Quantum-chemical studies of quasi-one-dimensional electron systems. 1. Polyenes
DOI:
https://doi.org/10.15587/2313-8416.2015.42643Keywords:
quasi-one-dimensional electron system, polyenes, 1D electron systems, local states, impurity states, generalized HF methodAbstract
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.
References
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.
Kventsel, G. F. Local electronic states in chains with two atoms in the unit cell. Theoretical and Experimental Chemistry, vol. 5, no. 4, pp. 287 – 292, 1969.
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, 10 (1), 23–32. doi: 10.1007/bf00529040
Ukrainsky, I. I. (1972). Electronic structure of long cumulene chains. International Journal of Quantum Chemistry, 6 (3), 473–489. doi: 10.1002/qua.560060309
Kventsel, G. F. (1982). Peierls- and Mott-type instabilities in one-dimensional chains?coexistence or contradiction. International Journal of Quantum Chemistry, 22 (4), 825–835. doi: 10.1002/qua.560220412
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.
Salem, L., Benjamin, W. A. (1966). The molecular orbital theory of conjugated systems. New York.
Peierls, R. E. (1955). Quantum Theory of Solids. Clarendon Press, Oxford.
Misurkin, I. A., Ovchinnikov, A. A. (1970). Electronic structure of long molecules with conjugated bonds. Teoreticheskaya i Eksperimental’naya Khimiya, 3 (4), 245–248. doi: 10.1007/bf01112374
Misurkin, I. A., Ovchinnikov, A. A. (1970). The electronic structures of large-electron systems (graphite, polyacenes, cumulenes). Theor Exp Chem, 4 (1), 1–5. doi: 10.1007/bf00525936
Ruedenberg, K. (1961). Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. I. General Analysis in the Tight-Binding Formulation. The Journal of Chemical Physics, 34 (6), 1861. doi: 10.1063/1.1731785
Murrell, J. N., Salem, L. (1961). Energies of Excited Electronic States as Calculated with the Zero Differential Overlap Approximation. The Journal of Chemical Physics, 34 (6), 1914. doi: 10.1063/1.1731791
Lifshits, I. M. (1947). About degenerate regular perturbations. 1. Discrete spectrum. Zhurnal eksperimentalnoi i teoreticheskoi fiziki, 17, 1017.
Lifshits, I. M. (1947). About degenerate regular perturbations. 2. Quasicontinuous spectrum. Zhurnal eksperimentalnoi i teoreticheskoi fiziki, 17, 1076.
Lifshits, I. M. (1952). On a problem of the theory of perturbations connected with quantum statistics. Uspekhi matematicheskikh nauk, 7/1 (47), 171–180.
Lifšic, M. (1956). Some problems of the dynamic theory of non-ideal crystal lattices. Il Nuovo Cimento, 3 (S4), 716–734. doi: 10.1007/bf02746071
Koster, G. F., Slater, J. C. (1954). Wave Functions for Impurity Levels. Phys. Rev., 95 (5), 1167–1176. doi: 10.1103/physrev.95.1167
Koutecký, J. (1957). Contribution to the Theory of the Surface Electronic States in the One-Electron Approximation. Physical Review, 108 (1), 13–18. doi: 10.1103/physrev.108.13
Kouteck, J. (1958). A contribution to the molecular-orbital theory of chemisorption. Transaction Faraday Society, 54, 1038‑1052. doi: 10.1039/tf9585401038
Montroll, E. W., Potts, R. B. (1955). Effect of Defects on Lattice Vibrations. Physical Review, 100 (2), 525–543. doi: 10.1103/physrev.100.525
Kruglyak, Yu. A. et. al. (1967). Methods of computations in quantum chemistry. Calculation of π-electronic molecular structure by simple molecular orbital methods. Kiev: Naukova Dumka.
