Quantum-chemical studies of quasi-one-dimensional electron systems. Part 2. Cumulenes and origin of the forbidden zone
DOI :
https://doi.org/10.15587/2313-8416.2015.44540Mots-clés :
quasi-one-dimensional electron system, polyenes, cumulenes, Peierls instability, bond alternation, Mott instability, electron correlationRésumé
This review is devoted to the basic problem in quantum theory of quasi-one-dimensional electron systems like polyenes (Part 1) and cumulenes (Part 2) – physical origin of the forbidden zone in these and analogous 1D electron systems due to two possible effects – Peierls instability (bond alternation) and Mott instability (electron correlation). Both possible contradiction and coexistence of the Mott and Peierls instabilities are summerized on the basis of the Kiev quantum chemistry team research projects.
Références
Kruglyak, Yu. A. (2015). Quantum-Chemical Studies of Quasi-One-Dimensional Electron Systems. 1. Polyenes. ScienceRise, 5/2 (10), 69–105. doi: 10.15587/2313-8416.2015.42643
Kventsel, G. F., Kruglyak, Y. A. (1968). Local electronic states in long polyene chains. Theoretica chimica Acta, 12 (1), 1–17. doi: 10.1007/bf00527002
Kventsel, G. F. (1968). Local electronic states in bounded polyene chains. Theoretical and Experimental Chemistry, 4 (3), 189–192.
Kventsel, G. F. (1969). Double substitution in long polyene chains. Theoretical and Experimental Chemistry, 5 (1), 17–19.
Kruglyak, Yu. A. (2014). Generalized Hartree-Fock method and its versions: from atoms and molecules up to polymers. ScienceRise, 5/3 (5), 6–21. doi: 10.15587/2313-8416.2014.30726
Kruglyak, Y. A., Ukrainsky, I. I. (1970). Study of the electronic structure of alternant radicals by theDODS method. International Journal of Quantum Chemistry, 4 (1), 57–72. doi: 10.1002/qua.560040106
Ukrainsky, I. I., Kventsel, G. F. (1972). Electronic structure of long polyene chains with an impurity atom. Theoretica chimica Acta, 25 (4), 360–371. doi: 10.1007/bf00526568
Kruglyak, Y. A., Dyadyusha, G. G. (1968). Torsion barriers of end-groups in cumulenes. Theoretica chimica Acta, 10 (1), 23–32. doi: 10.1007/bf00529040
Kruglyak, Y. A., Dyadyusha, G. G. (1968). Torsion barriers of end-groups in cumulenes. Theoretica chimica Acta, 12 (1), 18–28. doi: 10.1007/bf00527003
Ukrainsky, I. I. (1972). Electronic structure of long cumulene chains. International Journal of Quantum Chemistry, 6 (3), 473–489. doi: 10.1002/qua.560060309
Ukrainsky, I. I. (1972). Electronic structure of long cumulene chains. International Journal of Quantum Chemistry, 6 (3), 473–489. doi: 10.1002/qua.560060309
Ukrainskii, I. I., Shramko, O. V.; Ovchinnikov, A. A., Ukrainskii, I. I. (Eds.) (1991). Coexistence of Mott and Peierls instabilities in quasi-one-dimensional organic conductors. Electron – electron correlation effects in low-dimensional conductors and superconductors, Springer Verlag, Berlin, 62–72. doi: 10.1007/978-3-642-76753-1_8
Ovchinnikov, A. A., Ukrainskii, I. I.; Ovchinnikov, A. A., Ukrainskii, I. I. (Eds.). (1991). Introduction. Electron – electron correlation effects in low-dimensional conductors and superconductors, Springer Verlag, Berlin, 1–9.
Levina, R. Ya., Viktorova, E. A. (1958). Uspehi sinteza dienovyh uglevodorodov s kumulirovannoj sistemoj dvojnyh svjazej (allenov). Uspechi Khimii (USSR), 27 (2), 162.
Cadiot, P., Chodkiewicz, W., Rauss-Godineau, J. (1961). Cumulenes (review). Bull. Soc. Chim., 2176.
Fischer, H.; Patai, S. (Eds.) (1964). The Chemistry of Alkenes. N.Y.: Interscience, 1025.
Januszewski, J. A., Tykwinski, R. R. (2014). Synthesis and properties of long [n]cumulenes (n≥5). Chemical Society Reviews, 43 (9), 3184–3203. doi: 10.1039/c4cs00022f
Kruglyak, Y. A., Preuss, H., Janoschek, R. (1973). Electron structure of allene ab initio in the ground and excited states 1A1 and 1Ag. Theor Exp Chem, 7 (3), 241–248. doi: 10.1007/bf00525523
Dunitz, J. D., Orgel, L. E. (1952). Influence of Chain Length on the Symmetry of Conjugated Molecules. The Journal of Chemical Physics, 20 (8), 1328. doi: 10.1063/1.1700736
Popov, N. A. (1964). Calculation of the rotation barrier of end groups of a cumulative system. Journal of Structural Chemistry, 5 (1), 141–142. doi: 10.1007/bf00747970
van’t Hoff, J. H. (1877). Die Lagerung der Atome im Raume. Braunschweig, F. Vieweg und Sohn.
Pariser, R., Parr, R. G. (1953). A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II. The Journal of Chemical Physics, 21 (5), 767‑776. doi: 10.1063/1.1699030
Pople, J. A. (1953). Electron interaction in unsaturated hydrocarbons. Transactions of the Faraday Society, 49, 1375. doi: 10.1039/tf9534901375
Hinze, J., Jaffe, H. H. (1962). Electronegativity. I. Orbital Electronegativity of Neutral Atoms. Journal of the American Chemical Society, 84 (4), 540–546. doi: 10.1021/ja00863a008
Goeppert-Mayer, M., Sklar, A. L. (1938). Calculations of the Lower Excited Levels of Benzene. The Journal of Chemical Physics, 6 (10), 645. doi: 10.1063/1.1750138
Coulson, C. A., Rushbrooke, G. S. (1940). Note on the method of molecular orbitals. Mathematical Proceedings of the Cambridge Philosophical Society, 36 (02), 193. doi: 10.1017/s0305004100017163
Woolfson, M. M. (1953). The structure of 1:1:6:6 tetraphenylhexapentaene. Acta Crystallographica, 6 (11), 838–841. doi: 10.1107/s0365110x53002465
Dewar, M. J. S., Gleicher, G. J. (1965). Ground States of Conjugated Molecules. II. Allowance for Molecular Geometry 1a,b . Journal of the American Chemical Society, 87 (4), 685–692. doi: 10.1021/ja01082a001
Berggren, K.-F., Johansson, B. (1968). A field theoretical description of states with different orbitals for different spins. International Journal of Quantum Chemistry, 2 (4), 483–508. doi: 10.1002/qua.560020407
Johansson, B., Berggren, K.-F. (1969). Itinerant Antiferromagnetism in an Infinite Linear Chain. Physical Review, 181 (2), 855–862. doi: 10.1103/physrev.181.855
Fukutome, H. (1968). Spin density wave and charge transfer wave in long conjugated molecules. Progress in Theoretical Physics, 40 (5), 998–1012. doi: 10.1143/ptp.40.998
Fukutome, H. (1968). Spin density wave and charge transfer. Wave in long conjugated molecules. Progress in Theoretical Physics, 40 (6), 1227–1245. doi: 10.1143/ptp.40.1227
Misurkin, I. A., Ovchinnikov, A. A. (1969). Misurkin, I. A. Electronic structure of high π-electron systems (graphite, polyacenes, cumulenes). Theoretica Chimica Acta, 13 (2), 115–124. doi: 10.1007/bf00533435
Lieb, E. H., Wu, F. Y. (1968). Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension. Physical Review Letters, 20 (25), 1445–1448. doi: 10.1103/physrevlett.20.1445
Ovchinnikov, A. A. (1970). Excitation spectrum in the one-dimensional Hubbard model. Zhurnal eksper. Teor. Fiz. (USSR), 30 (6), 1160.
Hinze, J., Jaffe, H. H. (1962). Electronegativity. I. Orbital Electronegativity of Neutral Atoms. Journal of the American Chemical Society, 84 (4), 540–546. doi: 10.1021/ja00863a008
Pauncz, R., de Heer, J., Lowdin, P. O. (1962). Studies on the Alternant Molecular Orbital Method. I. General Energy Expression for an Alternant System with Closed-Shell Structure. The Journal of Chemical Physics, 36 (9), 2247. doi: 10.1063/1.1732872
Pauncz, R., de Heer, J., Löwdin, P. O. (1962). Studies on the Alternant Molecular Orbital Method. II. Application to Cyclic Systems. The Journal of Chemical Physics, 36 (9), 2257‑2265. doi: 10.1063/1.1732873
Pauncz, R. (1962). Studies on the Alternant Molecular Orbital Method. IV. Generalization of the Method to States with Different Multiplicities. The Journal of Chemical Physics, 37 (12), 2739. doi: 10.1063/1.1733098
Hardy, G. H., Littlewood, J. E., Polya, G. (1934). Inequalities. Cambridge Univ. Press.
Pauncz, R. (1967). Alternant Molecular Orbital Method. W. B. Saunders, London.
Harriman, J. E. (1964). Natural Expansion of the First-Order Density Matrix for a Spin-Projected Single Determinant. The Journal of Chemical Physics, 40 (10), 2827‑2839. doi: 10.1063/1.1724913
Van Leuven, P. (1969). An alternative derivation of the properties of the Alternant Molecular Orbital wave function. Physica, 45 (1), 86–94. doi:10.1016/0031-8914(69)90063-9
Van Leuven, P. (1970). Gaussian overlap approximation in the projected Hartree-Fock method. International Journal of Quantum Chemistry, 4 (4), 355–363. doi: 10.1002/qua.560040403
Lennard-Jones, J. E., Turkevich, J. (1937). The Electronic Structure of Some Polyenes and Aromatic Molecules. II. The Nature of the Links of Some Aromatic Molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 158 (894), 297–305. doi: 10.1098/rspa.1937.0021
Mott, N. F. (1949). The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals. Proceedings of the Physical Society. Section A, 62 (7), 416–422. doi: 10.1088/0370-1298/62/7/303
Mott, N. F. (1952). Recent advances in the electron theory of metals. Progress in Metal Physics, 3, 76–114. doi: 10.1016/0502-8205(52)90005-1
Mott, N. F. (1956). On the transition to metallic conduction in semiconductors. Canadian Journal of Physics, 34 (12A), 1356–1368. doi: 10.1139/p56-151
Mott, N. F. (1958). The transition from the metallic to the non-metallic state. II Nuovo Cimento, 7 (S2), 312–328. doi: 10.1007/bf02751484
Mott, N. F. (1961). The transition to the metallic state. Philosophical Magazine, 6 (62), 287–309. doi: 10.1080/14786436108243318
Austin, I. G., Mott, N. F. (1970). Metallic and Nonmetallic Behavior in Transition Metal Oxides. Science, 168 (3927), 71–77. doi: 10.1126/science.168.3927.71
Mott, N. F. (1971). The transition from the metallic to the non-metallic state. Usp. Fiz. Nauk (USSR), 105, 321–327.
Mott, N. F. (1974). Metal – Insulator Transitions. Taylor and Francis, London.
Schuster, H. G. (Ed.) (1974). One-Dimensional Conductors, Lecture Notes in Physics. Vol. 34. Berlin, Springer.
Ovchinnikov, A. A., Ukrainskii, I. I., Kventsel, G. F. (1972). Theory of one-dimensional Mott semiconductors and the electronic structure of long molecules with conjugated bonds. Uspekhi Fizicheskikh Nauk, 108 (1), 81–111.
Brandow, B. H. (1977). Electronic structure of Mott insulators. Advances in Physics, 26 (5), 651–808. doi: 10.1080/00018737700101443
Epstein, A. J., Etemad, S., Garito, A. F., Heeger, A. J. (1972). Metal-Insulator Transition and Antiferromagnetism in a One-Dimensional Organic Solid. Physical Review B, 5 (3), 952–977. doi: 10.1103/physrevb.5.952
Dieterich, W. (1976). Ginzburg-Landau theory of phase transitions in pseudo-one-dimensional systems. Advances in Physics, 25 (6), 615–655. doi: 10.1080/00018737600101462
Rice, M. J., Strässler, S. (1973). Theory of a quasi-one-dimensional band-conductor. Solid State Communications, 13 (1), 125–128. doi: 10.1016/0038-1098(73)90083-5
Keller, H. J. (Ed.) (1975). Low-Dimensional Cooperative Phenomena. N.Y. Plenum.
Dugay, M., Debarge, G. (1977). AMOS and insulator-to-metal transitions. International Journal of Quantum Chemistry, 11 (6), 1021–1033. doi: 10.1002/qua.560110615
Paldus, J., Čižek, J. (1970). Stability Conditions for the Solutions of the Hartree-Fock Equations for Atomic and Molecular Systems. VI. Singlet-Type Instabilities and Charge-Density-Wave Hartree-Fock Solutions for Cyclic Polyenes. Physical Review A, 2 (6), 2268–2283. doi: 10.1103/physreva.2.2268
Čížek, J., Paldus, J. (1971). Stability Conditions for the Solutions of the Hartree-Fock Equations for Atomic and Molecular Systems. V.The Nonanalytic Behavior of the Broken-Symmetry Solutions at the Branching Point. Physical Review A, 3 (2), 525–527. doi: 10.1103/physreva.3.525
Paldus, J. (1970). Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. II. Simple Open-Shell Case. The Journal of Chemical Physics, 52 (6), 2919. doi: 10.1063/1.1673419
Čížek, J. (1970). Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. III. Rules for the Singlet Stability of Hartree–Fock Solutions of π-Electronic Systems. The Journal of Chemical Physics, 53 (2), 821. doi: 10.1063/1.1674065
Paldus, J., Čížek, J., Keating, B. A. (1973). Stability Conditions for Maximum-Overlap (Brueckner) Independent-Particle Wave Functions. Physical Review A, 8 (2), 640–649. doi: 10.1103/physreva.8.640
Laforgue, A. (1973). Study of the correlation effects in a three-electron model system using the projected Hartree-Fock method and the natural spin orbital formalism. The Journal of Chemical Physics, 59 (5), 2560. doi: 10.1063/1.1680372
Fukutome, H. (1971). Theory of the Unrestricted Hartree-Fock Equation and Its Solutions. I. Progress in Theoretical Physics, 45 (5), 1382–1406. doi: 10.1143/ptp.45.1382
Fukutome, H. (1974). Theory of the Unrestricted Hartree-Fock Equation and Its Solutions II: Classification and Characterization of UHF Solutions by Their Behavior for Spin Rotation and Time Reversal. Progress in Theoretical Physics, 52 (1), 115–130. doi: 10.1143/ptp.52.115
Fukutome, H. (1974). Theory of the Unrestricted Hartree-Fock Equation and Its Solutions. III: Classification of Instabilities and Interconnection Relation between the Eight Classes of UHF Solutions. Progress in Theoretical Physics, 52 (6), 1766–1783. doi: 10.1143/ptp.52.1766
Fukutome, H. (1975). Theory of the Unrestricted Hartree-Fock Equation and Its Solutions. IV: Behavior of UHF Solutions in the Vicinity of Interconnecting Instability Threshold. Progress in Theoretical Physics, 53 (5), 1320–1336. doi: 10.1143/ptp.53.1320
Overhauser, A. W. (1960). Structure of Nuclear Matter. Physical Review Letters, 4 (8), 415–418. doi: 10.1103/physrevlett.4.415
Bryant, C. A., Keesom, P. H. (1960). Specific Heat of Indium Below 1°K. Physical Review Letters, 4 (9), 460–462. doi: 10.1103/physrevlett.4.460
Little, W. A. (1964). Possibility of Synthesizing an Organic Superconductor. Physical Review, 134 (6A), A1416–A1424. doi: 10.1103/physrev.134.a1416
Bychkov, Y. A., Gor’kov, L. P., Dzyaloshinsky, I. E. (1966). Possibility of Superconductivity Type Phenomena in a One-dimensional System. Zhurnal Eksp. Teor. Fiz. (USSR), 50, 738.
Andre, J.-M., Leroy, G. (1971). All-electrons band structure of Polyene. International Journal of Quantum Chemistry, 5 (5), 557–563. doi: 10.1002/qua.560050509
Harris, R. A. (1969). Self-Consistent Theory of Bond Alternation in Polyenes: Normal State, Charge-Density Waves, and Spin-Density Waves. The Journal of Chemical Physics, 51 (11), 5034. doi: 10.1063/1.1671900
Bogolyubov, N. N. (1958). O novom metode v teorii sverhprovodimosti. Zhurnal eksper.teor. Fiz. (USSR), 34, 58–73.
Bogolyubov, N. N., Tolmachev, V. V., Shirkov, D. V. (1958). New Method in Theory of Superconductivity. Publ. House of AS of USSR, Moscow.
Ovchinnikov, A. A. (1978). Multiplicity of the ground state of large alternant organic molecules with conjugated bonds. Theoretica Chimica Acta, 47 (4), 297–304. doi: 10.1007/bf00549259
Su, W. P., Schrieffer, J. R., Heeger, A. J. (1980). Soliton excitations in polyacetylene. Physical Review B, 22 (4), 2099–2111. doi: 10.1103/physrevb.22.2099
Brazovskii, S. A. (1980). Self-localized excitations in the Peierls-Fröhlich state. Zhurnal Eksp. Teor. Fiz. (USSR), 78, 677.
Ukrainskii, I. I. (1979). Effect of electron interaction on the Peierls instability. Zhurnal Eksp. Teor. Fiz. (USSR), 76, 760.
Ukrainskii, I. I. (1977). Novaja variacionnaja funkcija v teorii kvaziodnomernyh metallov. Teor. Matem. Fizika (USSR), 32 (3), 392–400.
Ukrainskii, I. I. (1977). New variational function in the theory of quasi-one-dimensional metals. Theor. Math. Physics (USSR), 32 (3), 816–822.
Ukrainskii, I. I. (1981). Effective Electron—Electron Interaction in Conjugated Polymers. Physica status solidi (b), 106 (1), 55–62. doi: 10.1002/pssb.2221060106
Mazumdar, S., Dixit, S. N. (1983). Coulomb Effects on One-Dimensional Peierls Instability: The Peierls-Hubbard Model. Physical Review Letters, 51 (4), 292–295. doi: 10.1103/physrevlett.51.292
Dixit, S. N., Mazumdar, S. (1984). Electron-electron interaction effects on Peierls dimerization in a half-filled band. Physical Review B, 29 (4), 1824–1839. doi: 10.1103/physrevb.29.1824
Hirsch, J. E. (1983). Effect of Coulomb Interactions on the Peierls Instability. Physical Review Letters, 51 (4), 296–299. doi: 10.1103/physrevlett.51.296
Baeriswyl, D., Maki, K. (1985). Electron correlations in polyacetylene. Physical Review B, 31 (10), 6633–6642. doi: 10.1103/physrevb.31.6633
Krivnov, V. Ya., Ovchinnikov, A. A. (1982). Correlation functions of one-dimensional systems. J. Exp. Theor. Phys. (USSR), 55 (1), 162.
Kuprievich, V. A. (1986). Electron correlation and bond-length alternation in polyene chains. Theoretical and Experimental Chemistry, 22 (3), 245–252. doi: 10.1007/bf00521148
Fincher, C. R., Chen, C.-E., Heeger, A. J., MacDiarmid, A. G., Hastings, J. B. (1982). Structural Determination of the Symmetry-Breaking Parameter in trans-(CH)x. Physical Review Letters, 48 (2), 100–104. doi: 10.1103/physrevlett.48.100
Hoekstra, A., Spoelder, T., Vos, A. (1972). The crystal structure of rubidium–7,7,8,8-tetracyanoquinodimethane, Rb–TCNQ, at –160 °C. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, 28 (1), 14–25. doi: 10.1107/s0567740872001803
Ovchinnikov, A. A., Belinskii, A. E., Misurkin, I. A., Ukrainskii, I. I. (1982). Peierls instability and vibrational spectra of polyacetylene. International Journal of Quantum Chemistry, 22 (4), 761–774. doi: 10.1002/qua.560220409
Bernasconi, J., Schneider, T. (Eds.). (1981). Physics in One Dimension. Springer Series in Solid-State Sciences, 368. doi: 10.1007/978-3-642-81592-8
Bednorz, J. G., Muller, K. A. (1986). Possible highT c superconductivity in the Ba?La?Cu?O system. Zeitschrift fur Physik B Condensed Matter, 64 (2), 189–193. doi: 10.1007/bf01303701
Yagubskii, E. B., Schegolev, I. F., Laukhin, V. N., Kononovich, P. A., Kartsovnik, M. V., Zvarykina, A. V., Bubarov, L. I. (1984). Normal-pressure Superconductivity in organic metal (BEDT-TTF)2I3 [bis(ethylenedithiolo)tetrathiafulvalene triiodide]. Zhurnal Eksp. Teor. Fiziki, Pisma (USSR), 39, 12.
Téléchargements
Publié-e
Numéro
Rubrique
Licence
(c) Tous droits réservés Юрій Олексійович Кругляк 2015
Cette œuvre est sous licence Creative Commons Attribution 4.0 International.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
