Skip to main content

Abstract

Ab initio calculations at the self-consistent-field and singles plus doubles configuration-interaction level are used to determine accurate spectroscopic parameters (De, re, ωu) for most of the alkali and alkaline-earth fluorides, chlorides, oxides, sulfides, hydroxides and isocyanides. Numerical Hartree-Fock (NHF) calculations are performed on selected systems to ensure that the extended Slater basis sets employed for the diatomic systems are near the Hartree-Fock limit. Extended gaussian basis sets of at least triple-zeta plus double polarization quality are employed for the triatomic systems. By dissociating to the ionic limits, most of the differential correlation effects can be embedded in the accurate experimental electron affinities and ionization potentials. With this model, correlation effects are relatively small (0.0–0.3 eV), but invariably increase Do. The importance of correlating the electrons on both the anion and the metal is discussed.

The theoretical dissociation energies (Do) are critically compared with the literature to rule out disparate experimental values. The theoretical studies combined with the experimental literature allow us to recommend Do values that are accurate to 0.1 eV for all systems considered. The systematic treatment of many different systems reveal many trends. For example, the dissociation energies of the alkali and alkaline-earth hydroxides are observed to be less than the corresponding fluorides by just slightly less than the difference in electron affinities of F and OH. In general, there is a strong correlation between the dissociation energy (to ions) and r, because the bonding is predominantly electrostatic in origin.

Theoretical 2Π-2Σ+ energy separations are presented for the alkali oxides and sulfides. The ground states of all the alkali sulfides are shown to be X2Π. An extensive study of the 2Π-2Σ+ energy separation in KO reveals a 2Σ+ ground state at all levels of theory. The separation is shown to be sensitive to basis set quality, and in the NHF limit the 2Σ+ state is lower by about 250 cm-1. The separation is almost unaffected when the 16 valence electrons are correlated at the singles plus doubles level using an extended Slater basis.

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. L. Brewer and E. Brackett, Chem. Rev. 61, 425 (1961).

    Article  CAS  Google Scholar 

  2. I.V. Veits and L.V. Gurvich, Zh. Fiz. Khim. 31, 2306 (1957).

    CAS  Google Scholar 

  3. J. Drowart, G. Exsteen and G. Verhaegen, Trans. Farad. Soc. 60, 1920 (1964).

    Article  CAS  Google Scholar 

  4. D.H. Cotton and D.R. Jenkins, Trans. Farad. Soc. 65, 376 (1969).

    Article  CAS  Google Scholar 

  5. P.J.T. Zeegers, W.P. Townsend and J.D. Winefordner, Spectrochim. Acta 26B, 234 (1969).

    Google Scholar 

  6. J.W. Cox and P.J. Dagdigian, J. Phys. Chem. 88, 2455 (1984).

    Article  CAS  Google Scholar 

  7. R.D. Srivastava, High Temp. Sci. 8, 225 (1976).

    CAS  Google Scholar 

  8. R.D. Srivastava, High Temp. Recommended values based on review of the experimental literature through 1975.

    Google Scholar 

  9. C.W. Bauschlicher, B.H. Lengsfield III and B. Liu, J. Chem. Phys. 77, 4084 (1982).

    Article  CAS  Google Scholar 

  10. F. Engelke, R.K. Sander and R.N. Zare, J. Chem. Phys. 65, 1146 (1976).

    Article  CAS  Google Scholar 

  11. J.A. Irvin and P.J. Dagdigian, J. Chem. Phys. 73, 176 (1980).

    Article  CAS  Google Scholar 

  12. C.W. Bauschlicher and H. Partridge, Chem. Phys. Letters 94, 366 (1983).

    Article  CAS  Google Scholar 

  13. R.R. Herrn and D.R. Herschbach, J. Chem. Phys. 52, 5783 (1970).

    Article  Google Scholar 

  14. D.M. Lindsay, D.R. Herschbach and A.L. Kwiram, J. Chem. Phys. 60, 315 (1974).

    Article  CAS  Google Scholar 

  15. S.P. So and W.G. Richards, Chem. Phys. Letters 32, 227 (1975).

    Article  CAS  Google Scholar 

  16. J.N. Allison and W.A. Goddard III, J. Chem. Phys. 77, 4259 (1982).

    Article  CAS  Google Scholar 

  17. See also J.N. Allison, R.J. Cave and W.A. Goddard III, J. Phys. Chem. 88, 1262 (1984).

    Article  CAS  Google Scholar 

  18. L. Pauling, “The Nature of the Chemical Bond,” (Cornell University Press, Ithaca, New York, 1944), Second edition, p. 46.

