Skip to main content

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

Abstract

The pseudopotential approximation is reviewed in detail for heavy and superheavy elements. It is shown that pseudopotentials are an effective and accurate way to treat relativistic effects in heavy element containing systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Scuseria, G. E., Ayala, P. Y. (1999). Linear scaling coupled cluster and perturbation theories in the atomic orbital basis. J. Chem. Phys. 111: 8330–8343.

    Article  CAS  Google Scholar 

  2. Burant, J. C., Scuseria, G. E., and Frisch, M. J. (1996). A linear scaling method for Hartree-Fock exchange calculations of large molecules. J. Chem. Phys. 105: 8969–8972.

    Article  CAS  Google Scholar 

  3. Stratmann, R. E., Scuseria, G. E., and Frisch, M. J. (1996). Achieving linear scaling in exchange-correlation density functional quadratures. Chem. Phys. Lett. 257: 213–223.

    Article  CAS  Google Scholar 

  4. Schwarz, W. H. E., Andrae, D., Arnold, S. R., Heidberg J., Hellmann jr., H., Hinze, J., Karachalios, A., Kovner, M. A., Schmidt, P. C., and Zülicke, L. (1999). Hans. G. A. Hellmann (1903–1938). I. Ein Pionier der Quantenchemie. Ber. Bunsenges (2) 60–70.

    Google Scholar 

  5. Schwarz, W. H. E., Karachalios, A., Arnold, S. R., Zülicke, L., Schmidt, P. C., Kovner, M. A., Hinze, J., Hellmann jr., H., Heidberg J., and Andrae, D. (1999). Hans. G. A. Hellmann (1903–1938). II. Ein deutscher Pionier der Quantenchemie in Moskau. Ber. Bunsenges (2) 60–70.

    Google Scholar 

  6. Hellmann, H. (1934). A New Approximation Method in the Problem of Many Electrons. J. Chem. Phys. 3: 61.

    Article  Google Scholar 

  7. Szasz, L. (1985). Pseudopotential Theory of Atoms and Molecules, Wiley, New York.

    Google Scholar 

  8. Pseudopotential calculations are less accurate than all-electron calculations, but they simulate the results of the latter often surprisingly well, for substantially smaller expenses. It is therefore not astonishing that in the chemistry of heavy atoms, relativistic pseudopotential theory is practically the method of choice. It is certainly the most successful of all approximate relativistic molecular theories (W. Kutzelnigg, 1987)

    Google Scholar 

  9. Pyykkö, P. (1988). Relativistic effects in structural chemistry. Chem. Rev. 88: 563–594.

    Article  Google Scholar 

  10. Dyall, K. (1998). Relativistic and nonrelativistic finite nucleus optimized double zeta basis sets for the 4p, 5p and 6p elements. Theor. Chem. Acc. 99: 366–371.

    CAS  Google Scholar 

  11. Faegri, K. (1999). Relativistic Gaussian basis sets for the elements K — Uuo. Theor. Chem. Acc. 105: 252–258.

    Article  Google Scholar 

  12. Tsuchiya, T., Abe, M., Nakajima, T., and Hirao, K. (2001). Accurate relativistic Gaussian basis sets for H through Lr determined by atomic self-consistent field calculations with the thirdorder Douglas-Kroll approximation. J. Chem. Phys. 115: 4463–4472.

    Article  CAS  Google Scholar 

  13. Tatewaki, H., Mochizuki, Y., Koga, T., and Karwowski, J. (2001). Modification of nonrelativistic Gaussian basis sets for relativistic calculations. J. Chem. Phys. 115: 9160–9164.

    Article  CAS  Google Scholar 

  14. Landau, A., Eliav, E., Ishikawa, E., and Kaldor, U. (2001). Benchmark calculations of electron affinities of the alkali atoms sodium to eka-francium (element 119). J. Chem. Phys. 115: 2389–2392.

    Article  CAS  Google Scholar 

  15. Eliav, E., and Kaldor, U. (1999). High-Accuracy Calculations for Heavy and Super-Heavy Elements. Adv. Quantum Chem. 31: 313–336.

    Google Scholar 

  16. Lim, I., Pernpointner, M., Seth, M., Laerdahl, J. K., Schwerdtfeger, P., Neogrady, P., Urban, M. (1999). Accurate Relativistic Coupled Cluster Static Dipole Polarizabilities of the Alkali Metals from Li to Element 119. Phys. Rev. A 60: 2822–2828.

    Article  CAS  Google Scholar 

  17. Kutzelnigg, W. (1990). Perturbation theory of relativistic corrections. II. Analysis and classification of known and other possible methods. Z Phys. D: At., Mol. Clusters 15: 27–50.

    Article  CAS  Google Scholar 

  18. Hess, B. A. (1986). Relativistic electronic-structure calculations employing a two-component no-pair formalism with external field projection operators. Phys. Rev. A 33: 3742–3748.

    Article  CAS  Google Scholar 

  19. van Lenthe, E., Snijders, J. G., and Baerends, E. J. (1996). The zero-order regular approximation for relativistic effects: The effect of spin-orbit coupling in closed shell molecules. J. Chem. Phys. 105: 6505–6516.

    Article  Google Scholar 

  20. Chang, C., Pélissier, M., and Durand, Ph. (1986). Regular two-component Pauli-like effective Hamiltonians in Dirac theory. Phys. Scr. 34: 394–404.

