Semiempirical Relativistic Molecular Structure Calculations

  • Pekka Pyykkö

Abstract

The consequences of relativistic effects on the chemical properties of heavy elements have been discussed in several reviews(1–7); others are quoted in Refs. 5–7. A concise overview is given in Figure 1.

Keywords

Mercury Boron Hydride Porphyrin 207Pb 

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References

  1. 1.
    P. Pyykkö, Relativistic quantum chemistry, Adv. Quantum Chem 11, 353–409 (1978) (see Chap. XI: Relativity and the periodic table).CrossRefGoogle Scholar
  2. 2.
    K. S. Pitzer, Relativistic effects on chemical properties, Acc. Chem. Res. 12, 271–276 (1979).CrossRefGoogle Scholar
  3. 3.
    P. Pyykkö and J. P. Desclaux, Relativity and the periodic system of elements. Acc. Chem. Res. 12, 276–281 (1979).CrossRefGoogle Scholar
  4. 4.
    P. A. Christiansen, W. C. Ermler, and K. S. Pitzer, Relativistic effects in chemical systems, Ann. Rev. Phys. Chem. 36, 407–432 (1985).CrossRefGoogle Scholar
  5. 5.
    P. Pyykkö, Relativistic Theory of Atoms and Molecules. A Bibliography 1916–1985 Lecture Notes in Chemistry, Vol. 41, Springer-Verlag, Berlin (1986).Google Scholar
  6. 6.
    K. Balasubramanian and K. S. Pitzer, Relativistic quantum chemistry, Adv. Chem. Phys. 67, 287–319 (1987).CrossRefGoogle Scholar
  7. 7.
    P. Pyykkö, Relativistic effects in structural chemistry. Chem. Rev 88, 563–594 (1988).CrossRefGoogle Scholar
  8. 8.
    J. P. Desclaux, Relativistic Dirac–Fock expectation values for atoms with Z = 1 to Z = 120, At. Data Nucl. Data Tables 12, 311–406 (1973).CrossRefGoogle Scholar
  9. 9.
    T. Ziegler, J. G. Snijders, and E. J. Baerends, On the origin of relativistic bond contrac-tion, Chem. Phys. Lett 75, 1–4 (1980).CrossRefGoogle Scholar
  10. 10.
    R. Hoffmann, T. A. Albright, and D. L. Thorn, Theoretical aspects of the coordination of molecules to transition metal centers, Pure Appl. Chem. 50, 55–64 (1978).CrossRefGoogle Scholar
  11. 11.
    A. D. Buckingham, P. Pyykkö, J. B. Robert, and L. Wiesenfeld, Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited, Mol. Phys. 46, 177–182 (1982).CrossRefGoogle Scholar
  12. 12.
    R. G. Egdell, M. Hotokka, L. Laaksonen, P. Pyykkö, and J. G. Snijders, Photoelectron spectra and their relativistic interpretation for gaseous bismuth trihalides, Chem. Phys. 72, 237–247 (1982).CrossRefGoogle Scholar
  13. 13.
    I. B. Bersuker, S. S. Budnikov, and B. A. Leizerov, Quasi-relativistic approximation in the SCF-MO-LCAO method, Int. J. Quantum Chem. 6, 849–858 (1972).CrossRefGoogle Scholar
  14. 14.
    I. B. Bersuker, S. S. Budnikov, and B. A. Leizerov, Quasirelativistic approximation in the MO LCAO approach including the Breit terms (in Russian), Teor. Eksp. Khim. 10, 586–589 (1974).Google Scholar
  15. 15.
    A. Rosen and D. E. Ellis, Relativistic molecular wavefunctions: XeF2, Chem. Phys. Lett. 27, 595–599 (1974).CrossRefGoogle Scholar
  16. 16.
    W. C. Mackrodt, Estimates of some molecular relativistic energies from single-centre expansions, Mol. Phys. 18, 697–709 (1970).CrossRefGoogle Scholar
  17. 17.
    J. P. Desclaux and P. Pyykkö, Relativistic and non-relativistic Hartree-Fock one-centre expansions calculations for the series CH4 to PbH4 within the spherical approximation, Chem. Phys. Lett 29, 534–539 (1974).CrossRefGoogle Scholar
  18. 18.
    L. A. Hemstreet, Jr., Cluster calculations of the effects of single vacancies of the electronic properties of PbS, Phys. Rev. B 11, 2260–2270 (1975).CrossRefGoogle Scholar
  19. 19.
    C. Y. Yang, Relativistic scattered-wave calculations for C2 and I2, Chem. Phys. Lett. 41, 588–592 (1976).CrossRefGoogle Scholar
  20. 20.
    G. Das and A. C. Wahl, A modified pseudopotential approach to the heavy-atomic molecular systems: application to the x 2Σ½+, A 2½, and A 3½ states of the HgH molecule, J. Chem. Phys. 64 4672–4679 (1976).CrossRefGoogle Scholar
  21. 21.
    J. G. Snijders, E. J. Baerends, and P. Ros, A perturbation theory approach to relativistic calculations. Part II. Molecules, Mol. Phys. 38, 1909–1929 (1979).CrossRefGoogle Scholar
  22. 22.
    Y. S. Lee and A. D. McLean, Relativistic effects on R e and D e in AgH and AuH from all-electron Dirac–Hartree–Fock calculations. J. Chem. Phys. 76, 735–736 (1982).CrossRefGoogle Scholar
  23. 23.
    C. P. Wood and N. C. Pyper, Ab initio relativistic calculation for (E113)2, Chem. Phys. Lett. 84, 614–621 (1981).CrossRefGoogle Scholar
  24. 24.
    L. Laaksonen and I. P. Grant, Two-dimensional fully numerical solution of molecular Dirac equations. One-electron molecules, Chem. Phys. Lett. 109, 485–487 (1984).CrossRefGoogle Scholar
  25. 25.
