Abstract
The Fourier representation method described in the previous paper of this series is used to make electronic structure calculations for a linear chain of equally spaced hydrogen atoms. The electronic wavefunction is assumed to be a determinant of doubly-occupied crystal orbitals of modulated-plane-wave type, built from one 1s Slater-type orbital of screening parameter ζ centered on each atom. The energy is calculated from the electrostatic zero-order Hamiltonian with exact evaluation of all Coulomb and exchange contributions, and is optimized with respect to the lattice spacing and ζ value. Good agreement with work by others is noted, indicating a near-equivalence of modulated-plane-wave and tight-binding wavefunctions for this half-filled-valence-band system. The linear chain is calculated to be far more stable than cubic three-dimensional hydrogen crystals. This fact sheds light on the unusually large calculated nearest-neighbor distances in the cubic crystals, and is related to a suggestion that under certain conditions the most stable structure for solid atomic hydrogen may be of lower symmetry than cubic.
Similar content being viewed by others
References
Harris, F. E.: J. Chem. Phys.56, 4422 (1972)
Keller, H. J., ed.: Low-dimensional cooperative phenomena, NATO ASI Series, Vol. B7. New York: Plenum Press 1974
André, J. M., Ladik, J., eds.: Electronic structure of polymers and molecular crystals, NATO ASI Series, Vol. B9. New York: Plenum Press 1975
Delhalle, J., André, J. M., Delhalle, S., Pireaux, J. J., Caudano, R., Verbist, J. J.: J. Chem. Phys.60, 595 (1974)
Delhalle, J., Delhalle, S., André, J. M.: Bull. Soc. Chim. Belges83, 107 (1974)
Pireaux, J. J., Riga, J., Caudano, R., Verbist, J. J., André, J. M., Delhalle, J., Delhalle, S.: J. Electron Spectry.5, 531 (1974)
Calais, J. L.: Arkiv Fysik29, 511 (1965)
Del Re, G., Ladik, J., Biczo, G.: Phys. Rev.155, 997 (1967)
André, J. M.: J. Chem. Phys.50, 1536 (1969)
Berggren, K. F., Martino, F.: Phys. Rev.184, 484 (1969)
Kislow, D. H., McKelvey, J. M., Bender, C. F., Schaefer, H. F.: Phys. Rev. Letters32, 933 (1974)
Kertesz, M., Koller, J., Azman, A.: Theoret. Chim. Acta (Berl.)41, 89 (1976)
Harris, F. E., Monkhorst, H. J.: Phys. Rev.B2, 4400 (1970)
Harris, F. E.: Theoretical chemistry, advances and perspectives, Vol. 1, pp. 147–218, Henderson, D., Eyring, H., eds. New York: Academic Press 1975
Harris, F. E., Ref. [3], pp. 453–477.
Harris, F. E., Kumar, L., Monkhorst, H. J.: Intern. J. Quantum Chem.5S, 527 (1971)
Harris, F. E., Kumar, L., Monkhorst, H. J.: Phys. Rev.B7, 2850 (1973)
Bonham, R. A., Peacher, J. L., Cox, H. L.: J. Chem. Phys.40, 3083 (1964)
Harris, F. E., Monkhorst, H. J.: Computational methods in band theory, p. 530. Marcus, P. M., Janak, J. F., Williams, A. R., eds. New York: Plenum Press 1971
See, for example: Callaway, J.: Quantum theory of the solid state, pp. 352 ff. New York: Academic Press 1974
Abramowitz, M., Stegun, I. A.:Handbook of mathematical functions Eq. (3.6.28.). Washington: U.S. Government Printing Office 1964
Oddershede, J., Kumar, L., Monkhorst, H. J.: Intern. J. Quantum Chem.8S, 447 (1974)
Brovman, E. G., Kagan, Yu., Kholas, A.: Zh. Eksp. Teor. Fiz.61, 2429 (1971) (Soviet Physics JETP34, 1300 (1972))
Brovman, E. G., Kagan, Yu., Kholas, A.: Zh. Eksp. Teor. Fiz.62, 1492 (1972) (Soviet Physics JETP35, 1783 (1972))
Delhalle, J., Harris, F. E.: Phys. Rev. Letters39, 1340 (1977)
Author information
Authors and Affiliations
Additional information
The previous paper of this series: Harris, F. E.: J. Chem. Phys.56, 4422 (1972) [1].
Chargé de Recherches du F.N.R.S. (Fonds National Belge de la Recherche Scientifique).
Rights and permissions
About this article
Cite this article
Delhalle, J., Harris, F.E. Fourier representation method for electronic structures of linear polymers. Theoret. Chim. Acta 48, 127–141 (1978). https://doi.org/10.1007/PL00020706
Received:
Issue Date:
DOI: https://doi.org/10.1007/PL00020706