Skip to main content
Log in

A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations

  • Original Investigations
  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Abstract

The crystal orbital formalism in the tight-binding approximation is combined with a recently developed CNDO/INDO model for transition metal species of the 3d series in order to allow band structure calculations on the Hartree-Fock (HF) SCF level for one-dimensional (1D) chains with organometallic unit cells. The band structure approach based on the CNDO and INDO approximation can be used for any atom combination up to bromine under the inclusion of the 3d series. The matrix elements for the tight-binding Hamiltonian are derived for an improved CNDO and INDO framework. The total energy of the 1D chain is partitioned into one-center contributions and into two-center increments of the intracell and intercell type. Semiempirical band structure calculations on simple model systems are compared with available ab initio data of high quality.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yoffe, A. D.: Chem. Soc. Rev. 5, 51 (1976); Goodings, E. P.: ibid. 5, 91 (1976); Miller, J. S., Epstein, A. J.: Prog. Inorg. Chem. 20, 1 (1976); Hanack, M.: Nachr. Chem. Techn. Lab. 8, 632 (1980)

    Google Scholar 

  2. Keller, H. J., Ed.: Chemistry and physics of one dimensional metals. New York: Plenum Press 1978; Keller, H. J., Ed.: Low dimensional cooperative phenomena. New York: Plenum Press 1975, Hatfield, W. E. Ed.: Molecular metals. New York: Plenum Press 1979

    Google Scholar 

  3. Krogmann, K.: Angew. Chem. 81, 10 (1969)

    Google Scholar 

  4. Cowan, D. O., Park, J., Pittmann, C. U., Sasaki, Y., Mukherjee, T. K., Diamond, N. A.: J. Am. Chem. Soc. 94, 5110 (1972).

    Google Scholar 

  5. Gleizes, A., Marks, T. J., Ibers, J. A.: J. Am. Chem. Soc. 97, 3546 (1975); Cowie, M., Gleizes, A., Grynkewich, G. W., Kalina, D. W., McGlure, M. S., Scaringe, R. P., Teitelbaum, R. C., Ruby, S. L., Ibers, J. A., Kannewurf, C. R., Marks, T. J.: ibid. 101, 2921 (1979); Kalina, D. W., Lyding, J. W., Ratajack, M. T., Kannewurf, C. R., Marks, T. J.: ibid, 102, 7854 (1980)

    Google Scholar 

  6. Brown, L. D., Kalina, D. W., McGlure, M. S., Schultz, S., Ruby, S. L., Ibers, J. A., Kannewurf, C. R., Marks, T. J.: J. Am. Chem. Soc. 101, 2937 (1979)

    Google Scholar 

  7. Schramm, C. J., Scaringe, R. P., Stojakovic, D. R., Hoffman, B. M., Ibers, J. A., Marks, T. J.: J. Am. Chem. Soc. 102, 6702 (1980)

    Google Scholar 

  8. Petersen, J. L., Schramm, C. S., Stojakovic, D. R., Hoffman, B. M., Marks, T. J.: J. Am. Chem. Soc. 99, 286 (1977); Phillips, T.E., Hoffman, B. M.: ibid. 99, 7734 (1977); Schramm, C. J., Stojakovic, D. R., Hoffman, B. M., Marks, T. J.: Science 200, 47 (1978)

    Google Scholar 

  9. Philips, T. E., Scaringe, R. P., Hoffman, B. M., Ibers, J. A.: J. Am. Chem. Soc. 102, 3435 (1980); Martinsen, J., Pace, L. J., Philipps, T. E., Hoffman, B. M., Ibers, J. A.: ibid. 104, 83 (1982)