    G. L. Malli and N. C. Pyper, Ab initio fully relativistic molecular calculations: Bonding in gold hydride, Proc. R. Soc. London Ser. A 407, 377–404 (1986).CrossRefGoogle Scholar
  26. 26.
    G. L. Malli (ed.), Relativistic Effects in Atoms, Molecules and Solids, Plenum Press, New York (1983).Google Scholar
  27. 27.
    P. Pyykkö (ed.), Proc. Symp. Rel. Effects Quantum Chemistry (Åbo, Finland, 1982), Int. J. Quantum Chem. 25(1), 1–271 (1984).Google Scholar
  28. 28.
    Proc. Adriatico ‘Research Cont. Relativistic Many-Body Problems,’ Trieste 1986 Phys. Scr. 36, 393–499 (1987).Google Scholar
  29. 29.
    R. S. Mulliken, Quelques aspects de la théorie des orbitales moléculaires, J. Chim. Phys. 46, 497–542 (1949).Google Scholar
  30. 30.
    M. Wolfsberg and L. Helmholz, The spectra and electronic structure of the tetrahedral ions Mn04-, Cr04--, and C104-, J. Chem. Phys. 20, 837–843 (1952).CrossRefGoogle Scholar
  31. 31.
    R. G. Woolley, Estimates for the extended Hueckel constant K, Nouv. J. Chim. 5, 227–232 (1981).Google Scholar
  32. 32.
    C. J. Ballhausen and H. B. Gray, The electronic structure of the vanadyl ion, Inorg. Chem. 1, 111–122 (1962).CrossRefGoogle Scholar
  33. 33.
    H. C. Longuet-Higgins and M. de V. Roberts, The electronic structure of the borides MB6, Proc. R. Soc. London Ser. A 224, 336–347 (1954);CrossRefGoogle Scholar
  34. b.
    H. C. Longuet-Higgins and M. de V. Roberts, The electronic structure of an icosahedron of boron atoms, Proc. R. Soc. London Ser. A 230, 110–119 (1955).CrossRefGoogle Scholar
  35. 34.
    E. B. Moore, Jr., L. L. Lohr, Jr., and W. N. Lipscomb, Molecular Orbitals in some boron compounds, J. Chem. Phys. 35, 1329–1334 (1961)CrossRefGoogle Scholar
  36. b.
    L. L. Lohr, Jr. and W.N. Lipscomb, Molecular orbital theory of spectra of Cr3+ ions in crystals, J. Chem. Phys. 38, 1607–1612 (1965).CrossRefGoogle Scholar
  37. 35.
    R. Hoffmann and W. N. Lipscomb, Theory of polyhedral molecules. I. Physical factorizations of the secular equation, J. Chem. Phys. 36, 2179–2189 (1962);CrossRefGoogle Scholar
  38. b.
    R. Hoffmann and W. N. Lipscomb, Boron hydrides: LCAO-MO and resonance studies, J. Chem. Phys. 37, 2872–2883 (1962).CrossRefGoogle Scholar
  39. 36.
    R. Hoffmann, An extended Hueckel theory. I. Hydrocarbons, J. Chem. Phys. 39, 1397–1412 (1963).CrossRefGoogle Scholar
  40. 37.
    J. H. Ammeter, H.-B. Bürgi, J. C. Thibeault, and R. Hoffmann, Counterintuitive orbital mixing in semiempirical and ab initio molecular orbital calculations, J. Am. Chem. Soc. 100, 3686–3692 (1978).CrossRefGoogle Scholar
  41. 38.
    R. Hoffmann, EXTHUC, QCPE, 30 (1964).Google Scholar
  42. 39.
    J. Howell, A. Rossi, D. Wallace, K. Haraki, and R. Hoffmann, FORTICON 8, QCPE, 344 (1977).Google Scholar
  43. 40.
    T. A. Albright, J. K. Burdett, and M. H. Whangbo, Orbital Interactions in Chemistry, Wiley, New York (1985).Google Scholar
  44. 41.
    R. Hoffmann and C. Zheng, Moving from discrete molecules to extended structures: A chemical and theoretical approach to the solid state, in: Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry (A. Veillard, ed.), Reidel, Dordrecht (1987).Google Scholar
  45. 42.
    H. Basch, A. Viste, and H. B. Gray, Valence orbital ionization potentials from atomic spectral data, Theor. Chim. Acta 3, 458–464 (1965);CrossRefGoogle Scholar
  46. b.
    H. Basch, A. Viste, and H. B. Gray, Molecular orbital theory for octahedral and tetrahedral metal complexes, J. Chem. Phys. 44, 10–19 (1966).CrossRefGoogle Scholar
  47. 43.
    M. Zerner and M. Couterman, Porphyrins. IV. Extended Hueckel calculations on transition metal complexes, Theor. Chim. Acta 4, 44–63 (1966).CrossRefGoogle Scholar
  48. 44.
    A. Viste and H. B. Gray, The electronic structure of the permanganate ion, Inorg. Chem. 3, 1113–1123 (1964).CrossRefGoogle Scholar
  49. 45.
    S. Larsson and P. Pyykkö, Relativistically parameterized extended Hueckel calculations. IX. An iterative version with applications to some xenon, thorium and uranium compounds, Chem. Phys. 101, 355–369 (1986).CrossRefGoogle Scholar
  50. 46.
    D. A. Liberman, D. T. Cromer, and J. T. Waber, Relativistic self-consistent field program for atoms and ions, Comp. Phys. Commun. 2, 107–113 (1971).CrossRefGoogle Scholar
  51. 47.
    K. Tatsumi and A. Nakamura, Actinide-to-carbon bonds in cp2 An (alkyl)2,— (butadiene),—(metalla-cyclopentadiene), and—(cyclobutadiene) complexes, J. Am. Chem. Soc. 109, 3195–3206 (1987).CrossRefGoogle Scholar
  52. 48.
    G. Berthier, P. Millie, and A. Veillard, Recherches théoriques sur les complexes. I. Une méthode de calcul des orbitales moléculaires dans les complexes des métaux de transition, J. Chim. Phys. 62, 8–19 (1965).Google Scholar
  53. 49.
