Abstract
A formalism for calculating a Hartree-Fock crystal is given in detail. This includes a description of the basis set used and integral approximations needed in the calculation. The results of the calculation of the ground and excited states are discussed. For the ground state the first order density matrix is compared with experiment by investigating the x-ray structure factors and the Compton profiles. The cohesive energy, lattice constant, and bulk modulus of the Hartree-Fock results are also compared with experiment to judge the correctness of this model. The Hartree-Fock excited stated plus correlation corrections are included. The corrections include relaxation of the electron and hole states by using two models. One is the screened exchange plus coulomb hole approximation where several approximations for the dielectric function are studied. The second model is the electronic polaron model where both the relaxation effects and a new scattering state are discussed. The correction to the electronic excited (or vitual) states so that they see the correct potential (namely a VN−1) is given in detail.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. B. Kunz, Phys. Stat. Sol. 36, 301 (1969).
F. E. Farris and H. J. Monkhorst, Phys. Rev. Letters 23, 1026 (1969).
L. Dagens and F. Perrot, Phys. Rev. B5, 641 (1972).
R. N. Euwena, D. L. Wihlhite and G. T. Surrat, Phys. Rev. 7B, 818 (1973).
J. C. Slater, Phys. Rev. 81, 385 (1951).
R. Gaspar, Acta Phys. Sci. Hung. 3, 263 (1954).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
W.B. Fowler, Phys. Rev. 151, 657 (1966).
L. Hedin, Phys. Rev. 139, A796 (1965).
L. Hedin and S. Lundqvist, Solid State Physics, Vol. 23 (Academie, New York, ed. by F. Seitz, D. Turnbull, and H. Ehrenreich) (1969).
A. B. Kunz, Phys. Rev. B6, 606 (1972).
A. B. Kunz, D. J. Michish and T. C. Collins, Phys. Rev. Letters 31, 756 (1973).
D. J. Michish, A. B. Kunz and T. C. Collins, Phys. Rev. B9, 4461 (1974).
J. T. Devreese, A. B. Kunz and T. C. Collins, Solid State Commun. 11, 673 (1972).
T. C. Collins, A. B. Kunz and P. W. Deutsh, Phys. Rev. Sept. (1974).
V. Fock, Z. Physik, Vol 61, 1261 (1930).
P. A. M. Dirac, Proc. Camb. Phil. Soc. 26, 376 (1930).
T. Koopmans, Physica 1, 104 (1933).
C. Herring, Phys. Rev. 57, 1169 (1940).
J. C. Slater, Phys. Rev. 36, 57 (1930).
R. N. Euwena, Phys. Rev. B4, 4332 (1971).
D. A. Liberman, Phys. Rev. 171, 1 (1966).
H. Preuss, Z. Naturforach 11, 823 (1956).
D. L. Wilhite and R. N. Euwema, J; Chem. Phys. 15 Jun 74.
R. N. Euwema, G. T. Surratt, D. L. Wilhite and G. G. Wepfer
G. T. Surratt, R. N. Euwema, D. L. Wilhite and G. G. Wepfer, Phys. Rev. (tobe published).
G. T. Surratt, R. N. Euwema, D. L. Wilhite and G. G. Wepfer, Phys. Rev. (to be published).
G. T. Surratt, R. N. Euwema, D. L. Wilhite, Phys. Rev. B8, 4019 (1973).
M. Krauss, “Compendium of ab initio Calculations of Molecular Energies and Properties”, NBS Technical Note No. 438 (U.S. GPO, Washington, D. C. (1971).
R. N. Euwema, G. T. Surratt, G. G. Wepfer and D. L. Wilhite, Phys. Rev. (to be published).
G. F. Chew and G. C. Wick, Phys. Rev. 85, 636 (1952).
G. G. Wepfer, R. N. Euwema, G. T. Surratt and D. L. Wilhite, Int. J. Q. M. SYM 7, 613 (1973).
R. N. Euwema and G. T. Surratt, Solid State Communication (to be published).
N. E. Brener and T. C. Collins, “Proceedings of the 12th International Conference on the Physics of Semiconductors”, Stuttgart, Germany, July 74.
N. E. Brener, Phys. Rev. (to be published).
D. R. Penn, Phys. Rev. 128, 2093 (1963).
N. E. Brener, Phys. Rev. (to be published).
T. C. Collins, A. B. Kunz and J. T. Devreese, Int. J. Ouan. Chem. Symp. No. 7, 551 (1973).
J. T. Devreese, J. De Sitter, and M. Govaerts, Phys. Rev. B5, 2367 (1972).
W. H. Adams, J. Chem. Phys. 34, 89 (1961); 36, 2009 (1962).
T. L. Gilbert in “Molecular Orbitals in Chemistry, Physics, and Biology”, ed. P. O. Löwdin and P. Pullman (Academie Press, New York, 1964).
A. B. Kunz, Phys. Stat. Sol. B46, 697 (1971).
D. F. Scofield, N. C. Dutta, and C. M. Dutta, Int. J. Quan. Chem. 6, 9 (1972).
K. A. Brueckner, Phys. Rev. 97, 1353 (1955).
J. Goldstone, Proc. Roy. Soc. (London) A239, 267 (1957).
C. E. Moore, “Atomic Energy Levels”, Circular 467, National Bureau of Standards.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 Plenum Press, New York
About this chapter
Cite this chapter
Collins, T.C. (1975). Ab-Initio SCF-LCAO Hartree-Fock Calculations and the Determination of Correlation Corrections in Three-Dimensional Crystals. In: André, JM., Ladik, J. (eds) Electronic Structure of Polymers and Molecular Crystals. Nato Advanced Study Institutes Series, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0319-1_11
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0319-1_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-0321-4
Online ISBN: 978-1-4757-0319-1
eBook Packages: Springer Book Archive