    Google Scholar 

  10. Schoch, K. F., Kundalkar, B. R., Marks, T. J.: J. Am. Chem. Soc. 101, 7071 (1979)

    Google Scholar 

  11. Interrante, L. V., Messmer, R. P.: Chem. Phys. Letters 26, 225 (1974)

    Google Scholar 

  12. Bullett, D. W.: Solid State Commun. 23, 893 (1977)

    Google Scholar 

  13. Whangbo, M.-H., Hoffmann, R.: J. Am. Chem. Soc. 100, 6093 (1978)

    Google Scholar 

  14. Seelig, F. F.: Z. Naturforsch. 34a, 986 (1979)

    Google Scholar 

  15. Whangbo, M.-H.: J. Chem. Phys. 70, 4963 (1979); Whangbo, M.-H.: ibid. 73, 3854 (1980)

    Google Scholar 

  16. Whangbo, M.-H., Foshee, M. J., Hoffmann, R.: Inorg. Chem. 19, 1723 (1980)

    Google Scholar 

  17. Böhm, M. C., Gleiter, R.: Theoret. Chim. Acta (Berl.) 59, 127 (1981)

    Google Scholar 

  18. Böhm, M. C., Gleiter, R.: Theoret. Chim. Acta (Berl.) 59, 153 (1981)

    Google Scholar 

  19. Böhm, M. C., Gleiter, R.: J. Organomet. Chem. 228, 1 (1982)

    Google Scholar 

  20. Böhm, M. C., Eckert-Maksić, M., Ernst, R. D., Wilson, D. R., Gleiter, R.: J. Am. Chem. Soc. 104, 2699 (1982)

    Google Scholar 

  21. Ionization energies determined by means of the ΔSCF or Transition Operator (TO) method: Böhm, M. C., Gleiter, R., Batich, C. D.: Helv. Chim. Acta 63, 990 (1980); Böhm, M. C., Gleiter, R.: Z. Naturforsch. 35b, 1028 (1980); Böhm, M. C., Gleiter, R.: Chem. Ber. 113, 3647, (1980); Böhm, M. C., Gleiter, R.: J. Comput. Chem. 1, 407 (1980)

    Google Scholar 

  22. Ionization energies determined by means of the Green's function method: Böhm, M. C., Gleiter, R.: Theoret. Chem. Acta (Berl.) 57, 315 (1980); Böhm, M. C.: Z. Naturforsch. 36a, 1361 (1981); Böhm, M. C., Gleiter, R.: Chem. Phys. 64, 183 (1982); Böhm, M. C., Gleiter, R., Petz, W.: Inorg. Chim. Acta 59, 255 (1982); Böhm, M. C.: Z. Phys. Chem. (Neue Folge) 129, 149 (1982); Böhm, M. C.: J. Molec. Struct. (Theochem) 89, 165 (1982)

    Google Scholar 

  23. Böhm, M. C.: Ber. Bunsenges. Phys. Chem. 85, 755 (1981); Böhm, M. C.: Chem. Phys. 60, 227 (1981); Böhm, M. C.: Theoret. Chim. Acta (Berl.) 60, 233 (1981); Böhm, M. C.: Mol. Phys. 46, 683 (1982); Böhm, M. C.: Int. J. Quantum Chem. submitted for publication.

    Google Scholar 

  24. Pople, J. A., Beveridge, D. L.: Approximate molecular orbital theory. New York: McGraw Hill, 1970

    Google Scholar 

  25. Del Re, G., Ladik, J., Biczó, G.: Phys. Rev. 155, 997 (1967)

    Google Scholar 

  26. Ladik, J.: Electronic structure of polymers and molecular crystals. Andre, J.-M., Ladik, J., Ed. New York: Plenum Press 1975

    Google Scholar 

  27. Morokuma, K.: J. Chem. Phys. 54, 962 (1971)

    Google Scholar 

  28. Fujita, H., Imamura, A.: J. Chem. Phys. 53, 4555 (1971)

    Google Scholar 

  29. McAloon, B. J., Perkins, P. G.: J.C.S. Faraday II 68, 1121 (1972)

    Google Scholar 

  30. Marwaha, A. K., Perkins, P. G., Steward, J. J. P.: Theoret. Chim. Acta (Berl.) 57, 1 (1980)

    Google Scholar 

  31. Cetina, E. A., Perkins, P. G.: Theoret. Chim. Acta (Berlin) 58, 257 (1981)

    Google Scholar 

  32. O'Shea, S., Santry, D. P.: J. Chem. Phys. 54, 2667 (1971)

    Google Scholar 

  33. Beveridge, D. L., Jano, I., Ladik, J.: I. Chem. Phys. 56, 4744 (1972)

    Google Scholar 

  34. Ladik, J.: Quantum theory of polymers. Andre, J.-M., Delhalle, J., Ladik, J., Ed. Dordrecht-Boston: D. Reidel Publ. Co. 1978

    Google Scholar 

  35. Kertész, M., Koller, J., Ažman, A. in: Recent advances in the quantum theory of polymers. Lecture Notes in Physics, Vol. 113 Berlin: Springer Verlag 1980

    Google Scholar 

  36. Perkins, P. G., Marwaha, A. K., Steward, J. J. P.: Theoret. Chim. Acta (Berl.) 59, 555 (1981); Perkins, P. G., Marwaha, A. K., Steward, J. J. P.: ibid. 59, 569 (1981)

    Google Scholar 

  37. Bullett, D. W. in: Solid state physics, Vol. 35, Ehrenreich, H., Seitz, F., Turnbull, D., Ed. New York: Academic Press 1980

    Google Scholar 

  38. Roothan, C. C. J.: Rev. Mod. Phys. 23, 69 (1951); Ruttink, D. J. A.: Theoret. Chim. Acta (Berl.) 6, 83 (1966)

    Google Scholar 

  39. Brown, R. D., Roby, K. R.: Theoret. Chim. Acta (Berl.) 16, 175 (1970)

    Google Scholar 

  40. Bloch, F.: Z. Physik 52, 555 (1928)

    Google Scholar 

  41. Slater, J. C.: Quantum theory of molecules and solids. Vol. 2 New York: McGraw Hill 1965

    Google Scholar 

  42. Sichel, J. M., Whitehead, M. A.: Theoret. Chim. Acta (Berl.) 11, 220 (1968); DiSipio, L., Tondello, E., DeMichaelis, G., Oleari, L.: Chem. Phys. Letters 3, 287 (1971)

    Google Scholar 

  43. Ruedenberg, K.: Rev. Mod. Phys. 34, 326 (1962); Feinberg, M. J., Ruedenberg, K., Mehler, E. L.: Advan. Quantum Chem. 5, 27 (1970); Kutzelnigg, W.: Angew. Chem. 85, 551 (1973)

    Google Scholar 

  44. Burns, G.: J. Chem. Phys. 41, 1521 (1964)

    Google Scholar 

  45. Figeys H. P., Geerlings, P., Vay Alsenoy, C.: Int. J. Quantum Chem. 11, 705 (1977); Nanda, D. N., Narasimhan, P. T.: ibid. 11, 215 (1977)

    Google Scholar 

  46. Condon, E. U., Shortley, G. H.: The theory of atomic spectra. Cambridge: Cambridge University Press 1970

    Google Scholar 

  47. Dewar, M. J. S., Hojvat (Sabelli), N. L.: J. Chem. Phys. 34, 1232 (1961); Dewar, M. J. S., Hojvat (Sabelli), N. L.: Proc. Roy. Soc. Ser. A 264, 431 (1961); Dewar, M. J. S., Sabelli, N. L.: J. Phys. Chem. 66, 2310 (1962); Ohno, K.: Theoret. Chim. Acta (Berl.) 3, 219 (1964); Klopman, G.: J. Am. Chem. Soc. 86, 4550 (1964)

    Google Scholar 

  48. Wilkinson, J. H.: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965; Smith, B. T., Boyle, J. M., Garbow, B. S., Ikebe, Y., Klema, V. C., Moler, C. B.: Matrix eigensystem routines. Berlin: Springer Verlag 1974

    Google Scholar 

  49. Bacon, A. D., Zerner, M. C.: Theoret. Chim. Acta (Berl.) 53, 21 (1979)

    Google Scholar 

  50. Hartree, D. R.: The calculation of atomic structures. New York: Wiley Interscience 1957

    Google Scholar 

  51. Pople, J. A., Segal, G. A.: J. Chem. Phys. 43, 5136 (1965)

    Google Scholar 

  52. Fischer, H., Kollmar, H.: Theoret. Chim. Acta (Berl.) 16, 163 (1970)

    Google Scholar 

  53. Imamura, A., Fujita, H.: J. Chem. Phys. 61, 115 (1974)

    Google Scholar 

  54. Dewar, M. J. S., Lo, D. H.: J. Am. Chem. Soc. 93, 7201 (1971)

    Google Scholar 

  55. Misurkin, I. A., Ovchinnikov, A. A.: Mol. Phys. 27, 237 (1974)

    Google Scholar 

  56. Girerd, J.-J., Charlot, M.-F., Kahn, O.: Mol. Phys. 34, 1063 (1977); Kahn, O., Charlot, M.-F.: Nouv. J. Chim. 4, 567 (1980)

    Google Scholar 

  57. Karpfen, A.: Chem. Phys. 47, 401 (1980)

    Google Scholar 

  58. Brédas, J. L., Chance, R. R., Silbey, R., Nicolas, G., Durand, P.: J. Chem. Phys. 75, 255 (1981)

    Google Scholar 

  59. Karpfen, A., Petkov, J.: Theoret. Chim. Acta (Berl.) 53, 65 (1979)

    Google Scholar 

  60. Karpfen, A.: J. Phys. C 13, 5673 (1980)

    Google Scholar 

  61. Karpfen, A.: J. Phys. C 12, 3227 (1979)

    Google Scholar 

  62. Armstrong, D. R.: Theoret. Chim. Acta (Berl.) 60, 159 (1981)

    Google Scholar 

  63. Ladik, J., Suhai, S., Otto, P., Collins.: Int. J. Quantum Chem. QBS 4, 55 (1977); Suhai, S. in: Quantum theory of polymers. Andre, J.-M., Delhalle, J., Ladik, J., Ed. Dordrecht-Boston: D. Reidel Publ. Co. 1978

    Google Scholar 

  64. Brandow, B. H.: Int. J. Quantum Chem. 15, 207 (1979); Cooper, I. L., Linderberg, J.: Mol. Phys. 25, 265 (1973); Yamaguchi, K.: Theor. Chim. Acta (Berl.) 49, 151 (1978)

    Google Scholar 

  65. Rose, M. E.: Elementary theory of angular momentum. New York: John Wiley 1957; Tinkham, M.: Group theory and quantum mechanics. New York: McGraw Hill 1964

    Google Scholar 

  66. Schäffer, C. E., Jørgensen, C. K.: Mol. Phys. 9, 401 (1965); Schäffer, C. E.: Struct. Bonding 5, 68 (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Böhm, M.C. A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations. Theoret. Chim. Acta 62, 351–372 (1983). https://doi.org/10.1007/BF00547893

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00547893

Key words

Navigation