Pople, J. A., Walmsley, S. H. (1962). Bond alternation defects in long polyene molecules. Molecular Physics, 5 (1), 15–20. doi: 10.1080/00268976200100021
Berlin, A. A., Blumenfeld, L. A., Cherkashin, M. I., Kalmanson, A. E., Selskaia, O. G. (1959). Polymers with conjugated bonds in the macromolecular chains. II. Magnetic and some other properties of polyarylvinylenes. Vysokomolekulyarnye Soedineniya, 1 (9), 1361–1363.
Blumenfeld, L. A., Voevodsky, V. V., Semenov, A. G. (1962). Application of electron paramagnetic resonance in chemistry. Academy of Sciences of the USSR, Novosibirsk.
Pen’kovskii, V. V. (1964). Compounds with conjugated double bonds. Russ. Chem. Rev., 33 (10), 532–549. doi: 10.1070/rc1964v033n10abeh001500
Kruglyak, Y. A. (1969). The electronic properties of polyenes and polyphenylacetylenes. J Struct Chem, 10 (1), 22–27. doi: 10.1007/bf00751947
Kruglyak, Y. A., Pen’kovskii, V. V. (1969). Electronic properties of polyenes and polyphenylacetylenes. J Struct Chem, 10(2), 211–216. doi: 10.1007/bf00745780
Pen’kovskii, V. V., & Kruglyak, Y. A. (1969). The electronic properties of polyenes and polyphenylacetylenes. J Struct Chem, 10 (3), 378–382. doi: 10.1007/bf00746728
Blyumenfel’d, L. A., Benderskii, V. A. (1964). States with charge transfer in organic systems. 1. J Struct Chem, 4 (3), 370–377. doi: 10.1007/bf00745539
Benderskii, V. A., Blyumenfel’d, L. A., Popov, D. A. (1967). Charge transfer states in organic systems. J Struct Chem, 7 (3), 353–360. doi: 10.1007/bf00744425
Lutoshkin, V. I., Dyadyusha, G. G., Kruglyak, Yu. A.; Brodsky, A. I. (Ed.). (1970). Quantitative estimation of the bond alternation in polyenes. Structure of molecules and quantum chemistry, Naukova Dumka, Kiev, Ukraine, 132–138.
Lutoshkin, V. I., Kruglyak, Y. A., Dyadyusha, G. G. (1974). Calculation of electronic structure and force field of alternant radicals with allowance for deformation of the σ-core. Theor Exp Chem, 7 (5), 473–477. doi:10.1007/bf00527149
Hartree, D. R. (1928). The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods. Math. Proc. Camb. Phil. Soc., 24 (01), 89. doi: 10.1017/s0305004100011919
Hartree, D. R. (1928). The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion. Proceedings Cambridge Philosophical Society, 24 (1), 111–132.
Fock, V. A. (1930). An approximate method for solving the quantum many-body problem. Zeitschrift fur Physik, 61 (1-2), 126‑148.
Rutherford, D. E. (1948). Substitutional Analysis. Edinburgh University Press, London.
Hammermesh, M. (1962). Group theory and its application to physical problems. Addison-Wesley, Reading.
Kaplan, I. G. (1969). Symmetry of many-electron systems. Nauka, Moscow.
Goddard III, W. A. (1967). Improved quantum theory of many-electron systems: I. Construction of eigenfunctions of which satisfy Pauli's principle. Physical Review, 157 (1), 73–80. doi: 10.1103/physrev.157.73
Goddard, W. A. (1967). Improved Quantum Theory of Many-Electron Systems. II. The Basic Method. Physical Review, 157 (1), 81–93. doi: 10.1103/physrev.157.81
Goddard, W. A. (1968). Improved Quantum Theory of Many-Electron Systems. III. The GF Method. The Journal of Chemical Physics, 48 (1), 450. doi: 10.1063/1.1667943
Goddard, W. A. (1968). Wavefunctions and Correlation Energies for Two-, Three-, and Four-Electron Atoms. The Journal of Chemical Physics, 48 (3), 1008. doi: 10.1063/1.1668754
Goddard, W. A. (1968). Improved Quantum Theory of Many-Electron Systems. IV. Properties of GF Wavefunctions. The Journal of Chemical Physics, 48 (12), 5337. doi: 10.1063/1.1668225
Ladner, R. C. (1969). Improved Quantum Theory of Many-Electron Systems. V. The Spin-Coupling Optimized GI Method. The Journal of Chemical Physics, 51 (3), 1073. doi: 10.1063/1.1672106
Goddard, W. A. (1969). The symmetric group and the spin generalized scf method. International Journal of Quantum Chemistry, 4 (S3B), 593–600. doi: 10.1002/qua.560040720
Slater, J. C. (1929). The theory of complex spectra. Physical Review, 34, 1293–1323.
Slater, J. C. (1930). Quantum theory of molecules and solids. Physical Review, 35 (2), 210–211.
Roothaan, C. C. J. (1951). New Developments in Molecular Orbital Theory. Review of Modern Physics, 23 (2), 69–89. doi: 10.1103/revmodphys.23.69
Amos, A. T., Hall, G. G. (1961). Single Determinant Wave Functions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 263 (1315), 483–493. doi: 10.1098/rspa.1961.0175
Ukrainskii, I. I., Kruglyak, Y. A., Preuss, H., Yanoshek, R. (1974). Projection of the wave function of the unlimited Hartree-Fock method on the doublet state in the case of benzyl radical. Theor Exp Chem, 8 (3), 242–249. doi: 10.1007/bf00529150
Amos, A. T.; Sinanoğlu, O. (Ed.) (1965). Some properties of π-ions and triplets. Modern quantum chemistry, Academic Press, New York, 157–170.
Pople, J. A., Nesbet, R. K. Self-Consistent Orbitals for Radicals (1954). The Journal of Chemical Physics, 22 (3), 571. doi: 10.1063/1.1740120
Löwdin, P.-O. (1955). Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects. Physical Review, 97 (6), 1509–1520. doi: 10.1103/physrev.97.1509
Lowdin, P.-O.; Prigogine, I. (Ed.) (1959). Correlation problem in many-electron quantum mechanics. I. Review of different approaches and discussion of some current ideas. Advances in Chemical Physics, 2, 207–322.
Löwdin, P.-O. (1964). Angular Momentum Wavefunctions Constructed by Projector Operators. Review of Modern Physics, 36 (4), 966–976. doi: 10.1103/revmodphys.36.966
Sasaki, F., Ohno, K. (1963). Spin-Component Analysis of Single-Determinant Wavefunctions. Journal of Mathematical Physics, 4 (9), 1140‑1147. doi: 10.1063/1.1704044
Smith, V. H. (1964). Construction of Exact Spin Eigenfunctions. The Journal of Chemical Physics, 41 (1), 277. doi: 10.1063/1.1725634
Sando, K. M. (1967). Spin-Projected and Extended SCF Calculations. The Journal of Chemical Physics, 47 (1), 180. doi: 10.1063/1.1711843
Harris, F. E. (1966). On the calculation of spin densities. Molecular Physics, 11 (3), 243–256. doi: 10.1080/00268976600101081
Pauncz, R. (1967). Alternant Molecular Orbital Method. W. B. Saunders, London.
Löwdin, P.-O. (1962). Band Theory, Valence Bond, and Tight-Binding Calculations. Journal of Applied Physics, 33 (1), 251‑280. doi: 10.1063/1.1777106
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
Hückel, E. (1930). Zur Quantentheorie der Doppelbindung. Zeitschrift Für Physik, 60 (7-8), 423–456. doi: 10.1007/bf01341254
Hückel, E. (1931). Quantentheoretische Beitrüge zum Benzolproblem. Zeitschrift Für Physik, 70 (3-4), 204–286. doi: 10.1007/bf01339530
Coulson, C. A., Longuet-Higgins, H. C. (1947). The Electronic Structure of Conjugated Systems. I. General Theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 191 (1024), 39–60. doi: 10.1098/rspa.1947.0102
Brickstock, A., Pople, J. A. (1954). Resonance energies and charge distributions of unsaturated hydrocarbon radicals and ions. Trans. Faraday Soc., 50, 901. doi: 10.1039/tf9545000901
Koopmans, T. (1934). Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms. Physica, 1 (1-6), 104–113. doi: 10.1016/s0031-8914(34)90011-2
Brillouin, L. (1933). La méthode du champ self-consistent, (Actualites Scientifiques et Industrielles, Vol. 71). Hermann, Paris.
Brillouin, L. (1934). Les champs "self-consistents" de Hartree et de Fock, (Actualites Scientifiques et Industrielles, Vol. 159). Hermann, Paris,.
Mozdor, E. V., Kruglyak, Y. A., Kuprievich, V. A. (1972). Matrix elements for operators for physical quantities in one-configuration functions of radicals. Theoretical and Experimental Chemistry, 5 (6), 509–514. doi: 10.1007/bf00526265
Kruglyak, Yu. A., Mozdor, E. V., Kuprievich, V. A. (1971). Study of the electronic structure of radicals by the CI method. I. Matrix elements of the physical value operators. Croatica Chemica Acta, 43, 15–22.
Popov, N. A. (1971). Symmetry properties of one-electron orbitals in the method of different orbitals for different spins. J Struct Chem, 11 (4), 670–676. doi: 10.1007/bf00743441
Hylleraas, E. A. (1929). Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium. Zeitschrift Für Physik, 54 (5-6), 347–366. doi: 10.1007/bf01375457
Eckart, C. (1930). The Theory and Calculation of Screening Constants. Physical Review, 36 (5), 878–892. doi: 10.1103/physrev.36.878
Shull, H., Löwdin, P.-O. (1959). Superposition of Configurations and Natural Spin Orbitals. Applications to the He Problem. The Journal of Chemical Physics, 30 (3), 617. doi: 10.1063/1.1730019
Chong, D. P. (1966). Different Orbitals for Different Spins. Singlet S Ground State of Helium. The Journal of Chemical Physics, 45 (9), 3317. doi: 10.1063/1.1728108
Green, L. C., Lewis, M. N., Mulder, M. M., Wyeth, C. W., Woll, J. W. (1954). Correlation energies and angular components of the wave functions of the ground states of H–, He, and Li+. Physical Review, 93 (2), 273–279. doi: 10.1103/physrev.93.273
Bonham, R. A. (1966). Simple Correlated Wavefunctions for the Ground State of Heliumlike Atoms. The Journal of Chemical Physics, 45 (7), 2471. doi: 10.1063/1.1727963
Dolgushin, M. D.; Jucys A. (Ed.) (1971). Splitted orbitals and correlation energies for ground state of two-electron atoms. Theory of electronic shells in atoms and molecules, Mintis, Vilnius, 108–111.
Fraga, S., Ransil, B. J. (1961). Studies in Molecular Structure. VI. Potential Curve for the Interaction of Two Hydrogen Atoms in the LCAO MO SCF Approximation. The Journal of Chemical Physics, 35 (6), 1967. doi: 10.1063/1.1732194
Kol̸os, W., Wolniewicz, L. (1964). Accurate Adiabatic Treatment of the Ground State of the Hydrogen Molecule. The Journal of Chemical Physics, 41 (12), 3663. doi: 10.1063/1.1725796
Swalen, J. D., de Heer, J. (1964). Many‐Parameter Alternant Molecular Orbital Calculations for Large Cyclic Systems with Closed‐Shell Structure. The Journal of Chemical Physics, 40 (2), 378–384. doi: 10.1063/1.1725122
Hall, G. G., Amos, A. T.; Bates, D. R., Estermann, I. (Eds.) (1965). Molecular orbital theory of the spin properties of conjugated molecules. Advances in Atomic and Molecular Physics, 1, 1–59. doi: 10.1016/s0065-2199(08)60279-1
Pople, J. A., Beveridge, D. L., Dobosh, P. A. (1968). Molecular orbital theory of the electronic structure of organic compounds. II. Spin densities in paramagnetic species. Journal of the American Chemical Society, 90 (16), 4201–4209. doi: 10.1021/ja01018a0
Kruglyak, Y. A., Preuss, H., Janoschek, R. (1972). Non-empirical computation of the electronic structure of benzyl radical. J Struct Chem, 12(4), 623–629. doi: 10.1007/bf00743678
Kruglyak, Yu. A., Preuss, H., Yanoshek, R. (1971). Calculation of the electron shells of the benzyl radical by the unrestricted Hartree-Fock method on a Gaussian basis. Zhurnal Strukturnoi Khimii, 12 (4), 689–696.
Kruglyak, Y. A., Ukrainskii, I. I., Preuss, H., Janoschek, R. (1974). An orbital analysis of the ab initio electron and spin populations of the atoms in the benzyl radical. Theoretical and Experimental Chemistry, 7 (6), 663–666. doi: 10.1007/bf00524983
Carrington, A., Smith, I. C. P. (1965). The electron spin resonance spectrum and spin density distribution of the benzyl radical. Molecular Physics, 9 (2), 137–147. doi: 10.1080/00268976500100151
Benson, H. G., Hudson, A. (1971). On the spin density distribution in the benzyl radical. Molecular Physics, 20 (1), 185–187. doi: 10.1080/00268977100100181
Lloyd, R. V., Wood, D. E. (1974). Free radicals in an adamantane matrix. VIII. EPR and INDO[intermediate neglect of differential overlap] study of the benzyl, anilino, and phenoxy radicals and their fluorinated derivatives. Journal of the American Chemical Society, 96 (3), 659–665. doi: 10.1021/ja00810a004
McConnell, H. M. (1956). Electron Densities in Semiquinones by Paramagnetic Resonance. The Journal of Chemical Physics, 24 (3), 632. doi: 10.1063/1.1742580
McConnell, H. M. (1956). Indirect Hyperfine Interactions in the Paramagnetic Resonance Spectra of Aromatic Free Radicals. The Journal of Chemical Physics, 24 (4), 764. doi: 10.1063/1.1742605
Fessenden, R. W., Schuler, R. H. (1963). Electron Spin Resonance Studies of Transient Alkyl Radicals. The Journal of Chemical Physics, 39 (9), 2147. doi: 10.1063/1.1701415
Kruglyak, Yu. A., Mozdor, E. V., Kuprievich, V. A. (1970). Full configuration interaction of the benzyl radical. Ukrainsky Fizichnyi Zhurnal, 15 (1), 47–57.
Kruglyak, Yu. A., Hibaum, G., Radomyselskaya, N. E. (1972). Electronic structure of the ground state of the benzyl radical in equilibrium geometry. Revue Roumaine de Chimie, 17 (5), 781–799.
Kruglyak, Y. A., Mozdor, E. V. (1969). Study of the electronic structure of radicals by the CI method. Theoretica Chimica Acta, 15 (5), 374–384. doi: 10.1007/bf00528626
Kruglyak, Yu. A., Ukrainskii, I. I.; Jucys, A. (Ed.) (1971). About calculation of spin density in the method of splitted orbitals. Theory of electronic shells in atoms and molecules, Mintis, Vilnius, 224–228.
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.
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
McLachlan, A. D. (1960). Self-consistent field theory of the electron spin distribution in π-electron radicals. Molecular Physics, 3 (3), 233–252. doi: 10.1080/00268976000100281
Hanna, M. W., McLachlan, A. D., Dearman, H. H., McConnell, H. M. (1962). Radiation Damage in Organic Crystals. III. Long Polyene Radicals. The Journal of Chemical Physics, 37 (2), 361. doi: 10.1063/1.1701327
Kruglyak, Yu. A. (2014). Configuration Interaction in the Second Quantization Representation: Basics with Applications up to Full CI. ScienceRise, 4/2(4), 98–115. doi: 10.15587/2313-8416.2014.28948
Fenton, E. W. (1968). Overhauser Phase and Bond Alternation in Long-Chain Molecules. Physical Review Letters, 21 (20), 1427–1430. doi: 10.1103/physrevlett.21.1427
Ruedenberg, K. (1961). Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. I. General Analysis in the Tight-Binding Formulation. The Journal of Chemical Physics, 34 (6), 1861. doi: 10.1063/1.1731785
Murrell, J. N., Salem, L. (1961). Energies of Excited Electronic States as Calculated with the Zero Differential Overlap Approximation. The Journal of Chemical Physics, 34 (6), 1914. doi: 10.1063/1.1731791
Lykos, P. G. (1964). The Pi-Electron Approximation. in Advances in Quantum Chemistry, 171–201. doi: 10.1016/s0065-3276(08)60378-0
Bogolyubov, N. N. (1958). O novom metode v teorii sverhprovodimosti. Zhurnal eksper.teor. Fiz., 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.
Janke, E., Emde, F., Losch, F. (1960). Tafeln Hoherer Funktionen. D. G. Teubner, Stuttgart.
Landau, L. D., Lifshits, E. M. (1963). Quantum Mechanics. Moscow: Fizmatgiz.
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
Fichtengolts, G. M. (1951). Course of Differential and Integral Calculus. Vol. 2. Moscow: GITTL, 93, 349.
Fichtengolts, G. M. (1962). Course of Differential and Integral Calculus. Vol. 1. Moscow: Fizmatgiz, 257.
Fock, V. A. (1940). On wave functions of many electron systems. Zhurnal eksper. Teor. Fiz., 10 (9-10), 961–979.
Murrell, J. N. (1963). The Theory of Electronic Spectra of Organic Molecules. N.Y., 78.
Longuet-Higgins, H. C., Salem, L. (1959). The Alternation of Bond Lengths in Long Conjugated Chain Molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 251 (1265), 172–185. doi: 10.1098/rspa.1959.0100
Ooshika, Y. (1957). A Semi-empirical Theory of the Conjugated Systems II. Bond Alternation in Conjugated Chains. Journal of the Physical Society of Japan, 12 (11), 1246–1250. doi: 10.1143/jpsj.12.1246
Popov, N. A. (1969). The alternation of bonds and the nature of the energy gap in the π-electronic spectrum of long polyenes. J Struct Chem, 10 (3), 442–448. doi: 10.1007/bf00746742
Maradudin, A. A., Montroll, F. W., Weiss, G. M. (1963). Theory of Lattice Dynamics in the Harmonic Approximation. N.Y.
Maradudin, A. A., Montroll, F. W., Weiss, G. M. (1963). Theory of Lattice Dynamics in the Harmonic Approximation. N.Y.
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
Musher, J. I. (1966). Energy of Interaction between Two Molecules. The Journal of Chemical Physics, 44 (8), 2943. doi: 10.1063/1.1727159
Falicov, L. M. (1969). Two-Electron Homopolar Molecule: A Test for Spin-Density Waves and Charge-Density Waves. The Journal of Chemical Physics, 51 (8), 3153. doi: 10.1063/1.1672488
Van-Catledge, F. A., Allinger, N. L. (1969). Organic quantum chemistry. XXI. Structure and spectrum of cyclooctadecanonaene ([18]annulene). Journal of the American Chemical Society, 91 (10), 2582–2589. doi: 10.1021/ja01038a033
Platt, J. R. (1956). Wavelength Formulas and Configuration Interaction in Brooker Dyes and Chain Molecules. The Journal of Chemical Physics, 25 (1), 80. doi: 10.1063/1.1742852
Downloads
Published
Issue
Section
License
Copyright (c) 2015 Юрій Олексійович Кругляк
This work is licensed under a Creative Commons Attribution 4.0 International License.
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.