    Article  CAS  Google Scholar 

  21. Heully, J.-L., Lindgren, I., Lindroth, E., Lundqvist, S., Mårtensson-Pendrill, A.-M. (1986). Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure. J. Phys. B 19: 2799–2815.

    Article  CAS  Google Scholar 

  22. Knappe, P., and Rösch, N. (1990). A Relativistic Linear Combination of Gaussian-Type Orbitals Density Functional Method Based on a Two-Component Formalism with External Field Projectors. J. Chem. Phys. 92: 1153–1161.

    Article  CAS  Google Scholar 

  23. Car, R., and Parinello, M. (1985). Unified approach for molecular dynamics and densityfunctional theory. Phys. Rev. Lett. 55: 2471–2474.

    Article  CAS  Google Scholar 

  24. Pacchioni, G., Chung, S.-C., Krüger, S., and Rösch, N. (1994). On the Evolution of Cluster to Bulk Properties: a Linear Combination of Gaussian-Type Orbitals Local Density Functional Study of Free and Coordinated Nin Clusters (n = 6 – 147). Chem. Phys. 184: 12–137.

    Article  Google Scholar 

  25. Seminario, J. M., and Politzer, P. (1995). Recent Developments and Applications of Modern Density Functional Theory. Theoretical and Computational Chemistry, Vol.2 (Elsevier, Amsterdam).

    Google Scholar 

  26. Engel, E., Höck, A., and Dreizler, R. M. (2000). van der Waals bonds in density-functional theory. Phys. Rev. A 61: 032502/1–5.

    Google Scholar 

  27. Singh, P. P. (1994). Relativistic effects in mercury: Atoms, clusters, and bulk. Phys. Rev. B 49: 4954–4958.

    Article  CAS  Google Scholar 

  28. Moyano, G. E., Wesendrup, R., Söhnel, T., Schwerdtfeger, P. (2002). Properties of Small to Medium Sized Mercury Clusters From a Combined Ab-Initio, Density-Functional and Simulated Annealing Study. To be published.

    Google Scholar 

  29. Goedecker, S., and Maschke, K. (1992). Transferability of pseudopotentials. Phys. Rev. A 45: 88–93.

    Article  Google Scholar 

  30. Barthelat, J.C., and Durand, Ph. (1978). Recent Progress of Pseudo-Potential Methods in Quantum Chemistry. Gazz. Chim. Acta 108: 225–236.

    Google Scholar 

  31. Krauss, M., and Stevens, W. J. (1984). Effective potentials in molecular quantum chemistry. Ann. Rev. Phys. Chem. 35: 357–385.

    Article  CAS  Google Scholar 

  32. Christiansen, P. A., Ermler, W. C., and Pitzer, K. S. (1985). Relativistic effects in chemical systems. Ann. Rev. Phys. Chem. 36: 407–432.

    Article  CAS  Google Scholar 

  33. Ermler, W. C., Ross, R.B., and Christiansen, P. A., (1988). Spin-orbit coupling and other relativistic effects in atoms and molecules. Adv. Quantum Chem. 19: 139–182.

    Article  CAS  Google Scholar 

  34. Pickett, W. E. (1989). Pseudopotential Methods in Condensed Matter Applications. Comput. Phys. Rep. 9: 115–198.

    Article  Google Scholar 

  35. Huzinaga, S. (1995). 1994 Polanyi Award lecture: Concept of active electrons in chemistry. Can. J. Chem. 73: 619–628.

    Article  Google Scholar 

  36. Frenking, G., Antes, I., Böhme, M., Dapprich, S., Ehlers, A. W., Jonas, V., Neuhaus, A., Otto, M., Stegmann, R., Veldkamp, A., and Vyboishikov, S. F. (1996). Pseudopotential Calculations of Transition Metal Compounds. Scope and Limitations. In ‘Reviews in Computational Chemistry’, ed. K. B. Lipkowitz and D. B. Boyd, VCH, New York, vol.8; pgs. 63–144.

    Chapter  Google Scholar 

  37. Pyykkö, P., and Stoll, H. (2000). Relativistic pseudopotential calculations, 1993-June 1999. in R.S.C. Specialist Periodical Reports, Chemical Modelling, Applications and Theory. Vol. 1: 239–305.

    Google Scholar 

  38. Dolg, M. (2002). Relativistic Effective Core Potentials. In: Relativistic Electronic Structure Theory. Part 1. Fundamental Aspects. P. Schwerdtfeger (ed.), Elsevier, Amsterdam; in preparation.

    Google Scholar 

  39. Fock, V., Veselov, M., and Petrashen, M. (1940). J. Expt. Theor. Phys. (USSR) 10: 723–739.

    Google Scholar 

  40. Herring, C. (1940). A New Method for Calculating Wave Functions in Crystals. Phys. Rev. 57: 1169–1177.

    Article  Google Scholar 

  41. Preuss, H. (1955). Untersuchungen zum kombinierten Näherungsverfahren. Z. Naturforschg. 10A: 365–373.

    CAS  Google Scholar 

  42. Phillips, J. C., and Kleinman, L. (1959). A new method for calculating wavefunctions in crystals and molecules. Phys. Rev. 116: 287–294.

    Article  CAS  Google Scholar 

  43. Kahn L. R., Baybutt, P., Truhlar, D. G. (1976). Ab initio effective core potentials: Reduction of all-electron molecular structure calculations to calculations involving only valence electrons. J. Chem. Phys. 65: 3826–3853.

    Article  CAS  Google Scholar 

  44. Schwerdtfeger, P., Bowmaker, G. A. (1994). Relativistic Effects in gold chemistry. V. Group 11 dipole polarizabilities and weak bonding in monocarbonyl compounds. J. Chem. Phys. 100: 4487–4497

    Article  CAS  Google Scholar 

  45. Schwerdtfeger, P., Fischer, T., Dolg, M., Igel-Mann, G., Nicklass, A., Stoll, H., Haaland, A. (1995). The Accuracy of the Pseudopotential Approximation. I. An Analysis of the Spectroscopic Constants for the Electronic Ground States of InCl and InCl3. J. Chem. Phys. 102: 2050–2062.

    Article  CAS  Google Scholar 

  46. Lim, I., Laerdahl, J. K., Schwerdtfeger, P. (2002). Fully Relativistic Coupled Cluster Dipole Polarizabilities of the Positively Charged Alkali Ions from Li+ to Element 119+, J. Chem. Phys. 116: 172–178.

    Article  CAS  Google Scholar 

  47. Huzinaga, S., and Cantu, A. A. (1971). Theory of separability of many-electron systems. J. Chem. Phys. 55: 5543–5549.

    Article  CAS  Google Scholar 

  48. M. Klobukowski, S. Huzinaga, Sakai, Y. (1999). Model Core Potentials: Theory and Applications. in Computational Chemistry, Reviews of Current Trends, J. Leszynski (ed.), World Scientific, Singapore; Vol.3, pgs.49–74.

    Chapter  Google Scholar 

  49. Sakai, Y., Miyoshi, E., Klobukowski, M., and Huzinaga, S. (1987). Model Potentials for Molecular Calculations. I. The spd-MP Set for Transition Metal Atoms Sc through Hg. J. Comput. Chem. 8: 226–255.

    Article  CAS  Google Scholar 

  50. Sakai, Y., Miyoshi, E., Klobukowski, M., and Huzinaga, S. (1987). Model Potentials for Molecular Calculations. II. The spd-MP Set for Transition Metal Atoms Sc through Hg. J. Comput. Chem. 8: 256–264.

    Article  CAS  Google Scholar 

  51. Miyoshi, E., Sakai, Y., Tanaka, K., and Masamura, M. (1998). Relativistic dsp-model core potentials for main group elements in the fourth, fifth and sixth row and their applications. J. Mol. Struct. (Theochem) 451: 73–79.

    Article  CAS  Google Scholar 

  52. Höjer, G., and Chung, J. (1978). Some aspects of the model potential method. Int. J. Quantum Chem. 14: 623–634.

    Article  Google Scholar 

  53. Andzelm, J., Radzio, E., Barandiarán, Z., and Seijo, L. (1985) New developments in the model potential method: ScO molecule. J. Phys. Chem. 83: 4565–4572.

    CAS  Google Scholar 

  54. Katsuki, S., and Huzinaga, S. (1988). An effective-Hamiltonian method for valence-electron molecular calculations. Chem. Phys. Lett. 147: 597–602.

    Article  CAS  Google Scholar 

  55. The AIMP parameters and basis sets of Seijo and co-workers can be obtained from: http://www.qui.uam.es/DATA/AIMPLibs.html/.

    Google Scholar 

  56. Casarrubios, M., and Seijo, L. (1999). The ab-initio model potential method: Third series transition metal elements. J. Chem. Phys. 110: 784–796.

    Article  CAS  Google Scholar 

  57. Flad, J., Stoll, H., and Preuss, H. (1979). Calculation of equilibrium geometries and ionization energies of sodium clusters up to Na8. J. Chem. Phys. 71: 3042–3052.

    Article  CAS  Google Scholar 

  58. Schwarz, W. H. E. (1968). Hellmann’s pseudopotential method. I. Theoretical basis. Theor. Chim. Acta 11: 307–324.

    Article  CAS  Google Scholar 

  59. Schwarz, W. H. E. (1968). Hellmann’s pseudopotential method. III. Calculations on atomic systems with two valence electrons. Theor. Chim. Acta 11: 377–384.

    Article  CAS  Google Scholar 

  60. Schwarz, W. H. E. (1969). Combined approximation method. II. Correct choice of the effective potential and description of the atomic core-atomic core interaction. Acta Phys. 27: 391–403.

    Article  CAS  Google Scholar 

  61. Schwarz, W. H. E. (1969). Calculations with the pseudopotential method on alkali-metal molecules. Theor. Chim. Acta 15: 235–243.

    Article  CAS  Google Scholar 

  62. The Stuttgart group pseudopotentials and valence basis sets of Stoll and co-workers can be obtained from: http://www.theochem.uni-stuttgart.de/pseudopotentials/.

    Google Scholar 

  63. Stoll, H., Metz, B. and Dolg, M. (2002). Relativistic energy-consistent pseudopotentials — recent developments. J. Comp. Chem. 23: 767–778.

    Article  CAS  Google Scholar 

  64. Hay, P. J., and Wadt, W. R. (1985). Ab-initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J. Chem. Phys. 82: 270–283.

    Article  CAS  Google Scholar 

  65. Wadt, W. R., and Hay, P. J. (1985). Ab-initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J. Chem. Phys. 82: 284–298.

    Article  CAS  Google Scholar 

  66. Hay, P. J., and Wadt, W. R. (1985). Ab-initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J. Chem. Phys. 82: 299–310.

    Article  CAS  Google Scholar 

  67. The pseudopotential parameters and basis sets of Christiansen and co-workers can be obtained from: http://www.clarkson.edu/∼pac/reps.html.

