Abstract
A classification is proposed for the variation functions in the variable localized geminals (VLG) approximation based on the types of variational function in the unrestricted Hartree-Fock (UHF) method for one-dimensional systems. It has been found that functions of VLG type provide better incorporation of electron-correlation effects than do UHF ones. A study has been made on the phase diagram for the electronic states of polyacetylene in relation to the electron-electron parameters in the extrended Hubbard Hamiltonian containing certain types of VLG function.
Similar content being viewed by others
Literature cited
S. N. Dixit and S. Mazumdar, "Electron-electron interaction effects on Peierls dimerization in half-filled band," Phys. Rev. B, 29, No. 4, 1824–1835 (1984).
I. A. Misurkin and A. A. Ovchinnikov, "Electronic structures of long molecules having conjugated bonds," Teor. Éksp. Khim., 3, No. 4, 431–436 (1967).
I. A. Misurkin and A. A. Ovchinnikov, "Spin projection and spin properties of polyene singlet states," ibid., 8, No. 3, 291–298 (1972).
I. A. Misurkin and A. A. Ovchinnikov, "Effects from the long-range part of the Coulomb potential on the ground states in polymers containing conjugated bonds," ibid., 12, No. 3, 291–298 (1976).
V. A. Kuprievich, V. E. Klimenko, and O. V. Shramko, "Symmetrical and localized solutions to the equations in multiconfiguration self-consistent field theory for even polyenes," ibid., 12, No. 5, 678–680 (1976).
V. A. Kuprievich, V. E. Klimenko, and O. V. Shramko, "Effects of carbon-chain length on even-polyene correlation energies," ibid., 12, No. 6, 732–738 (1976).
Z. G. Soos and S. Ramasascha, "Valence-bond theory of linear Hubbard and Parizer-Parr-Pople models," Phys. Rev. B 29, No. 10, 5410–5422 (1984).
I. I. Ukrainskii, "A new variational function in the theory of quasi-one-dimensional metals," Teoret. Mat. Fiz., 32, No. 3, 392–399 (1977).
V. A. Kuprievich, "A study on bond-length alternation in polyene chains with allowance for electron correlation," Teor. Éksp. Khim., 22, No. 3, 263–270 (1986).
M. V. Bazilevskii, "The best localized description for a cyclic polyene and the correlation energy," Zh. Strukt. Khim., 11, No. 2, 339–349 (1970).
I. I. Ukrainskii, "The influence of electron-electron effects on Peierls instability," Zh. Éksp. Teor. Fiz., 76, No. 2, 760–769 (1979).
A. A. Ovchinnikov, A. E. Belinskii, I. A. Misurkin, and I. I. Ukrainskii, "Peierls instability and vibrational spectra of polyacetylene," Int. J. Quant. Chem., 22, No.5, 761–774 (1982).
L. Zulike, Quantum Chemistry [Russian translation], Mir, Moscow (1976), Vol. 1.
I. I. Ukrainskii, "Effective electron-electron interaction in conjugated polymers," Phys. Status Solidi b, 106, No. 1, 55–62 (1981).
A. C. Hearn, REDUCE-2, State Univ. of Utah Publ., Salt Lake City (1979).
J. E. Hirsch, "Phase diagram of the one-dimensional molecular crystal model with Coulomb interactions: half-filled bond sector," Phys. Rev. B, 31, No. 9, 6022–6031 (1985).
V. J. Emery, "Theory of one-dimensional electron gas," Highly Conducting One-Dimensional Solids, Plenum Press, New York (1979).
J. Solyom, "The Fermi gas model of one-dimensional conductors," Adv. Phys., 28, No. 2, 201–303 (1979).
I. I. Ukrainskii, Electron-Electron Interaction and Kink Dynamics in Polyacetylenes, Preprint, Acad. Sci. Ukr. SSR, Inst. Theor. Phys., 173 E, Kiev 1975.
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 6, pp. 665–672, November–December, 1987.
We are indebted to V. Ya. Krivnov and A. Yu. Kon for a valuable discussion and to V. M. Pak for providing the optimization program.
Rights and permissions
About this article
Cite this article
Chugreev, A.L., Misurkin, I.A. Classifying variational functions for quasi-one-dimensional systems and incorporating electron correlation. Theor Exp Chem 23, 613–620 (1988). https://doi.org/10.1007/BF00534601
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00534601