    P. Millie and A. Veillard, Recherches théorique sur les complexes. II. Complexes cyanés du fer, du cobalt, du nickel et composés analogues, J. Chim. Phys. 62, 20–31 (1965).Google Scholar
  54. 50.
    M. D. Newton, F. B. Boer, and W. N. Lipscomb, Molecular orbitals for organic systems parametrized from SCF model calculations, J. Am. Chem. Soc. 88, 2367–2384 (1966).CrossRefGoogle Scholar
  55. 51.
    F. E. Harris, A. Trautwein, and J. Delhalle, FAKE molecular-orbital calculations, Chem. Phys. Lett. 72, 315–318 (1980).CrossRefGoogle Scholar
  56. 52.
    C. K. Jørgensen, S. M. Horner, W. E. Hatfield, and S. Y. Tyree Jr., Influence of Madelung (interatomic Coulomb) energy on Wolfsberg-Helmholz calculations, Int. J. Quantum Chem. 1, 191–215 (1967).CrossRefGoogle Scholar
  57. 53.
    S. Aronowitz, L. Coyne, J. Lawless, and J. Rishpon, Quantum-chemical modeling of smectite clays, Inorg. Chem. 21, 3589–3593 (1982).CrossRefGoogle Scholar
  58. 54.
    M. B. Hall and R. F. Fenske, Electronic structure and bonding in methyl-and perfluoromethyl (pentacarbonyl) manganese, Inorg. Chem. 11, 768–775 (1972).CrossRefGoogle Scholar
  59. 55.
    M. Grodzicki, A self-consistent charge Xα method. I. Theory, J. Phys. B: At. Mol. Phys. 13, 2683–2691 (1980).CrossRefGoogle Scholar
  60. 56.
    R. G. Parr, Quantum Theory of Molecular Electronic Structure, Benjamin, New York (1963).Google Scholar
  61. 57.
    C. J. Ballhausen and H. B. Gray, Molecular Orbital Theory, Benjamin, New York (1964).Google Scholar
  62. 58.
    R. Rein, G. A. Clarke, and F. E. Harris, Iterative extended Hiickel studies of electronic structure with aplication to heterocyclic compounds, in Quantum Aspects of Heterocyclic Compounds in Chemistry (E. D. Bergmann and B. Pullman, eds.) Israel Acad. Sci. Hum., Jerusalem (1970), pp. 86–117.Google Scholar
  63. 59.
    O. Sinanoglu and K. B. Wiberg (ed.), Sigma Molecular Orbital Theory, Yale Univ. Press, New Haven (1970).Google Scholar
  64. 60.
    S. P. McGlynn, L. G. Vanquickenborne, M. Kinoshita, and D. G. Carroll, Applied Quantum Chemistry, Holt, Rinehart and Winston, New York (1972).Google Scholar
  65. 61.
    B. M. Gimarc, Molecular Structure and Bonding. The Qualitative Molecular Orbital Approach, Academic Press, New York (1979).Google Scholar
  66. 62.
    G. Del Re, G. Berthier, and J. Serre, Electronic States of Molecules and Atom Clusters. Foundations and Prospects of Semiempirical Methods, Lecture Notes in Chemistry 13, Springer-Verlag, Berlin (1980).Google Scholar
  67. 63.
    M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York (1969).Google Scholar
  68. 64.
    J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory, McGraw-Hill, New York (1970).Google Scholar
  69. 65.
    G. Klopman and B. O’Leary, All-valence electrons S.C.F. calculations, Topics Current Chem. 15, 445–534 (1970).Google Scholar
  70. 66.
    G. A. Segal (ed.), Semiempirical Methods of Electronic Structure Calculation, Parts A and B, Plenum, New York (1977).Google Scholar
  71. 67.
    J. Sadlej, Semi-Empirical Methods of Quantum Chemistry, Ellis Horwood, Chichester (1985).Google Scholar
  72. 68.
    J. A. Pople, D. P. Santry, and G. A. Segal, Approximate self-consistent molecular orbital theory. I. Invariant procedures, J. Chem. Phys. 43, S129-S135 (1965).CrossRefGoogle Scholar
  73. 69.
    J. L. Berkosky, F. O. Ellison, T. H. Lee, and J. W. Rabalais, Model for calculating spin-orbit interactions with application to photoelectron spectroscopy, J. Chem. Phys. 59, 5342–5349 (1973).CrossRefGoogle Scholar
  74. 70.
    B. D. Bird and P. Day, Analysis of the charge-transfer spectra of some first-transition-series tetrahalide complexes, J. Chem. Phys. 49, 392–403 (1968).CrossRefGoogle Scholar
  75. 71.
    H. Bock and B. G. Ramsey, Photoelectron spectra of nonmetal compounds and their interpretation by MO models, Angew. Chem. (Int. Ed.) 12, 734–752 (1973).CrossRefGoogle Scholar
  76. 72.
    N. B. Borkovskii and A. M. Lyudchik, Electronic structure of uranyl halide complexes including spin-orbit interactions (in Russian), Dokl. Akad. Nauk Belor. SSR 29(2), 137–140 (1985).Google Scholar
  77. 73.
    F. Brogli and E. Heilbronner, The competition between spin orbit coupling and conjugation in alkyl halides and its repercussion on their photoelectron spectra, Helv. Chim. Acta 54, 1423–1434 (1971).CrossRefGoogle Scholar
  78. 74.
    P. Burroughs, S. Evans, A. Hamnett, A. F. Orchard, and N. V. Richardson, Evidence from the photoelectron spectra of some mercury (II) compounds for the involvement of the inner 5d electrons in covalent bonding, Chem. Commun. 921–922 (1974).Google Scholar
  79. 75.
    L. C. Cusachs, F. A. Grimm, and G. K. Schweitzer, Theoretical insights relating to the photoelectron spectra of gaseous halides of the group 2B metals, J. El. Sp. Rel. Phen. 3, 229–231 (1974).CrossRefGoogle Scholar
  80. 76.
    R. N. Dixon, J. N. Murell, and B. Narayan, The photoelectron spectra of the halomethanes, Mol. Phys. 20, 611–623 (1971).CrossRefGoogle Scholar
  81. 77.
    J. C. Green, M. L. H. Green, P. J. Joachim, A. F. Orchard, and D. W. Turner, A study of the bonding in group IV tetrahalides by photoelectron spectroscopy, Phil. Trans. R. Soc. (London) Ser.A 268, 111–130 (1970).CrossRefGoogle Scholar
  82. 78.
    R. Gleiter, H. Köppel, P. Hofmann, H. R. Schmidt, and J. Ellermann, Electronic struc-ture of the P3, As3, and Sb3 units in a nortricyclane skeleton, Inorg. Chem. 24, 4020–4023 (1985).CrossRefGoogle Scholar
  83. 79.
    M. B. Hall, A semiquantitative model of spin-orbit coupling in doublet states and its application to the photoelectron spectra of diatomic halogens, Int. J. Quantum Chem. S9, 237–243 (1975).Google Scholar
  84. 80.
    M. B. Hall, The use of spin-orbit coupling in the interpretation of photoelectron spectra. I. Application to substituted rhenium pentacarbonyls, J. Am. Chem. Soc. 97, 2057–2065 (1975).CrossRefGoogle Scholar
  85. 81.
    L. E. Harris, H. J. Maria, and S. P. McGlynn, Spin-orbit coupling in nitrite ion and nitrite salts, Czech. J. Phys. B20, 1007–1017 (1970).CrossRefGoogle Scholar
  86. 82.
    M. Jungen, Spin-Bahn-Kopplungseffekte verschiedener Ordnung bei Jod und Dijodazetylen, Theor. Chim. Acta 27, 33–47 (1972).CrossRefGoogle Scholar
  87. 83.
    S.-T. Lee, S. Süzer, and D. A. Shirley, Relativistic effects in the UV photoelectron spectra of group VI diatomic molecules, Chem. Phys. Lett. 41, 25–28 (1976).CrossRefGoogle Scholar
  88. 84.
    T. H. Lee and J. W. Rabalais, Model for spin-orbit interactions with inclusion of d elec-trons: Applications to photoelectron spectroscopy, J. Chem. Phys. 60, 1172–1176 (1974).CrossRefGoogle Scholar
  89. 85.
    A. M. Lyudchik and N. B. Borkovskii, Nonrelativistic-to-relativistic conversion of molecular electronic-structure calculations (in Russian), Dokl. Akad. Nauk Belor. SSR 28, 624–627 (1984).Google Scholar
  90. 86.
    A. M. Lyudchik and A. B. Kovrikov, Use of semiempirical methods for the calculation of spin-orbit interaction constants in linear molecules (in Russian), Dokl. Akad. Nauk Belor. SSR 25, 317–320 (1981).Google Scholar
  91. 87.
    R. Manne, K. Wittel, and B. S. Mohanty, Spin-orbit interaction in molecular photoelectron spectra. An intermediate coupling approach, Mol. Phys. 29, 485–500 (1975).CrossRefGoogle Scholar
  92. 88.
    D. P. Nanda and B. S. Mohanty, Calculation of multiplet splittings of A 2 states of some diatomic alkaline-earth halides by extended Hueckel approach, Indian J. Pure Appl. Phys. 18, 324–326 (1980).Google Scholar
  93. 89.
    A. W. Potts and M. L. Lyus, Photoelectron spectra of the valence d shell of T1(I), In(I), Pb(II) and Sn(II) halides, J. Electron Spin Rel. Phen. 13, 327–336 (1978).CrossRefGoogle Scholar
  94. 90.
    K. Wittel, Spin-orbit coupling in I2+, Chem. Phys. Lett. 15, 555–557 (1972).CrossRefGoogle Scholar
  95. 91.
    K. Wittel, H. Bock, A. Haas, and K. H. Pflegler, Photoelectron spectra and molecular properties. XLVII. F3C-substituted mercury compounds, J. Electron Spin Rel. Phen. 7, 365–376 (1975).CrossRefGoogle Scholar
  96. 92.
    K. Wittel, H. Bock, and R. Manne, Photoelectron spectra of iodo ethylenes. A simple method to incorporate spin-orbit coupling in molecular orbital models, Tetrahedron 30, 651–658 (1974).CrossRefGoogle Scholar
  97. 93.
    K. Wittel and R. Manne, Atomic spin-orbit interaction parameters from spectral data for 19 elements, Theor. Chim. Acta 33, 347–349 (1974).CrossRefGoogle Scholar
  98. 94.
    K. Wittel and R. Manne, Photoelectron spectrum and structure of Gal3, J. Chem. Phys. 63, 1322–1323 (1975). (This sample was later shown to be dimeric!)CrossRefGoogle Scholar
  99. 95.
    K. Wittel, B. S. Mohanty, and R. Manne, Higher-order spin-orbit interaction in photoelectron spectra of mercury halides, J. Electron Spin Rel. Phen. 5, 1115–1124 (1974).CrossRefGoogle Scholar
  100. 96.
    M. Wu and T. P. Fehlner, Valence level photoelectron spectra of some heavy group 4–6 diatomic molecules, J. Am. Chem. Soc. 98, 7578–7585 (1976).CrossRefGoogle Scholar
  101. 97.
    R. L. Ellis, R. Squire, and H. H. Jaffe, Use of the CNDO method in spectroscopy. V. Spin orbit coupling, J. Chem. Phys. 55, 3499–3505 (1971).CrossRefGoogle Scholar
  102. 98.
    F. A. Grimm, A semi-empirical method for the calculation of spin-orbit splitting in degenerate electronic states of linear polyatomic molecules, J. Electron Spin Rel. Phen. 2, 475–481 (1973).Google Scholar
  103. 99.
    R. K. Hinkley, T. E. H. Walker, and W. G. Richards, Spin–orbit coupling constants from semi-empirical wavefunctions, Mol. Phys. 24, 1095–1102 (1972).CrossRefGoogle Scholar
  104. 100.
    R. G. Hyde and J. B. Peel, Non-empirical valence-electron calculations on the diatomic halogens and interhalogens, J. Chem. Soc. Faraday II 72, 571–578 (1976).CrossRefGoogle Scholar
  105. 101.
    R. G. Hyde and J. B. Peel, Non-empirical valence electron molecular orbital calculations: spin–orbit splitting in the ion states of the tin and antimony halides, Mol. Phys. 33, 887–896 (1977).CrossRefGoogle Scholar
  106. 102.
    M. LiŠka, P. Pelikán, P. Černay, and L. Turi Nagy, Molecular orbital calculation of spin-orbit splittings in some halogeno-compounds, J. Mol. Struct. 72, 177–181 (1981).CrossRefGoogle Scholar
  107. 103.
    S. L. Altmann, Rotations, Quaternions, and Double Groups, Clarendon Press, Oxford (1986), and forthcoming work.Google Scholar
  108. 104.
    G. Herzberg, Molecular Spectra and Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, Van Nostrand, Princeton (1966).Google Scholar
  109. 105.
    G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the Thirty-Two Point Groups, MIT Press, Cambridge, Massachusetts (1963).Google Scholar
  110. 106.
    P. Pyykkö and H. Toivonen, Tables of representation and rotation matrices for the relativistic irreducible representations of 38 point groups, Acta Acad. Aboensis, Ser. B 43(2), 1–50 (1983) (reprints still available from the author).Google Scholar
  111. 107.
    J. B. Newman, Exchange and relativistic effects on pi bonding in the uranyl ion, J. Chem. Phys. 43, 1691–1694 (1965).CrossRefGoogle Scholar
  112. 108.
    R. G. Hayes and N. Edelstein, An elementary molecular orbital calculation on U(C8H8)2, Np(C8H8)2, and Pu(C8H8)2, J. Am. Chem. Soc. 94, 8688–8691 (1972).CrossRefGoogle Scholar
  113. 109.
    D. W. Hafemeister, Relativistic corrections to the electron density at the nuclear surface and to the alkali halide overlap integrals, J. Chem. Phys. 46, 1929–1934 (1967).CrossRefGoogle Scholar
  114. 110.
    K. Tatsumi and R. Hoffmann, Bent cis d0 MoO22+ vs. linear trans d 0 f 0 UO22+: A significant role for nonvalence 6p orbitals in uranyl, Inorg. Chem. 19, 2656–2658 (1980).CrossRefGoogle Scholar
  115. 111.
    K. Tatsumi and R. Hoffmann, δ vs. π bonding to organo-actinides and possibilities of CO coordination to actinides, Inorg. Chem. 23, 1633–1634 (1984).CrossRefGoogle Scholar
  116. 112.
    K. Tatsumi and A. Nakamura, Electronic structures of tris (cyclopentadienyl) uranium(IV)-ligand complexes, J. Organomet. Chem. 272, 141–154 (1984).CrossRefGoogle Scholar
  117. 113.
    K. Tatsumi and A. Nakamura, On the uranium-to-carbon bonds in cp3 UL complexes, in Applied Quantum Chemistry (V. H. Smith Jr., ed.), Reidel, Dordrecht (1986), pp. 299–311.CrossRefGoogle Scholar
  118. 114.
    K. Tatsumi and A. Nakamura, Unusual Th-C-C angles in bis(cyclopentadienyl)-dialkyl complexes of thorium, Organometallics 6, 427–428 (1987).CrossRefGoogle Scholar
  119. 115.
    K. Tatsumi, A. Nakamura, P. Hofmann, R. Hoffmann, K. G. Moloy, and T.J. Marks, Double carbonylation of actinide bis(cyclopentadienyl) complexes. Experimental and theoretical aspects, J. Am. Chem. Soc. 108, 4467–4476 (1986).CrossRefGoogle Scholar
  120. 116.
    K. Tatsumi, A. Nakamura, P. Hofmann, P. Stauffert, and R. Hoffmann, CO activation by biscyclopentadienyl complexes of group 4 metals and actinides: η2-acyl complexes, J. Am. Chem. Soc. 107, 4440–4451 (1985).CrossRefGoogle Scholar
  121. 117.
    R. E. Cramer, A. L. Mori, R. B. Maynard, J. W. Gilje, K. Tatsumi, and A. Nakamura, Structure and bonding of a nearly homoleptic uranium phosphoylide complex, J. Am. Chem. Soc. 106, 5920–5926 (1984).CrossRefGoogle Scholar
  122. 118.
    F. A. Cotton and C. B. Harris, Molecular orbital calculations for complexes of heavier transition elements. I. Study of parameter variation in the case of tetrachloro-platinate (II), Inorg. Chem. 6, 369–376 (1967).CrossRefGoogle Scholar
  123. 119.
    M. J. S. Dewar, G. L. Grady, K. M. Merz, Jr., and J. J. P. Stewart, MNDO calculations for compounds containing mercury, Organometallics 4, 1964–1966 (1985).CrossRefGoogle Scholar
  124. 120.
    M. J. S. Dewar, M. K. Holloway, G. L. Grady, and J. J. P. Stewart, MNDO calculations for compounds containing lead, Organometallics 4, 1973–1980 (1985).CrossRefGoogle Scholar
  125. 121.
    R. C. Baetzold, Electronic properties of metal clusters: Size effects, Inorg. Chem. 20, 118–123 (1981).CrossRefGoogle Scholar
  126. 122.
    R. Jostes, A. Müller, and E. Diermann, Electronic structure and spectra of oxothiometalates Electronic structure and spectra of oxothiometalates MO4-nSn2- (M = Mo, W; n = 0-4), J. Mol. Struct. (Theochem.) 137, 311–328 (1986).CrossRefGoogle Scholar
  127. 123.
    S. C. Richtsmeier, J. L. Gole, and D. A. Dixon, Theoretical prediction of the vibrational spectra of group IB trimers, Proc. Natl. Acad. Sci. USA 77, 5611–5615 (1980);CrossRefGoogle Scholar
  128. (b).
    J. C. Tully, Diatomics-in-molecules potential energy surfaces. II. Nonadiabatic and spin-orbit interactions, J. Chem. Phys. 59, 5122–5134 (1973);CrossRefGoogle Scholar
  129. (C).
    N. C. Firth and R. Grice, Topography of potential-energy surfaces. Spin-orbit interaction for H + F2, Cl2, J. Chem. Soc. Faraday Trans. 2 83, 1011–1012 (1987) (and following articles).CrossRefGoogle Scholar
  130. 124.
    K. Tatsumi, R. Hoffmann, A. Yamamoto, and J. K. Stille, Reductive elimination of d8-organotransition metal complexes, Bull. Chem. Soc. Jpn. 54, 1857–1867 (1981).CrossRefGoogle Scholar
  131. 125.
    I. B. Bersuker, S. S. Budnikov, and B. A. Leizerov, “Semi-quantitative and semi-empirical versions in the quasi-relativistic SCF-MO-LCAO methods: Numerical calculations for (PtCl6)2-, Int. J. Quantum Chem. 11, 543–559 (1977).CrossRefGoogle Scholar
  132. 126.
    G. V. Ionova, V. G. Pershina, and V. I. Spitsyn, Electronic Structure of the Actinoids (in Russian), Nauka Moscow (1986).Google Scholar
  133. 127.
    T. P. Carsey and E. A. Boudreaux, Self-consistent modified extended Hiickel (SC-MEH) calculations on heavy metal systems. I. Platinum (II) tetragonal planar complexes with and without relativistic effects, Theor. Chim. Acta 56, 211–230 (1980).CrossRefGoogle Scholar
  134. 128.
    E. A. Boudreaux and T. P. Carsey, Quasirelativistic calculations on platinum complexes (anticancer drugs) and their interaction with DNA, Int. J. Quantum Chem. 18, 469–479 (1980).CrossRefGoogle Scholar
  135. 129.
    E. A. Boudreaux, S. P. Doussa, and M. Klobukowski, Nonempirical self-consistent modified extended Hückel calculations on heavy-metal systems. II. Electronic structure, bonding and spectra of the binuclear Pt2(P2O5H2)4 4-ion, Int. J. Quantum Chem. S20, 239–252 (1986).CrossRefGoogle Scholar
  136. 130.
    B. Bigot and C. Minot, Extended Hiickel study of the metallic growth of amall platinum clusters: Structure and energies, J. Am. Chem. Soc. 106, 6601–6615 (1984).CrossRefGoogle Scholar
  137. 131.
    C. Minot, B. Bigot, and A. Hariti, A theoretical study of successive hydrogénations of small platinum clusters: Structure and energies, J. Am. Chem. Soc. 108, 196–206 (1986).CrossRefGoogle Scholar
  138. 132.
    C. Minot, B. Bigot, and A. Hariti, Thermodynamic versus kinetic control in the selective hydrogenation of the small platinum clusters: A theoretical investigation, Nouv. J. Chim. 10, 461–472 (1986).Google Scholar
  139. 133.
    A. M. Lyudchik and N. B. Borkovskii, Nonrelativistic-to-relativistic conversion of molecular electronic structur calculations (in Russian), Dokl. Akad. Nauk Belor. SSR 28, 624–627 (1984).Google Scholar
  140. 134.
    A. M. Lyudchik, N. B. Borkovskii, and A. B. Kovrikov, Semiempirical methods of calculating relativistic effects in coordination compounds (in Russian), Koord. Khim. 12, 1038–1043 (1986).Google Scholar
  141. 135.
    L. L. Lohr Jr. and P. Pyykkö, Relativistically parameterized extended Hückel theory, Chem. Phys. Lett. 62, 333–338 (1979).CrossRefGoogle Scholar
  142. 136.
    L. L. Lohr Jr., M. Hotokka, and P. Pyykkö, Relativistically parameterized extended Hückel calculations. II. Orbital energies of group-IV tetrahalides and tetramethyls, Int. J. Quantum Chem. 18, 347–355 (1980). (The double-zeta halogen orbitals in this work contain a small normalization error. For corrected ones, see Ref. 12.)CrossRefGoogle Scholar
  143. 137.
    P. Pyykkö and L. L. Lohr Jr., Relativistically parameterized extended Hückel calculations. 3. Structure and bonding for some compounds of uranium and other heavy elements, Inorg. Chem. 20, 1950–1959 (1981).CrossRefGoogle Scholar
  144. 138.
    P. Pyykkö and L. Wiesenfeld, Relativistically parameterized extended Hueckel calculations. IV. Nuclear spin-spin coupling tensors for main group elements, Mol. Phys. 43, 557–580 (1981).CrossRefGoogle Scholar
  145. 139.
    L. L. Lohr Jr., Relativistically parametrized extended Hueckel calculations. 5. Charged polyhedral clusters of germanium, tin, lead, and bismuth atoms, Inorg. Chem. 20, 4229–4235 (1981).CrossRefGoogle Scholar
  146. 140.
    P. Pyykkö, Relativistically parameterized extended Hueckel calculations. VI. Interpretation of nuclear spin-spin coupling constants in some organolead compounds, J. Organomet. Chem. 232, 21–32 (1982).CrossRefGoogle Scholar
  147. 141.
    A. Viste, M. Hotokka, L. Laaksonen, and P. Pyykkö, Relativistically parameterized extended Hueckel calculations. VII. Nuclear spin-spin coupling tensors and densities of states for cluster models of CdTe, HgTe and PbTe, Chem. Phys. 72, 225–235 (1982).CrossRefGoogle Scholar
  148. 142.
    P. Pyykkö and L. Laaksonen, Relativistically parameterized extended Hueckel calculations. 8. Double-ζ parameters for the actinoids Th, Pa, U, Np, Pu, and Am and an application on uranyl, J. Phys. Chem. 88, 4892–4895 (1984).CrossRefGoogle Scholar
  149. 143.
    L. L. Lohr and Y. Q. Jia, Relativistically parameterized extended Hückel calculations. 10. Lanthanide trihalides, Inorg. Chim. Acta 119, 99–105 (1986).CrossRefGoogle Scholar
  150. 144.
    L. L. Lohr, Relativistically parametrized extended Hückel calculations. 11. Energy bands for elemental tellurium and polonium, Inorg. Chem. 26, 2005–2009 (1987).CrossRefGoogle Scholar
  151. 145.
    P. Pyykkö, Can the ionic dissociation potentials of halogen molecules be interpreted as support for Pitzer’s relativistic hybridization rules?, Finn. Chem. Lett. 119–121 (1982).Google Scholar
  152. 146.
    A. Viste and P. Pyykkö, Spin-orbit excitation in the system I +I2: Relativistically parameterized extended-Hückel calculations, Int. J. Quantum Chem. 25, 223–231 (1984).CrossRefGoogle Scholar
  153. 147.
    W. L. Wilson, R. W. Rudolph, L. L. Lohr, R. C. Taylor, and P. Pyykkö, Multinuclear NMR characterization of anionic clusters of the main-group elements Ge, Sn, Sb, Tl, Pb, and Bi in nonaqueous solution, Inorg. Chem. 25, 1535–1541 (1986).CrossRefGoogle Scholar
  154. 148.
    N. Rösch and P. Pyykkö, On the relativistic theory of nuclear spin-spin coupling constants. Time-reversal symmetry aspects and applications to some heavy-element fluorides, Mol. Phys. 57, 193–200 (1986).CrossRefGoogle Scholar
  155. 149.
    P. Pyykkö, A. Görling, and N. Rösch, A transparent interpretation of the relativistic contribution to the NMR “heavy atom chemical shift,” Mol. Phys. 61, 195–205 (1987).CrossRefGoogle Scholar
  156. 150.
    U. Edlund, T. Lejon, P. Pyykkö, T. K. Venkatachalam, and E. Buncel, 7Li, 29Si, 119Sn and 207Pb NMR studies of phenyl substituted group 4 anions, J. Am. Chem. Soc. 109, 5982–5985 (1987).CrossRefGoogle Scholar
  157. 151.
    A. L. Barra, J. B. Robert, and L. Wiesenfeld, Parity nonconservation and NMR observables. Calculation of Tl resonance frequency differences in enantiomers, Phys. Lett. A 115, 443–447 (1986);CrossRefGoogle Scholar
  158. (b).
    M.-B. Krogh-Jespersen, Theoretically derived absorption and MCD spectral data for the cellular species produced in the hydrolysis of cis-diammino dichloroplatinum(II), J. Comp. Chem. 6, 614–624 (1985);CrossRefGoogle Scholar
  159. (c).
    M.-B. Krogh-Jespersen and A. Altonen, Theoretical studies of the potential hydrolysis products from cis-Pt(NH3)2Cl2 and acetamide, Inorg. Chem. 26, 2084–2090 (1987).CrossRefGoogle Scholar
  160. 152.
    S. Larsson, J. S. Tse, J. L. Esquivel, and A. Tang Kai, Electronic structure and ESCA shake-up of the UF6 molecule, Chem. Phys. 89, 43–50 (1984).CrossRefGoogle Scholar
  161. 153.
    J. L. A. Alves and S. Larsson, A comparative study of nonrelativistic and relativistic 5d atoms as impurities in silicon, J. Phys. Solids 46, 1207–1214 (1985);CrossRefGoogle Scholar
  162. (b).
    D. Courteix, J. Chayrouse, L. Heintz, and R. Baptist, XPS study of plutonium oxides, Solid State Commun. 39, 209–213 (1981);CrossRefGoogle Scholar
  163. (c).
    S. Larsson, L.-F. Olsson, and A. Rosén, Electronic structure of the PdCl42- and PtCl42-ions, Int. J. Quantum Chem. 25, 201–209 (1984).CrossRefGoogle Scholar
  164. 154.
    J. T. Gleghorn and N. D. A. Hammond, Charge iterative relativistic extended Hiickel theory and its application to the digermene, distannene and diplumbene systems, Chem. Phys. Lett. 105, 621–624 (1984).CrossRefGoogle Scholar
  165. 155.
    J. Gleghorn, Etude théorique de la mercuration du benzene, C. R. Acad. Sci. (Paris), Sér. II 16, 1425–1428 (1986);Google Scholar
  166. (b).
    R. Viruela-Martin, I. Nebot-Gil, F. Tomas-Vert, and P. M. Viruela-Martin, Theoretical EHT study of propene adsorption on model clusters. Part II. Nickel VlIIb and Zinc IIb transition metal oxides, J. Mol. Catal. 34, 47–55 (1986).CrossRefGoogle Scholar
  167. 156.
    A. Trunschke and H. Miessner, Relativistische Modellrechnungen (REX) zur Chemisorption von Kohlenmonoxid an der Platin(lll)Oberfläche, Z. Chem. 26, 416–417 (1986).CrossRefGoogle Scholar
  168. 157.
    L. L. Lohr, M. Hotokka, and P. Pyykkö, REX: Relativistically parameterized extended Hückel program, QCPE 12, 387 (1980).Google Scholar
  169. 158.
    N. Rösch, Time-reversal symmetry, Kramers’ degeneracy and the algebraic eigenvalue problem, Chem. Phys. 80, 1–5 (1983).CrossRefGoogle Scholar
  170. 159.
    N. Rösch, QATREX: Relativistically parameterized Extended Hueckel progean employing quaternionic algebra, QCPE 3, 468 (1983).Google Scholar
  171. 160.
    P. Pyykkö, Relativistic extended Hueckel program ITEREX-85, Report HUKI 1–86, Department of Chemistry, University of Helsinki (1986).Google Scholar
  172. 161.
    M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten Jr., The 3-j and 6-j Symbols, The Technology Press, MIT, Cambridge, Massachusetts (1959).Google Scholar
  173. 162.
    V. A. Glebov and V. S. Nefedov, Electronic structure and properties of uranyl compounds. A quasirelativistic MO LCAO calculation on uranyl (in Russian), Koord. Khim. 7, 1664–1672 (1981).Google Scholar
  174. 163.
    V. A. Glebov and V. S. Nefedov, Electronic structure and properties of uranyl com-pounds. Degree of overlap of outer and inner uranium shells, and oxygen (in Russian), Koord. Khim. 7, 586–591 (1981).Google Scholar
  175. 164.
    V. A. Glebov and V. S. Nefedov, Electronic structure and properties of uranyl com-pounds. Charge distribution and the nature of bonding in the uranyl group (in Russian), Koord. Khim. 7, 1673–1681 (1981).Google Scholar
  176. 165.
    R. Boča, Inclusion of relativistic effects into ZDO methods. I. A quasirelativistic CNDO/1, Int. J. Quantum Chem. 31, 941–950 (1987).CrossRefGoogle Scholar
  177. 166.
    J. C. Culberson, P. Knappe, N. Rösch, and M. C. Zerner, An intermediate neglect of dif-ferential overlap (INDO) technique for lanthanide complexes: studies on lanthanide halides, Theor. Chim. Acta 71, 21–39 (1987).CrossRefGoogle Scholar
  178. 167.
    L.-M. Li, J.-Q. Ren, G.-X. Xu, and X.-Z. Wang, INDO studies on the electronic structure of lanthanoid complexes, Int. J. Quantum Chem. 23, 1305–1316 (1983).CrossRefGoogle Scholar
  179. 168.
    G.-X. Xu and J.-Q. Ren, Electronic structure and chemical bonding of the dimer of bis(η5-cyclopentadienyl) ytterbium methyl, Int. J. Quantum Chem. 29, 1017–1024 (1986).CrossRefGoogle Scholar
  180. 169.
    J. Li, J.-Q. Ren, and G.-X. Xu, Localized INDO study on the dimer of bis(η5-methylcyclopentadienyl) ytterbium, Inorg. Chem. 26, 1077–1080 (1987);CrossRefGoogle Scholar
  181. (b).
    G.-X. Xu and J.-Q. Ren, INDO studies on the electronic structure and chemical bonding of a rare earth cluster compound, Gd10C4Cl18, Lanth. Act. Res. 2, 67–78 (1987).Google Scholar
  182. 170.
    S. Sakaki, N. Hagiwara, N. Iwasaki, and A. Ohyoshi, A CNDO-type MO Method of the third transition metal complexes and the electronic structure of methylmercury(II) halides, Bull. Chem. Soc. Jpn 50, 14–21 (1977).CrossRefGoogle Scholar
  183. 171.
    J. J. Dongarra, J. R. Gabriel, D. D. Koelling, and J. H. Wilkinson, Solving the secular equation including spin orbit coupling for systems with inversion and time reversal symmetry, J. Comp. Phys. 54, 278–288 (1984).CrossRefGoogle Scholar
  184. 172.
    H. Eschrig, Kramers’ theorem in the relativistic electronic structure calculations, Int. Symp. El. Str. Metals and Alloys Gaussig, DDR, 19–26 (1984).Google Scholar
  185. 173.
    H. Eschrig and M. Richter, Kramers’ theorem in the relativistic electronic structure calculation, Solid State Commun. 59, 861–864 (1986).CrossRefGoogle Scholar
  186. 174.
    W. R. Wadt, Why UO2 2+ is linear and isoelectronic ThO2 is bent, J. Am. Chem. Soc. 103, 6053–6057 (1981).CrossRefGoogle Scholar
  187. 175.
    L. J. Laakkonen and P. Pyykkö, unpublished results.Google Scholar
  188. 176.
    K. S. Pitzer, Are elements 112, 114 and 118 relatively inert gases? J. Chem. Phys. 63, 1032–1033 (1975).Google Scholar
  189. 177.
    J. M. Dyke, G. D. Josland, J. G. Snijders, and P. M. Boerrigter, Ionization energies of the diatomic halogens and interhalogens studied with relativistic Hartree-Fock-Slater calculations, Chem. Phys. 91, 419–424 (1984).CrossRefGoogle Scholar
  190. 178.
    P. Pyykkö, Relativistic theory of nuclear spin-spin coupling in molecules, Chem. Phys. 22, 289–296 (1977).CrossRefGoogle Scholar
  191. 179.
    P. Pyykkö, On the relativistic theory of NMR chemical shifts, Chem. Phys. 74, 1–7 (1983).CrossRefGoogle Scholar
  192. 180.
    B. D. Dunlap, Relativistic effects in hyperfine interactions, in Mössbauer Effect Methodology 7 (I. Gruverman, ed.), Plenum Press, New York (1971), pp. 123–145.Google Scholar
  193. 181.
    S. Larsson, private communication.Google Scholar
  194. 182.
    R. S. Mulliken, C. A. Rieke, D. Orloff, and H. Orloff, Formulas and numerical tables for overlap integrals, J. Chem. Phys. 17, 1248–1267 (1949).CrossRefGoogle Scholar
  195. 183.
    One difference is, though, that Wadt obtains a clearly linear uranyl, even with the 6p functions in the core while REX requires the 6p functions to make uranyl clearly linear.Google Scholar
  196. 184.
    The 1J(U – F) coupling constant was later found experimentally to be small, J = 213 Hz: I. Ursu, M. Bogdan, P. Fitori, F. Balibanu, and D. E. Demco, 19F – 235U scalar interact–tion in liquid UF6 by NMR relaxation in the rotating frame, Mol. Phys. 62, 793–796 (1987).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Pekka Pyykkö
    • 1
  1. 1.Department of ChemistryUniversity of HelsinkiHelsinkiFinland

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