    Google Scholar 

  68. Barthelat, J. C., Durand, Ph., and Serafini, A. (1977). Non-empirical pseudopotentials for molecular calculations. I. The PSIBMOL algorithm and test calculations. Mol. Phys. 33: 159–180.

    Article  CAS  Google Scholar 

  69. Maron, L., and Teichteil, C. (1998). On the accuracy of averaged relativistic shape-consistent pseudopotentials. Chem. Phys. 237: 105–122.

    Article  CAS  Google Scholar 

  70. Stevens, W. J., Krauss, M., Basch, H., and Jasien, P. G. (1992). Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms. Can. J. Chem. 70: 612–630.

    Article  CAS  Google Scholar 

  71. Kleinman, L. (1980). Relativistic norm-conserving pseudopotential. Phys. Rev. B 21: 2630–2631.

    Article  Google Scholar 

  72. Hamann, D. R., Schlüter, M., and Chiang, C. (1979). Norm-Conserving Pseudopotentials. Phys. Rev. Lett. 43: 1494–1497.

    Article  CAS  Google Scholar 

  73. Bachelet, G. B., and Schlüter, M. (1982). Relativistic norm-conserving pseudopotentials. Phys. Rev. B 25: 2103–2108.

    Article  CAS  Google Scholar 

  74. Focher, P., Lastri, A., Covi, M., and Bachelet, G. B. (1991). Pseudopotentials and physical ions. Phys. Rev. B 44: 8486–8495.

    Article  CAS  Google Scholar 

  75. Bachelet, G. B., Hamann, D. R., and Schlüter, M. (1982). Pseudopotentials that work: From H to Pu. Phys. Rev. B 26: 4199–4228.

    Article  CAS  Google Scholar 

  76. Mosyagin, N. S., Titov, A. V., and Tulub, A. V. (1994). Generalized effective-core-potential method: Potentials for the atoms Xe, Pd and Ag. Phys. Rev. A 50: 2239–2247.

    Article  CAS  Google Scholar 

  77. Titov, A. V., Mitrushenkov, A. O., and Tupitsyn, I. I. (1991). Effective core potential for pseudo-orbitals with nodes. Chem. Phys. Lett. 185: 330–334.

    Article  CAS  Google Scholar 

  78. Titov, A.V., and Mosyagin, N. S. (1999). Generalized Relativistic Effective Core Potentials: Theoretical Grounds. Int. J. Quantum Chem. 71: 359–401.

    Article  Google Scholar 

  79. Klobukowski, M. (1992). Comparison of the effective core potential and model potential methods in studies of electron correlation energy in molecules: Dihalides and halogen hydrides. Theor. Chim. Acta 83: 239–248.

    Article  CAS  Google Scholar 

  80. Kolar, M. (1981). Pseudopotential matrix elements in the Gaussian basis. Comput. Phys. Commun. 23: 275–286.

    Article  CAS  Google Scholar 

  81. McMurchie, L. E., and Davidson, E. R. (1981). Calculation of Integrals over ab initio Pseudopotentials. J. Comput. Phys. 44: 289–301.

    Article  Google Scholar 

  82. Piccolo, R. (1990). Analytical evaluation of Gaussian pseudopotential matrix elements with any angular momentum. Phys. Rev. A 41: 4704–4710.

    Article  CAS  Google Scholar 

  83. Pelissier, M., Komiha, N., and Daudey, J. P. (1988). One-Center Expansion for Pseudopotential Matrix Elements. J. Comput. Chem. 9: 298–302.

    Article  CAS  Google Scholar 

  84. Skylaris, C.-K., Gagliardi, L., and Handy, N. C. (1998). An efficient method for calculating effective core potential integrals which involve projection operators. Chem Phys. Lett. 2967: 445–451.

    Article  Google Scholar 

  85. Breidung, J., Thiel, W., and Kormornicki, A. (1988). Analytical second derivatives for effective core potentials. Chem. Phys. Lett. 153: 76–81.

    Article  CAS  Google Scholar 

  86. Goll, E. (2001). Pseudopotentialintegrale und Energiegradienten. Diploma Thesis, Stuttgart.

    Google Scholar 

  87. Datta, S. N., Ewig, C. S., Van Wazer, J. R. (1978). Application of Effective Potentials to Relativistic Hartree-Fock Theory. Chem Phys. Lett. 57: 83–89.

    Article  CAS  Google Scholar 

  88. Cowan, R. D., and Griffin, D. C. (1976). Approximate relativistic corrections to atomic radial wavefunctions. J. Opt. Soc. Am. 66: 1010–1014.

    Article  CAS  Google Scholar 

  89. Casarrubios, M., and Seijo, L. (1998). The ab initio model potential method. Relativistic Wood-Boring valence spin-orbit potentials and spin-orbit-corrected basis sets from B(Z=5) to Ba(Z=56). J. Mol. Stuct. 426: 59–74.

    CAS  Google Scholar 

  90. Barandiarán, Z., and Seijo, L. (1992). The ab initio model potential method. Cowan-Griffin relativistic core potentials and valence basis sets from Li (Z=3) to La (Z=57). Can. J. Chem. 70: 409–415.

    Article  Google Scholar 

  91. Wittbom, C., and Wahlgren, U. (1995). New relativistic effective core potentials for heavy elements. Chem. Phys. 201: 357–362.