    Google Scholar 

  19. E.S. Rittner, J. Chem. Phys. 19,1030 (1951). The Rittner model is expected to be a good approximation only when the condition r6 ≫ 4α+α- is satisfied. Since this is not the case for the alkaline-earth monohalides owing to the much larger polarizabilities of the alkaline-earth ions, improved ionic models have recently been proposed. See e.g. S.F. Rice, H. Martin and R.W. Field (J. Phys. Chem. in press)

    Article  CAS  Google Scholar 

  20. T. Torring, W.E. Ernst and S. Kindt, J. Chem. Phys. 81, 4614 (1984).

    Article  Google Scholar 

  21. Y.S. Kim and R.G. Gordon, J. Chem. Phys. 60, 4332 (1974).

    Article  CAS  Google Scholar 

  22. R.L. Matcha, J. Chem. Phys. 47, 4595 (1967);

    Article  CAS  Google Scholar 

  23. R.L. Matcha, J. Chem. Phys.47, 5295 (1967);

    Article  CAS  Google Scholar 

  24. R.L. Matcha, J. Chem. Phys.48, 335 (1968);

    Article  CAS  Google Scholar 

  25. R.L. Matcha, J. Chem. Phys.49, 1264 (1968);

    Article  CAS  Google Scholar 

  26. R.L. Matcha, J. Chem. Phys. 53, 485 (1970).

    Article  CAS  Google Scholar 

  27. C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand. (US) Circ. 467 (1949).

    Google Scholar 

  28. H. Hotop and W.C. Lineberger, J. Phys. and Chem. Ref. Data 4, 530 (1975).

    Google Scholar 

  29. E. Clementi and C. Roetti, At. Data Nuc. Data Tables 14, 177 (1974).

    Article  CAS  Google Scholar 

  30. S.R. Langhoff, C.W. Bauschlicher and H. Partridge, “Theoretical dissociation energies of the alkali and alkaline-earth fluorides and chlorides” (to be published).

    Google Scholar 

  31. S.R. Langhoff, C.W. Bauschlicher and H. Partridge, “Theoretical dissociation energies of the alkali and alkaline-earth oxides” (to be published).

    Google Scholar 

  32. H. Partridge, C.W. Bauschlicher and S.R. Langhoff, “The Dissociation energy of SrO” (to be published).

    Google Scholar 

  33. H. Partridge, C.W. Bauschlicher and S.R. Langhoff, “Theoretical dissociation energies of the alkali and alkaline-earth sulfides” (to be published).

    Google Scholar 

  34. C.W. Bauschlicher, S.R. Langhoff and H. Partridge, “Ab initio study of the alkali and alkaline-earth hydroxides” (to be published).

    Google Scholar 

  35. H. Partridge, C.W. Bauschlicher and S.R. Langhoff, “Ab initio study of the positive ions of alkaline-earth hydroxides” (to be published).

    Google Scholar 

  36. E.A. McCullough Jr., J. Chem. Phys. 62, 3991 (1975);

    Article  CAS  Google Scholar 

  37. L. Adamowicz and E.A. McCullough Jr., J. Chem. Phys. 75, 2475 (1981);

    Article  CAS  Google Scholar 

  38. E.A. McCullough Jr., J. Phys. Chem. 86, 2178 (1982).

    Article  CAS  Google Scholar 

  39. A.T. Amos and G.G. Hall, Proc. R. Soc. London Ser. A 263, 483 (1961).

    Article  Google Scholar 

  40. S.R. Langhoff and E.R. Davidson, Int. J. Quant. Chem. 8, 61 (1974).

    Article  CAS  Google Scholar 

  41. See also E.R. Davidson LUANDTin “The World of Quantum Chemistry,” edited by R. Daudel and B. Pullman (Reidel, Dordrecht, 1974).

    Google Scholar 

  42. W. Meyer, Int. J. Quant. Chem. 55, 341 (1971).

    Google Scholar 

  43. R. Ahlrichs, H. Lischka, V. Staemmler and W. Kutzelnigg, J. Chem. Phys. 62, 1225 (1975).

    Article  CAS  Google Scholar 

  44. A. Bunge, J. Chem. Phys. 53, 20 (1970);

    Article  CAS  Google Scholar 

  45. A.D. McLean and B. Liu, ibid. 58, 1066 (1973);

    Article  CAS  Google Scholar 

  46. C.F. Bender and H.F. Schaefer, ibid. 55, 7498 (1971).

    Google Scholar 

  47. MOLECULE is a gaussian integral program written by J. Almlof. SWEDEN is a vectorized SCF-MCSCF-CI program written by P.E.M. Siegbahn, C.W. Bauschlicher, B.O. Roos, P.R. Taylor, A. Heiberg and J. Almlof.

    Google Scholar 

  48. The codes have been modified and vectorized for the Cyber 205 by R. Ahlrichs and coworkers. See also R. Ahlrichs, H.-J. Bohm, C. Ehrhardt, P. Scharf, H. Schiffer, H. Lischka and M. Schindler, J. Comp. Chem., in press.

    Google Scholar 

  49. The Columbus codes include the Gaussian integral and SCF programs of R. Pitzer and the unitary group CI codes of I. Shavitt, F. Brown, H. Lischka and R. Shepard.

    Google Scholar 

  50. R.M. Pitzer, J. Chem. Phys. 58, 3111 (1973).

    Article  Google Scholar 

  51. H. Lischka, R. Shepard, F.B. Brown and I. Shavitt, Int. J. Quant. Chem. Symp. 15, 91 (1981).

    CAS  Google Scholar 

  52. R. Shepard, I. Shavitt and J. Simons, J. Chem. Phys. 76, 543 (1982).

    Article  CAS  Google Scholar 

  53. S. Hagstrom, QCPE 10, 252 (1975); S. Hagstrom and H. Partridge (unpublished).

    Google Scholar 

  54. E.M. Bulewicz, L.F. Phillips and T.M. Sugden, Trans. Faraday Soc. 57, 921 (1961).

    Article  CAS  Google Scholar 

  55. D.O. Ham, J. Chem. Phys. 60, 1802 (1974).

    Article  CAS  Google Scholar 

  56. J. Berkowitz, J. Chem. Phys. 50, 3503 (1969);

    Article  CAS  Google Scholar 

  57. J. Berkowitz, J. Chem. Adv. High Temp. Chem. 3, 158 (1971).

    Google Scholar 

  58. E.K. Parks and S. Wexler, J. Phys. Chem. 88, 4492 (1984).

    Article  Google Scholar 

  59. M.D. Scheer and J. Fine, J. Chem. Phys. 36, 1647 (1961).

    Article  Google Scholar 

  60. D.L. Hildenbrand and E. Murad, J. Chem. Phys. 44, 1524 (1966).

    Article  CAS  Google Scholar 

  61. M. Farber and R.D. Srivastava, J. Chem. Soc. Faraday Trans. I. 70, 1581 (1974).

    Article  CAS  Google Scholar 

  62. See also M. Farber and R.D. Srivastava, High Temp. Sci. 8, 1985 (1976).

    Google Scholar 

  63. T.C. Ehlert, G.D. Blue, J.W. Green and J.L. Margrave, J. Chem. Phys. 41, 2250 (1964).

    Article  CAS  Google Scholar 

  64. P.D. Kleinschmidt and D.L. Hildenbrand, J. Chem. Phys. 68, 2823 (1978). See also D.L. Hildenbrand, J. Chem. Phys. 48, 3657 (1968).

    Google Scholar 

  65. Z. Karny and R.N. Zare, J. Chem. Phys. 68, 3360 (1978).

    Article  CAS  Google Scholar 

  66. G.D. Blue, J.W. Green, R.G. Bautista and J.L. Margrave, J. Chem. Phys. 67, 877 (1963).

    Article  CAS  Google Scholar 

  67. See also CD. Blue, J.W. Green, T.C. Ehlert and J.L. Margrave, Nature 199, 804 (1963).

    Google Scholar 

  68. V.G. Ryabova and L.V. Gurvich, High Temperature 2, 749 (1964).

    Google Scholar 

  69. R.L. Jaffe (private communication).

    Google Scholar 

  70. D.L. Hildenbrand and L.P. Theard, J. Chem. Phys. 50,5350 (1969).

    Article  CAS  Google Scholar 

  71. M. Farber and R.D. Srivastava, J. Chem. Soc. Faraday I 69, 390 (1973).

    Article  CAS  Google Scholar 

  72. D.L. Hildenbrand, J. Chem. Phys. 52, 5751 (1970).

    Article  CAS  Google Scholar 

  73. M. Farber and R.D. Srivastava, Chem. Phys. Letters 42, 567 (1976).

    Article  CAS  Google Scholar 

  74. K.F. Zmbov, Chem. Phys. Letters 4, 191 (1969).

    Article  CAS  Google Scholar 

  75. L.V. Gurvich, V.G. Ryabova and A.N. Khitrov, Faraday Symp. Chem. Soc. 8, 83 (1973).

    Article  Google Scholar 

  76. CD. Jonah and R.N. Zare, Chem. Phys. Letters 9, 65 (1971).

    Article  CAS  Google Scholar 

  77. M. Yoshimine, J. Chem. Phys. 57, 1108 (1972).

    Article  CAS  Google Scholar 

  78. P.A.G. O’Hare and A.C. Wahl, J. Chem. Phys. 56, 4516 (1972).

    Article  Google Scholar 

  79. B.C. Laskowski, S.R. Langhoff and P.E.M. Siegbahn, Int. J. Quant. Chem. 23, 483 (1983).

    Article  CAS  Google Scholar 

  80. S.M. Freund, E. Herbst, R.P. Mariella and W. Kleraperer, J. Chem. Phys. 56, 1467 (1972);

    Article  CAS  Google Scholar 

  81. R.A. Berg, L. Wharton, W. Klemperer, A. Buchler and J.L. Stauffer, ibid 43, 2416 (1965).

    Google Scholar 

  82. D.L. Hildenbrand, J. Chem. Phys. 57, 4556 (1972).

    Article  CAS  Google Scholar 

  83. D.L. Hildenbrand and E. Murad, J. Chem. Phys. 53, 3403 (1970).

    Article  CAS  Google Scholar 

  84. T.C. Ehlert, High Temp. Science 9, 237 (1977).

    CAS  Google Scholar 

  85. A.V. Gusarov and L.N. Gorokhov, Teplofiz Vys. Temp. 9, 505 (1971).

    CAS  Google Scholar 

  86. K.P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure,” (Van Nostrand Reinhold, New York, 1979).

    Google Scholar 

  87. H. Lavendy, B. Pouilly and J.M. Robbe, J. Mol. Spectrosc. 103, 379 (1984).

    Article  Google Scholar 

  88. W.A. Chupka, J. Berkowitz and CF. Giese, J. Chem. Phys. 30, 827 (1959).

    Article  CAS  Google Scholar 

  89. T. Ikeda, N.B. Wong, D.O. Harris and R.W. Field, J. Mol. Spectrosc. 68, 452 (1977). See also R.W. Field, Air Force Goephysics Laboratory Report No. AFGL-TR-83–0021.

    Article  CAS  Google Scholar 

  90. R.N. Zare (private communication).

    Google Scholar 

  91. C.W. Bauschlicher, B.H. Lengsfield III, D.M. Silver and D.R. Yarkony, J. Chem. Phys. 74, 2379 (1981).

    Article  CAS  Google Scholar 

  92. C.W. Bauschlicher and D.R. Yarkony, J. Chem. Phys. 68, 3990 (1978).

    Article  CAS  Google Scholar 

  93. G.A. Capelle, H.P. Broida and R.W. Field, J. Chem. Phys. 62, 3131 (1975).

    Article  CAS  Google Scholar 

  94. R.W. Field, J. Chem. Phys. 60, 2400 (1974).

    Article  CAS  Google Scholar 

  95. B. Pouilly, J.M. Robbe, J. Schamps, R.W. Field and L. Young, J. Mol. Spectrosc. 96, 1 (1982).

    Article  CAS  Google Scholar 

  96. See also C.J. Cheetham, W.J.M. Gissane and R.F. Barrow, Trans. Faraday Soc. 61, 1308 (1965).

    Article  CAS  Google Scholar 

  97. M.W. Chase, Jr., J.L. Curnutt, J.R. Downey, Jr., R.A. McDonald and A.N. Syverud, J. Phys. and Chem. Ref. Data 11, 695 (1982). JANAF Thermochemical Tables, 1982 supplement and related volumes.

    CAS  Google Scholar 

  98. D.L. Hildenbrand,LUANDT “Advances in High Temperature Chemistry,” Vol. 1, L. Eyring (ed.), pp. 198–206, Academic Press.

    Google Scholar 

  99. R. Colin, P. Goldfinger and M. Jeunehoramer, Trans. Faraday Soc. 60, 306 (1964).

    Article  CAS  Google Scholar 

  100. J.R. Marquart and J. Berkowitz, J. Chem. Phys. 39, 283 (1963).

    Article  CAS  Google Scholar 

  101. D.H. Cotton and D.R. Jenkins, Trans. Faraday Soc. 65, 1537 (1969).

    Article  CAS  Google Scholar 

  102. P.J.Th. Zeegers and C.Th.J. Alkemade, Combustion and Flame 15, 193 (1970).

    Article  CAS  Google Scholar 

  103. D.E. Jensen, J. Phys. Chem. 74, 207 (1970).

    Article  CAS  Google Scholar 

  104. See also D.E. Jensen and P.J. Padley, Trans. Faraday Soc. 62, 2132 (1966).

    Article  CAS  Google Scholar 

  105. H.C. Ko, M.A. Greenbaum and M. Farber, J. Phys. Chem. 71, 1875 (1967).

    Article  CAS  Google Scholar 

  106. Y.H. Inami and F. Ju, work reported in JANAF Thermochemical Tables (Ref. 87).

    Google Scholar 

  107. M.W. Chase, J.L. Curnutt, R.A. McDonald and A.N. Syverud, J. Phys. and Chem. Ref. Data 7, 793 (1978).

    Article  CAS  Google Scholar 

  108. D.H. Cotton and D.R. Jenkins, Trans. Faraday Soc. 65, 376 (1969).

    Article  CAS  Google Scholar 

  109. E.M. Bulewicz and T.M. Sugden, Trans. Faraday Soc. 55, 720 (1959).

    Article  CAS  Google Scholar 

  110. E. Murad, Chem. Phys. Letters 72, 295 (1980).

    Article  CAS  Google Scholar 

  111. P.J. Kalff and C.Th.J. Alkeraade, J. Chem. Phys. 59, 2572 (1973).

    Article  CAS  Google Scholar 

  112. D.H. Cotton and D.R. Jenkins, Trans. Faraday Soc. 64, 2988 (1968).

    Article  CAS  Google Scholar 

  113. V.G. Ryabova, A.N. Khitrov and L.V. Gurvich, High Temp. 10, 669 (1972).

    Google Scholar 

  114. E. Murad, J. Chem. Phys. 75, 4080 (1981).

    Article  CAS  Google Scholar 

  115. J. van der Hurk, Tj. Hollander and C.Th.J. Alkemade, J. Quant. Spectrosc. Radiat. Transfer 14, 1167 (1974).

    Article  Google Scholar 

  116. L.V. Gurvich, V.G. Ryabova, A.N. Khitrov and E.M. Starovoitov, High Temp. 9, 261 (1971).

    Google Scholar 

  117. F.E. Stafford and J. Berkowitz, J. Chem. Phys. 40, 2963 (1964).

    Article  Google Scholar 

  118. R.J. Celotta, R.A. Bennet and J.L. Hall, J. Chem. Phys. 60, 1740 (1974).

    Article  CAS  Google Scholar 

  119. C.W. Bauschlicher and H. Partridge, Chem. Phys. Letters 106, 65 (1984).

    Article  CAS  Google Scholar 

  120. S.M. Freund, P.D. Godfrey and W. Klemperer, 25th Symposium on Molecular Structure and Spectroscopy, Ohio State University, Columbus, Ohio, 1970, paper E-8- moment of inertia reported for LiOH.

    Google Scholar 

  121. P. Kuijpers, T. Torring and A. Dymanus, Chem. Phys. 15, 457 (1976).

    Article  CAS  Google Scholar 

  122. N. Acquista and S. Abramowitz, J. Chem. Phys. 51, 2911 (1969).

    Article  CAS  Google Scholar 

  123. E.F. Pearson, B.P. Winnewisser and M.B. Trueblood, Z. Naturfosch 31, 1259 (1976).

    Google Scholar 

  124. A.A. Belyaeva, M.I. Dvorkin and L.D. Sheherba, Opt. Spectrosc. 31, 210 (1966).

    Google Scholar 

  125. D.R. Lide and C. Matsumura, J. Chem. Phys. 50, 3080 (1969).

    Article  CAS  Google Scholar 

  126. D.R. Lide and R.L. Kuczkowski, J. Chem. Phys. 46, 4768 (1967).

    Article  CAS  Google Scholar 

  127. N. Aquista, S. Abramowitz and D.R. Lide, J. Chem. Phys. 49, 780 (1968).

    Article  Google Scholar 

  128. R.C. Hilborn, Z. Qingshi and D.O. Harris, J. Mol. Spectrosc. 97, 73 (1983).

    Article  CAS  Google Scholar 

  129. J. Nakagawa, R.F. Wormsbecher and D.O. Harris, J. Mol. Spectrosc. 97, 37 (1983).

    Article  CAS  Google Scholar 

  130. C.W. Bauschlicher, S.R. Langhoff and H. Partridge, “Ab Initio Study of BeCN, MgCN, CaCN and BaCN,” Chem. Phys. Letters (in press).

    Google Scholar 

  131. T. Torring, J.P. Bekooy, W.L. Meerts, J. Hoeft, E. Tiemann and A. Dymanus, J. Chem. Phys. 13, 4875 (1980).

    Article  Google Scholar 

  132. J.J. Van Vaals, W.L. Meerts and A. Dymanus, Chera. Phys. 86, 147 (1984).

    Article  Google Scholar 

  133. P.E.S. Wormer and J. Tennyson, J. Chera. Phys. 75, 1245 (1981).

    Article  CAS  Google Scholar 

  134. M.L. Klein, J.D. Goddard and D.G. Bounds, J. Chera. Phys. 75, 3909 (1981).

    Article  CAS  Google Scholar 

  135. C.J. Marsden, J. Chera. Phys. 76, 6451 (1982).

    Article  CAS  Google Scholar 

  136. L. Pasternack and P.J. Dagdigian, J. Chera. Phys. 65, 1320 (1976).

    Article  CAS  Google Scholar 

  137. J. Berkowitz, W.A. Chupka and T.A. Walter, J. Chera. Phys. 50, 1497 (1969).

    Article  CAS  Google Scholar 

  138. B.V. L’vov and L.A. Pelieva, Prog. Analyt. Atomic Spectrosc. 3, 65 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 D. Reidel Publishing Company

About this paper

Cite this paper

Langhoff, S.R., Bauschlicher, C.W., Partridge, H. (1985). Theoretical Dissociation Energies for Ionic Molecules. In: Bartlett, R.J. (eds) Comparison of Ab Initio Quantum Chemistry with Experiment for Small Molecules. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5474-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-5474-8_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8917-3

  • Online ISBN: 978-94-009-5474-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics