed. (Springer Verlag, Berlin, 1986).

    Google Scholar 

  73. Hughes S.R. and Kaldor U. (1992) Chem. Phys. Lett. 194, 99; ibid. 204, 339 (1993); (1993) Phys. Rev. A 47, 4705; (1993) J. Chem. Phys. 99, 6773; (1995) Intern. J. Quantum Chem. 55, 127.

    CAS  Google Scholar 

  74. Blundell S. A., Johnson W. R., Liu Z. W., and Sapirstein J. (1989) Phys. Rev. A 39, 3768;

    CAS  Google Scholar 

  75. Blundell S. A., Johnson W. R., Liu Z. W., and Sapirstein J. (1989) Phys. Rev. A 40, 2233;

    CAS  Google Scholar 

  76. Blundell S. A., Johnson W. R., and Sapirstein J. (1990) Phys. Rev. Lett. 65, 1411;

    Google Scholar 

  77. Blundell S. A., Johnson W. R., and Sapirstein J. (1991) Phys. Rev. A 43, 3407.

    CAS  Google Scholar 

  78. Liu Z. W. and Kelly H. P. (1991) Phys. Rev. A 43, 3305.

    CAS  Google Scholar 

  79. Salomonson S. and Öster P. (1989) Phys. Rev. A 40, 5548.

    CAS  Google Scholar 

  80. Pal S. and Mukherjee D. (1989) Adv. Quantum Chem. 20, 292.

    Google Scholar 

  81. Kaldor U. (1991) Theor. Chim. Acta 80, 427.

    CAS  Google Scholar 

  82. Kaldor U. and Eliav E. (1998) Adv. Quantum Chem. 31, 313.

    CAS  Google Scholar 

  83. Landau A., Eliav E., and Kaldor U. (1999) Chem. Phys. Lett. 313, 399;

    Google Scholar 

  84. Landau A., Eliav E., Ishikawa Y., and Kaldor U. (2000) J. Chem. Phys. 113, 9905;

    CAS  Google Scholar 

  85. Landau A., Eliav E., and Kaldor U. (2001) Adv. Quantum Chem. 39, 172.

    Google Scholar 

  86. Malrieu J.-P., Durand Ph., and Daudey J.-P. (1985) J. Phys. A 18, 809.

    CAS  Google Scholar 

  87. Eliav E., Kaldor U., and Ishikawa Y. (1994) Phys. Rev. A 49, 1724.

    CAS  Google Scholar 

  88. Eliav E., Kaldor U., and Ishikawa Y. (1994) Phys. Rev. A 50, 1121.

    CAS  Google Scholar 

  89. Mårtensson-Pendrill A.-M. in Methods in Computational Chemistry, Vol. 5, ed. Wilson S. (Plenum Press, New York, 1992) p. 99.

    Google Scholar 

  90. Johnson W. R., Liu Z. W., and Sapirstein J. (1996) At. Data Nucl. Data Tables 64, 279.

    CAS  Google Scholar 

  91. Blundell S. A., Johnson W. R., and Sapirstein J. (1992) Phys. Rev. D 45, 1602.

    CAS  Google Scholar 

  92. Moore C.E., Atomic Energy Levels, Natl. Bur. of Stand. (U.S.) Circ. No. 467 (U.S. GPO, Washington, DC, 1948).

    Google Scholar 

  93. Hay P.J., Wadt W.R., Kahn L.R., and Bobrowicz F.W. (1978) J. Chem. Phys. 69, 984.

    CAS  Google Scholar 

  94. Pizlo A., Jansen G., and Hess B.A. (1993) J. Chem. Phys. 98, 3945.

    CAS  Google Scholar 

  95. Eliav E., Kaldor U., Schwerdtfeger P., Hess B.A., and Ishikawa Y. (1994) Phys. Rev. Lett. 73, 3203.

    CAS  Google Scholar 

  96. E. Eliav, U. Kaldor, and Y. Ishikawa, (1995) Phys. Rev. A 52, 2765.

    CAS  Google Scholar 

  97. Eliav E., Kaldor U., Ishikawa Y., Seth M., and Pyykkö P. (1996) Phys. Rev. A 53, 3926.

    CAS  Google Scholar 

  98. Martin W.C., Zalubas R., and Hagan L. Atomic Energy Levels The Rare-Earth Elements, Natl. Bur. Stand. Ref. Data Series, NBS Circ. No. 60 (U.S. GPO, Washington, DC, 1978) .

    Google Scholar 

  99. Cai Z., Meiser Umar V., and Froese Fischer C. (1992) Phys. Rev. Lett. 68, 297.

    CAS  Google Scholar 

  100. Eliav E., Kaldor U., and Ishikawa Y. (1995) Phys. Rev. A 51, 225.

    CAS  Google Scholar 

  101. Hess B.A., Marian C.M., and Peyerimhoff S.D. in Modern Electronic Structure Theory, ed. Yarkony D.R. (World Scientific, Singapore, 1995) p. 152.

    Google Scholar 

  102. Keller O.L. (1984) Radiochim. Acta 37, 169.

    CAS  Google Scholar 

  103. See also Mann J. B., quoted by Fricke B. and Waber J. T. (1971) Actinides Rev. 1, 433.

    Google Scholar 

  104. Glebov V.A., Kasztura L., Nefedov V.S., and Zhuikov B.L. (1989) Radiochim. Acta 46, 117.

    CAS  Google Scholar 

  105. Johnson E., Fricke B., Keller O.L., Nestor C.W. Jr., and Tucker T. C. (1990) J. Chem. Phys. 93, 8041.

    CAS  Google Scholar 

  106. Desclaux J.-P. and Fricke B. (1980) J. Phys. 41, 943.

    CAS  Google Scholar 

  107. Eliav E., Kaldor U., and Ishikawa Y. (1995) Phys. Rev. Lett. 74, 1079.

    CAS  Google Scholar 

  108. Schädel M. (1995) Radiochim. Acta 70/71, 207.

    Google Scholar 

  109. Hofmann S. et al. (1995) Z. Phys. A 350, 277.

    CAS  Google Scholar 

  110. Hofmann S. et al. (1995) Z. Phys. A 350, 281.

    CAS  Google Scholar 

  111. Hofmann S. et al. (1996) Z. Phys. A 354, 229.

    CAS  Google Scholar 

  112. For a recent review see Hofmann S. (1998) Rep. Progr. Phys. 61, 639.

    CAS  Google Scholar 

  113. Oganessian Yu. Ts. et al. (1999) Phys. Rev. Lett. 83, 3154.

    CAS  Google Scholar 

  114. Ninov V. et al. (1999) Phys. Rev. Lett. 83, 1104.

    CAS  Google Scholar 

  115. Sobiczewski A. (1994) Phys. Part. Nuclei 25, 295;

    Google Scholar 

  116. Möller P. and Nix J. R. (1994) J. Phys. G 20, 1681;

    Google Scholar 

  117. Smolanczuk R., Skalski J., and Sobiczewski A. (1995) Phys. Rev. C 52, 1871.

    CAS  Google Scholar 

  118. Rutz K., Bender M., Bürvenich T., Schilling T., Reinhard P. G., Maruhn J. A., and Greiner W. (1997) Phys. Rev. C 56, 238.

    CAS  Google Scholar 

  119. Wiok S., Dobaczewski J., Heenen P. H., Magierski P., and Nazarewicz W.(1996) Nucl. Phys. A 611, 211.

    Google Scholar 

  120. Landau A., Eliav E., Ishikawa Y., and Kaldor U., (2001) J. Chem. Phys. 114, 2977.

    CAS  Google Scholar 

  121. Seth M., Fægri K., and Schwerdtfeger P. (1998) Angew. Chem. Int. Ed. 37, 2493.

    CAS  Google Scholar 

  122. Lide D. R. (Ed.), Handbook of Chemistry and Physics, 74th Ed., (CRC Press, Boca Raton FL, 1993).

    Google Scholar 

  123. Eliav E., Kaldor U., Ishikawa Y., and Pyykkö P., (1996) Phys. Rev. Lett. 77, 5350.

    CAS  Google Scholar 

  124. Eliav E., Shmuliyan S., Kaldor U., and Ishikawa Y. (1998) J. Chem. Phys. 109, 3954.

    CAS  Google Scholar 

  125. Hotop H. and Lineberger W. C. (1975) JPCRD 4, 539;

    CAS  Google Scholar 

  126. Hotop H. and Lineberger W. C. (1985) J. Phys. Chem. Ref. Data 14, 731.

    CAS  Google Scholar 

  127. Bahrim C. and Thumm U. (2000) Phys. Rev. A 61, 022722.

    Google Scholar 

  128. Fabrikant I.I. (1982) Opt. Spektrosk. 53, 223 [Opt. Spectrosc. (USSR) 53, 131].

    CAS  Google Scholar 

  129. Froese Fischer C. and Chen D. (1989) J. Mol. Struct. 199, 61.

    Google Scholar 

  130. Greene C. H., (1990) Phys. Rev. A 42, 1405.

    CAS  Google Scholar 

  131. Scheer M., Thogersen J., Bilodeau R. C., Brodie C. A., Haugen H. K., Andersen H. H., Kristensen P., and Andersen T. (1998) Phys. Rev. Lett. 80, 684.

    Google Scholar 

  132. Landau A., Eliav E., Ishikawa Y., and Kaldor U., (2001) J. Chem. Phys. 115, 2389.

    CAS  Google Scholar 

  133. Scheer M., Bilodeau R.C., and Haugen H.K. (1998) Phys. Rev. Lett. 80, 2562.

    CAS  Google Scholar 

  134. Scheer M., Bilodeau R.C., Thøgersen J., and Haugen H.K. (1998) Phys. Rev. A 57, R1493.

    Google Scholar 

  135. Williams W.W., Carpenter D.L., Covington A.M., Koepnick M.C., Calabrese D., and Thompson J.S. (1998) J. Phys. B 31, L341.

    CAS  Google Scholar 

  136. Williams W.W., Carpenter D.L., Covington A.M., Thompson J.S., Kvale T.J., and Seely D.G. (1998) Phys. Rev. A 58, 3582.

    CAS  Google Scholar 

  137. Carpenter D.L., Covington A.M., and Thompson J.S. (2000) Phys. Rev. A 61, 042501.

    Google Scholar 

  138. Arnau F., Mota F., and Novoa J.J. (1992) Chem. Phys. 166, 77.

    CAS  Google Scholar 

  139. Wijesundera W.P. (1997) Phys. Rev. A 55, 1785.

    CAS  Google Scholar 

  140. Eliav E., Ishikawa Y., Pyykkö P., and Kaldor U. (1997) Phys. Rev. A 56, 4532.

    CAS  Google Scholar 

  141. Malli G.L., Da Silva A.B.F., and Ishikawa Y. (1993) Phys. Rev. A 47, 143.

    CAS  Google Scholar 

  142. Sundholm D., Tokman M., Pyykkö P., Eliav E., and Kaldor U. (1999) J. Phys. B 32, 5853.

    CAS  Google Scholar 

  143. Davis V.T. and Thompson J.S. (2001) J. Phys. B 34, L433.

    CAS  Google Scholar 

  144. Covington A.M., Calabrese D., Thosmpson J.S., and Kvale T.J. (1998) J. Phys. B 31, L855.

    CAS  Google Scholar 

  145. Johnson W. R., Plante D. R., and Sapirstein J. (1995) Adv. Atom. Molec. Phys. 35, 255.

    CAS  Google Scholar 

  146. Safronova M. S., Johnsom W. R., and Safronova U. I. (1996) Phys. Rev. A 53, 4036;

    Google Scholar 

  147. Safronova M. S., Johnsom W. R., and Safronova U. I. (1997) J. Phys. B 30, 2375;

    CAS  Google Scholar 

  148. Safronova U. I., Derevianko A., Safronova M. S., and Johnson W. R. (1999) J. Phys. B 32, 3527.

    CAS  Google Scholar 

  149. Safronova M. S., Johnson W. R., and Derevianko A. (1999) Phys. Rev. A 60, 4476.

    CAS  Google Scholar 

  150. Bieroń J., Parpia F. A., Froese Fischer C., and Jönsson P. (1995) PRA 51, 4603;

    Google Scholar 

  151. Bieroń J., Jönsson P., and Froese Fischer C. (1996) Phys. Rev. A 53, 2181;

    Google Scholar 

  152. Bieroń J., and Grant I. P. (1998) Phys. Rev. A 58, 4401;

    Google Scholar 

  153. Bieroń J. (1999) Phys. Rev. A 59, 4295.

    Google Scholar 

  154. Indelicato S., Boucard P., and Lindroth E. (1998) Eur. J. Phys. D 3, 29.

    CAS  Google Scholar 

  155. Hartley C. A., Lindroth E., and Mårtensson-Pendrill A.-M. (1990) J. Phys. B 23, 1990;

    Google Scholar 

  156. Hartley C. A. and Mårtensson-Pendrill A.-M. (1990) Z. Phys. D 15, 309;

    CAS  Google Scholar 

  157. Hartley C. A. and Mårtensson-Pendrill A.-M. (1991) J. Phys. B 24, 1193.

    CAS  Google Scholar 

  158. Pyykkö P. (2001) Molec. Phys. 99, 1617.

    Google Scholar 

  159. Bieroń J., Pyykkö P., Sundholm D., Kellö V., and Sadlej A. J. (2001) Phys. Rev. A 64, 052507.

    Google Scholar 

  160. Eliav E., Kaldor U., and Ishikawa Y. (1995) Phys. Rev. A 52, 291.

    CAS  Google Scholar 

  161. Eliav E., Kaldor U., and Ishikawa Y. (1998) Molec. Phys. 94, 181.

    CAS  Google Scholar 

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Authors and Affiliations

  1. School of Chemistry, Tel Aviv University, Tel Aviv, Israel

    Uzi Kaldor, Ephraim Eliav & Arie Landau

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  1. Uzi Kaldor
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  2. Ephraim Eliav
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  1. School of Chemistry, Tel Aviv University, Tel Aviv, Israel

    U. Kaldor

  2. Rutherford Appleton Laboratory, Chilton, Oxfordshire, England

    S. Wilson

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Kaldor, U., Eliav, E., Landau, A. (2003). Four-Component Electronic Structure Methods for Atoms. In: Kaldor, U., Wilson, S. (eds) Theoretical Chemistry and Physics of Heavy and Superheavy Elements. Progress in Theoretical Chemistry and Physics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0105-1_5

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