    Article  Google Scholar 

  92. Rakowitz, F., Marian, C. M., Seijo, L., and Wahlgren, U. (1999). Spin-free relativistic no-pair ab-initio core model potentials and valence basis sets for the transition metal elements Sc to Hg. II. J. Chem. Phys. 111: 10436–10443.

    Article  CAS  Google Scholar 

  93. Rakowitz, F., Marian, C. M., and Seijo, L. (1999). Spin-free relativistic no-pair ab-initio core model potentials and valence basis sets for the transition metal elements Sc to Hg. Part 1. J. Chem. Phys. 110: 3678–3686.

    Article  CAS  Google Scholar 

  94. Heinemann, C., Koch, W., and Schwarz, H. (1995). An approximate method for treating spinorbit effects in platinum. Chem. Phys. Lett. 245: 509–518.

    Article  CAS  Google Scholar 

  95. Hafner, P., and Schwarz, W. H. E. (1979). Molecular Spinors from the Quasi-Relativistic Pseudopotential Approach. Chem. Phys. Lett. 63: 537–541.

    Article  Google Scholar 

  96. Ermler, W. C., Ross, R. R., and Christiansen, P. A. (1988). Spin-Orbit Coupling and Other Relativistic Effects in Atoms and Molecules. Adv. Quantum Chem. 19: 139–182.

    Article  CAS  Google Scholar 

  97. Ermler, W. C., Lee, Y. S., Christiansen, P. A., and Pitzer, K. S. (1981). Ab intio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular calculations. Chem. Phys. Lett. 81: 70–73.

    Article  CAS  Google Scholar 

  98. Pitzer, R. M., and Winter, N. W. (1988). Electronic-Structure Methods for Heavy-Atom Molecules. J. Phys. Chem. 92: 3061–3063.

    Article  CAS  Google Scholar 

  99. Pitzer, R. M., and Winter, N. W. (1991). Spin-Orbit (Core) and Core Potential Integrals. Int. J. Quantum Chem. 40: 773–780.

    Article  CAS  Google Scholar 

  100. Lee, S. Y., and Lee, Y. S. (1992). Kramers’ Restricted Hartree-Fock Method for Polyatomic Molecules Using Ab Initio Relativistic Effective Core Potentials with Spin-Orbit Operators. J. Comput. Chem. 5: 595–601.

    Article  Google Scholar 

  101. Yabushita, S., Zhang, Z., and Pitzer, R. M. (1999). J. Phys. Chem. A 103: 5791–5800.

    Article  CAS  Google Scholar 

  102. Datta, S., Ewig, C. S., and Van Wazer, J. R. (1978). Application of effective potentials to relativistic Hartree-Fock calculations. Chem. Phys. Lett. 57: 83–89.

    Article  CAS  Google Scholar 

  103. Ishikawa, Y., and Malli, G. L. (1981). Fully relativistic effective core potentials (FRECP). In Relativistic Effects in Atoms, Molecules and Solids, G. L. Malli (ed.), NATO ASI Series B: Physics, Vol. 87, Plenum, New York; pgs. 363–381.

    Google Scholar 

  104. Ishikawa, Y., and Malli, G. L. (1981). Effective core potentials for fully relativistic Dirac-Fock calculations. J. Chem. Phys. 75: 5423–5431.

    Article  CAS  Google Scholar 

  105. Doig, M. (1996). Fully relativistic pseudopotentials for alkaline atoms: Dirac-Hartree-Fock and configuration interaction calculations of alkaline monohydrides. Theor. Chim. Acta 93: 141–156.

    Google Scholar 

  106. Pyper, N. C. (1980). Relativistic pseudopotential theories and corrections in the Hartree-Fock method. Mol. Phys. 39: 1327–1358.

    Article  CAS  Google Scholar 

  107. Boys, S. F., and Bernardi, F. (1970). The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 19: 553–566.

    Article  CAS  Google Scholar 

  108. Hermann, H. L., Boche, G., Schwerdtfeger, P. (2001). Metallophilic Interactions between Closed-Shell Copper(I) Molecules — A Theoretical Study. Chem. Eur. J. 7: 5333–5342; and references therein.

    Article  CAS  Google Scholar 

  109. Martin, J. M., and Sundermann, A. J. (2001). Correlation consistent valence basis sets for use with the Stuttgart-Dresden-Bonn relativistic effective core potentials: The atoms Ga-Kr and In-Xe. J. Chem. Phys. 114: 3408–3420.

    Article  CAS  Google Scholar 

  110. Schwerdtfeger, P., Wesendrup, R., Moyano, G. E., Sadlej, A. J., Greif, J., Hensel, F. (2001). The Potential Energy Curve and Dipole Polarizability Tensor of Mercury Dimer , J. Chem. Phys. 115: 7401–7412

    Article  CAS  Google Scholar 

  111. Dolg, M., and Flad, H.-J. (1996). Ground State Properties of Hg2. 1. A Pseudopotential Configuration Interaction Study. J. Phys. Chem. 100: 6147–6151.

    Article  CAS  Google Scholar 

  112. Yu, M., and Dolg, M. (1997). Covalent contributions to bonding in group 12 dimers M2 (M = Zn, Cd, Hg). Chem. Phys. Lett. 273: 329–336.

    Article  CAS  Google Scholar 

  113. Stoll, H., Fuentealba, P., Dolg, M., Flad, J., Szentpály, L. v., and Preuss, H. (1983). Cu and Ag as one-valence-electron atoms: Pseudopotential results for Cu2, Ag2, CuH, AgH, and the corresponding cations. J. Chem. Phys. 79: 5532–5542.

    Article  CAS  Google Scholar 

  114. Schwerdtfeger, P. (1987). Relativistic effects in molecules: Pseudopotential calculations for TlH+, TlH and TlH3. Phys. Scr. 36: 453–459.

    Article  CAS  Google Scholar 

  115. Bernier, A., Millie, Ph., and Pelissier, M. (1986). Three-electron approach of HgH using relativistic effective core, core polarization and spin-orbit operators: the low-lying states. Chem. Phys. 106: 195–203.

    Article  CAS  Google Scholar 

  116. Nicklass, A., and Stoll, H. (1995). On the Importance of Core Polarization in Heavy Post-d Elements: a Pseudopotential Calibration Study for X2H6 (X = Si, Ge, Sn, Pb), Mol. Phys. 86, 317–326.

    Article  CAS  Google Scholar 

  117. Jeung, G. H., Spiegelmann, F., Daudey, J. P., and Malrieu, J. P. (1983). Theoretical study of the lowest states of CsH and Cs2. J. Phys. B 16: 2659–2675.

    Article  CAS  Google Scholar 

  118. Schwerdtfeger, P. (1986), Pseudopotentials for the Investigation of Relativistic Effects, PhD thesis, University of Stuttgart.

    Google Scholar 

  119. Müller, W., Flesch, J., and Meyer, W. (1984). Treatment of intershell correlation effects in ab initio calculations by use of core polarization potentials. Method and application to alkali and alkaline earth atoms. J. Chem. Phys. 80: 3297–3310.

    Article  Google Scholar 

  120. Nicklass, A., Dolg, M., Stoll, H., and Preuss, H. (1995). Ab initio energy-adjusted pseudopotentials for the noble gases Ne through Xe: Calculation of atomic dipole and auadrupole polarizabilities. J. Chem. Phys. 102: 8942–8952.

    Article  CAS  Google Scholar 

  121. Schwerdtfeger, P., Silberbach, H. (1988). Multicenter integrals over long-range operators using Cartesian Gaussian functions. Phys. Rev. A 37: 2834–2842; ibid. (1988). 42: 665.

    Article  CAS  Google Scholar 

  122. Barthelat, J. C., Pelissier, M., Villemur, P., Devilliers, R., Trinquier, G., and Durand, Ph., (1981). Program PSHONDO (PSATOM), Manuel d’utilisation, Universite de Paul Sabatier, Toulouse, France.

    Google Scholar 

  123. Lajohn, L. A., Christiansen, P. A., Ross, R. B., Atashroo, T., and Ermler, W. C. (1987). Ab initio relativistic effective core potentials with spin-orbit operators. III. Rb through Xe. J. Chem. Phys. 87: 2812–2824.

    Article  CAS  Google Scholar 

  124. Igel-Mann, G., Stoll, H., and Preuss, H. (1988). Pseudopotentials for main group elements (IIIa through VIIa). Mol. Phys. 65: 1321–1328.

    Article  CAS  Google Scholar 

  125. Leininger, T., Nicklass, A., Stoll, H., Dolg, M., and Schwerdtfeger, P. (1996). The Accuracy of the Pseudopotential Approximation. II. A Comparison of Various Core Sizes for In Pseudopotentials in Calculations for Spectroscopic Constants of InH, InF, InCl. J. Chem. Phys. 105: 1052–1059.

    Article  CAS  Google Scholar 

  126. Andrae, D., Häussermann, U., Dolg, M., Stoll, H., and Preuss, H. (1990). Energy-adjusted ab initio pseudopotentials for the second and third row transition elements. Theor. Chim. Acta 77: 123–141.

    Article  CAS  Google Scholar 

  127. Bergner, A., Dolg, M., Küchle, W., Stoll, H., and Preuss, H. (1993). Ab initio-adjusted pseudopotentials for elements of group 13 through 17. Mol. Phys. 80: 1431–1441.

    Article  CAS  Google Scholar 

  128. Eliav, E., Kaldor, U., and Ishikawa, Y. (1995). Transition energies of mercury and ekamercury (element 112) by the relativistic coupled-cluster method. Phys. Rev. A 52: 2765–27.

    Article  CAS  Google Scholar 

  129. Moore, C. E. (1958). Atomic Energy Levels, US GPO, Washington.

    Google Scholar 

  130. Dyall, K. G., Bauschlicher Jr., C. W., Schwenke, D. W., and Pyykkö, P. (2001). Is the Lamb shift chemically significant?, Chem. Phys. Lett. 348: 497–500.

    Article  CAS  Google Scholar 

  131. Mosyagin, N. S., Eliav, E., Titov, A. V., and Kaldor, U. (2000). Comparison of relativistic effective core potential and all-electron Dirac-Coulomb calculations of mercury transition energies by the relativistic coupled-cluster method. J. Phys. B: At. Mol. Opt. Phys. 33: 667–676.

    Article  CAS  Google Scholar 

  132. Küchle, W., Dolg, M., Stoll, H., and Preuss, H. (1991). Ab initio pseudopotentials for Hg through Rn. I. Parameter sets and atomic calculations. Mol. Phys. 74: 1245–1263.

    Article  Google Scholar 

  133. Häussermann, U., Dolg, M., Stoll, H., Preuss, H., Schwerdtfeger, P., and Pitzer, R. M. (1993). Accuracy of energy-adjusted quasirelativistic ab-initio pseudopotentials: all-electron and pseudopotential benchmark calculations for Hg, HgH and their cations. Mol. Phys. 87: 1211–1224.

    Article  Google Scholar 

  134. Dolg, M., personal communication.

    Google Scholar 

  135. Goebel, D., and Hohm, U. (1995). Dispersion of the refractive index of cadmium vapor and the dipole polarizability of the atomic cadmium 1S0 state. Phys. Rev. A 52: 3691–3694.

    Article  CAS  Google Scholar 

  136. Goebel, D., and Hohm, U. (1996). Dipole polarizability, Cauchy moments, and related properties of Hg. J. Phys. Chem. 100: 7710–7712.

    Article  CAS  Google Scholar 

  137. Kellö, V., and Sadlej, A., (1995). Polarized basis sets for high-level-correlated calculations of molecular properties. VIII. Elements of the group IIb: Zn, Cd, Hg. Theor. Chim. Acta 91: 353–371.

    Google Scholar 

  138. Siekierski, S., Autschbach, J., Schwerdtfeger, P., Seth, M. and Schwarz, W.H.E. (2002). The dependence of relativistic effects on the electronic configurations in the atoms of the d- and f-block elements. J. Comput. Chem., in press.

    Google Scholar 

  139. Ziegler, T., Tschinke, V., Baerends, E. J., Snijders, J. G., and Ravenek, W. (1989). Calculation of Bond Energies in Compounds of Heavy Elements by a Quasi-Relativistic Approach. J. Phys. Chem. 93: 3050–3062.

    Article  CAS  Google Scholar 

  140. Strömberg, D., and Wahlgren, U. (1990). First-order relativistic calculations on Au2 and Hg2 2+. Chem. Phys. Lett. 169: 109–115.

    Article  Google Scholar 

  141. Schwerdtfeger, P., (1991). Relativistic and Electron Correlation Contributions in Atomic and Molecular Properties. Benchmark Calculations on Au and Au2. Chem Phys. Lett. 183: 457–463.

    Article  CAS  Google Scholar 

  142. Häberlen, O. D., and Rösch, N. (1992). A scalar-relativistic extension of the linear combination of Gaussian-type orbitals local density functional method: application to AuH, AuCl and Au2. Chem. Phys. Lett. 199: 491–496.

    Article  Google Scholar 

  143. Bastug, T., Heinemann, D., Sepp, W.-D., Kolb, D., and Fricke, B. (1993). All-electron Dirac-Fock-Slater SCF calculations of the Au2 molecule. Chem. Phys. Lett. 211: 119–124.

    Article  CAS  Google Scholar 

  144. Hess, B. A. and Kaldor, U. (2000). Relativistic all-electron coupled cluster calculations on Au2 in the framework of the Douglas-Kroll transformation. J. Chem. Phys. 112: 1809–1813.

    Article  CAS  Google Scholar 

  145. van Lenthe, E., Baerends, E. J., and Snijders, J. G. (1994). Relativistic total energy using regular approximations. J. Chem. Phys. 101: 9783–9792.

    Article  Google Scholar 

  146. Park, C., and Almlöf, J. E. (1994). Two-electron relativistic effects in molecules. Chem. Phys. Lett. 231: 269–276.

    Article  CAS  Google Scholar 

  147. van Wüllen, C. (1995). A relativistic Kohn-Sham density functional procedure by means of direct perturbation theory. J. Chem. Phys. 103: 3589–3599.

    Article  Google Scholar 

  148. Wesendrup, R., Laerdahl, J.K., and Schwerdtfeger, P. (1999). Relativistic Effects in Gold Chemistry. VI. Coupled Cluster Calculations for the Isoelectronic Series AuPt- , Au2 and AuHg+. J. Chem. Phys. 110: 9457–9462.

    Article  CAS  Google Scholar 

  149. Suzumura, T., Nakajima, T., and Hirao, K. (1999). Ground State Properties of MH, MCl and M2 (M = Cu, Ag and Au) Calculated by a Scalar Relativistic Density Functional Theory. Int. J. Quantum Chem. 75: 757–766.

    Article  CAS  Google Scholar 

  150. Han, Y.-K., and Hirao, K. (2000). On the transferability of relativistic pseudopotentials in density-functional calculations: AuH, AuCl and Au2. Chem. Phys. Lett. 324: 453–458.

    Article  CAS  Google Scholar 

  151. Collins, C. L., Dyall, K. G., and Schaefer, H. F. (1995). Relativistic and correlation effects in CuH, AgH, and AuH: Comparison of various relativistic methods. J. Chem. Phys. 102: 2024–2031.

    Article  CAS  Google Scholar 

  152. Lee, H.-S., Han, Y.-K., Kim, M. C., Bae, C., and Lee, Y. S., Spin-orbit effects calculated by two-component coupled-cluster methods: test calculations on AuH, Au2, TlH and Tl2. Chem. Phys. Lett. 293: 97–102.

    Google Scholar 

  153. Schwerdtfeger, P., Boyd, P. D. W., Burrell, A. K., Taylor, M. J. (1990). Relativistic effects in gold chemistry. III. Gold(I) Complexes. Inorg. Chem. 29: 3593–3607.

    Article  CAS  Google Scholar 

  154. Huber, K. P., and Herzberg, G. (1979). Molecular Spectra and Molecular Structure, Constants of Diatomic Molecules, Van Nostrand, New York.

    Google Scholar 

  155. Schwerdtfeger, P., Brown, J. R. , Laerdahl, J. K., and Stoll, H. (2000). The accuracy of the pseudopotential approximation. III. A comparison between pseudopotential and all electron methods for Au and AuH. J. Chem. Phys. 113: 7110–7118.

    Article  CAS  Google Scholar 

  156. Kaldor, U., and Hess, B. A. (1994). Relativistic all-electron coupled-cluster calculations on the gold atom and gold hydride in the framework of the Douglas-Kroll transformation. Chem. Phys. Lett. 230: 1–7.

    Article  CAS  Google Scholar 

  157. Ross, R. B., Powers, J. M., Atashroo, T., Ermler, W. C., Lajohn, L. A., and Christiansen, P. A. (1990). Ab initio relativistic effective core potentials with spin-orbit operators. IV. Cs through Rn. J. Chem. Phys. 93: 6654–6670.

    Article  CAS  Google Scholar 

  158. Nakajima, T., and Hirao, K. (1999). A new relativistic theory: a relativistic scheme by eliminating small components (RESC). Chem. Phys. Lett. 302: 383–391.

    Article  CAS  Google Scholar 

  159. Filatov, M., and Cremer, D. (2002). A new quasi-relativistic approach for density functional theory based on the normalized elimination of the small component. Chem. Phys. Lett. 351: 259–266.

    Article  CAS  Google Scholar 

  160. Metz, B., Schweizer, M., Stoll, H., Dolg, M., and Liu, W. (2000). A small-core multiconfiguration Dirac-Hartree-Fock-adjusted pseudopotential for Tl — application to TlX (X= F, Cl, Br, I). Theor. Chem. Acta 104: 22–28.

    Article  CAS  Google Scholar 

  161. Eliav, E., Kaldor, U., Ishikawa, Y., Seth, M., and Pyykkö, P. (1996). Calculated energy levels of thallium and eka-thallium (element 113). Phys. Rev. A 53: 3926–3933.

    Article  CAS  Google Scholar 

  162. Schwerdtfeger, P., and Ischtwan, J. (1994). The Convergence of the Møller-Plesset Series in Molecular Properties of Group 13 compounds. Comparison between HF, MP and QCI Calculations of MH and MF (M= B, Al, Ga, In, Tl). J. Molec. Stuct. (THEOCHEM) 306: 9–19.

    Article  Google Scholar 

  163. Seijo, L. (1995). Relativistic ab initio model potential calculations including spin-orbit effects through the Wood-Boring Hamiltonian. J. Chem. Phys. 102: 8078–8088.

    Article  CAS  Google Scholar 

  164. Rakowitz, F.; and Marian, C. M. (1997). An extrapolation for spin-orbit configuration interaction energies to the ground state and excited electronic states of thallium hydride. Chem. Phys. 225: 223–238.

    Article  CAS  Google Scholar 

  165. Seth, M., Schwerdtfeger, P., and Faegri, K. (1999). The chemistry of superheavy elements. III. Theoretical studies of element 113 compounds. J. Chem. Phys. 111: 6422–6433.

    Article  CAS  Google Scholar 

  166. Han, Y., Bae, C., and Lee, Y. S. (1999). Two-component calculations for the molecules containing superheavy elements: Spin-orbit effects for (117)H, (113)H, and (113)F. J. Chem. Phys. 110: 8969–8975.

    Article  CAS  Google Scholar 

  167. Nash, C. S., Bursten, B. E., and Ermler, W. C. (1997). Ab initio relativistic effective potentials with spin-orbit operators. VII. Am through element 118. J. Chem. Phys. 106: 5133–5142.

    Article  CAS  Google Scholar 

  168. Teichteil, C., Malrieu, J. P., and Barthelat, J. C. (1977). Non-empirical pseudopotentials for molecular calculations. II. Basis set extension and correlation effects on the X2 molecules (X= f, Cl, Br, I). Mol. Phys. 33: 181–197.

    Article  CAS  Google Scholar 

  169. Pittel, B., and Schwarz, W. H. E. (1977). Correlation energies from pseudopotential calculations. Chem. Phys. Lett. 46: 121–124.

    Article  CAS  Google Scholar 

  170. Dolg, M. (1996). Valence correlation energies from pseudopotential calculations. Chem. Phys. Lett. 250: 75–79.

    Article  CAS  Google Scholar 

  171. Dolg, M. (1996). On the accuracy of valence correlation energies in pseudopotential calculations. J. Chem. Phys. 104: 4061–4067.

    Article  CAS  Google Scholar 

  172. Hetényi, B., De Angelis, F., Giannozzi, P., and Car, R. (2001). Reconstruction of frozen-core all-electron orbitals from pseudo-orbitals. J. Chem. Phys. 115: 5791–5795.

    Article  CAS  Google Scholar 

  173. Leininger, T., Riehl, J.-F., Jeung, G.-H., and Pélissier, M. (1993). Comparison of the widely used HF pseudo-potentials: MH+ (M=Fe, Ru, Os). Chem. Phys. Lett. 205: 301–305.

    Article  CAS  Google Scholar 

  174. Andrae, D., Dolg, M., Stoll, H., and Ermler, W. C. (1994). Comment on “Comparison of the widely used HF pseudo-potentials: MH+ (M=Fe, Ru, Os)”. Chem. Phys. Lett. 220: 341–344.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Schwerdtfeger, P. (2003). Relativistic Pseudopotentials. 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_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0105-1_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6313-7

  • Online ISBN: 978-94-017-0105-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics