Bulletin of the Korean Chemical Society

  • 제24권6호
  • /
  • Pages.864-880
  • /
  • 2003
  • /
  • 0253-2964(pISSN)
  • /
  • 1229-5949(eISSN)
대한화학회 (Korean Chemical Society)
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Spin and Pseudo Spins in Theoretical Chemistry. A Unified View for Superposed and Entangled Quantum Systems

  • Yamaguchi, Y. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Nakano, M. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Nagao, H. (Department of Computational Science, Faculty of Science, Kanazawa University) ;
  • Okumura, M. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Yamanaka, S. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Kawakami, T. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Yamaki, D. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Nishino, M. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Shigeta, Y. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Kitagawa, Y. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Takano, Y. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Takahata, M. (Department of Chemistry, Graduate School of Science, Osaka University) ;
  • Takeda, R. (Department of Chemistry, Graduate School of Science, Osaka University)
  • 발행 : 2003.06.20
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A unified picture for magnetism, superconductivity, quantum optics and other properties of molecule-based materials has been presented on the basis of effective model Hamiltonians, where necessary parameter values have been determined by the first principle calculations of cluster models and/or band models. These properties of the matetials are qualitatively discussed on the basis of the spin and pseudo-spin Hamiltonian models, where several quantum operators are expressed by spin variables under the two level approximation. As an example, ab initio broken-symmetry DFT calculations are performed for cyclic magnetic ring constructed of 34 hydrogen atoms in order to obtain effective exchange integrals in the spin Hamiltonian model. The natural orbital analysis of the DFT solution was performed to obtain symmetry-adapted molecular orbitals and their occupation numbers. Several chemical indices such as information entropy and unpaired electron density were calculated on the basis of the occupation numbers to elucidate the spin and pair correlations, and bonding characteristic (kinetic correlation) of this mesoscopic magnetic ring. Both classical and quantum effects for spin alignments and singlet spin-pair formations are discussed on the basis of the true spin Hamiltonian model in detail. Quantum effects are also discussed in the case of superconductivity, atom optics and quantum optics based on the pseudo spin Hamiltonian models. The coherent and squeezed states of spins, atoms and quantum field are discussed to obtain a unified picture for correlation, coherence and decoherence in future materials. Implications of theoretical results are examined in relation to recent experiments on molecule-based materials and molecular design of future molecular soft materials in the intersection area between molecular and biomolecular materials.

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참고문헌

  1. Washrurn, S.; Webb, R. A. Adv. Phys. 1986, 35, 375. https://doi.org/10.1080/00018738600101921
  2. Beenakker, C. W. J.; Houten, H. V. Solid State Phys. 1990, 44, 1.
  3. Schon, G.; Zaikin, A. D. Phys. Reports 1990, 198, 237. https://doi.org/10.1016/0370-1573(90)90156-V
  4. Kastner, M. A. Rev. Mod. Phys. 1992, 64, 849. https://doi.org/10.1103/RevModPhys.64.849
  5. Bout, F. A. Phys. Reports 1993, 234, 73. https://doi.org/10.1016/0370-1573(93)90097-W
  6. Levy, P. N. Solid State Phys. 1993, 47, 367.
  7. Meservey, R.; Tedrow, P. M. Phys. Reports 1994, 238, 173. https://doi.org/10.1016/0370-1573(94)90105-8
  8. Ferry, D. K.; Grubin, H. L. Solid State Phys. 1995, 49, 283.
  9. Gijs, M. A. M.; Bauer, G. E. W. Adv. Phys. 1997, 46, 285. https://doi.org/10.1080/00018739700101518
  10. Hecht, S.; Frechet, J. M. Angew. Chem. Int. Ed. 2001, 40, 74. https://doi.org/10.1002/1521-3773(20010105)40:1<74::AID-ANIE74>3.0.CO;2-C
  11. Segura, J. L.; Martin, N. Angew. Chem. Int. Ed. 2001, 40, 1372. https://doi.org/10.1002/1521-3773(20010417)40:8<1372::AID-ANIE1372>3.0.CO;2-I
  12. Niemeyer, C. M. Angew. Chem. Int. Ed. 2001, 40, 4128. https://doi.org/10.1002/1521-3773(20011119)40:22<4128::AID-ANIE4128>3.0.CO;2-S
  13. Foster, S.; Plantenberg, T. Angew. Chem. Int. Ed. 2002, 41, 688. https://doi.org/10.1002/1521-3773(20020301)41:5<688::AID-ANIE688>3.0.CO;2-3
  14. Nakamura, A.; Ueyama, N.; Yamaguchi, K. OrganometallicConjugation (Kodanshya-Springer, Springer Series in ChemicalPhys. 73, 2002).
  15. Ito, T. et al. Metal Assembled Complexes to be published.
  16. Yamaguchi, K. Self-Consistent Field Theory and Applications;Carbo, R., Klobukowski, M., Eds.; Elsevier: Amsterdam, 1990; p727.
  17. Mitani, M.; Yamaki, D.; Takano, Y.; Kitagawa, Y.; Yoshioka, Y.;Yamaguchi, K. J. Chem. Phys. 2000, 113, 10486. https://doi.org/10.1063/1.1290008
  18. Yamaguchi, K.; Kawakami, T.; Yamaki, D.; Yoshioka, Y.Molecular Magnetism; Ito, K., Kinoshita, M., Eds.; Kodansha-Gordon Breach: 2000; p 9 (part I).
  19. Kawakami, T.; Yamanaka, S.; Takano, Y.; Yoshioka, Y.;Yamaguchi, K. Bull. Chem. Soc. Jpn. 1998, 71, 2097. https://doi.org/10.1246/bcsj.71.2097
  20. Yamaguchi, K.; Kawakami, T.; Takano, Y.; Kitagawa, Y.;Yamashita, Y.; Fujita, H. Int. J. Quant. Chem. 2002, 90, 370. https://doi.org/10.1002/qua.979
  21. Yamaguchi, K.; Ohta, K.; Yabushita, S.; Fueno, T. Chem. Phys.Lett. 1977, 49, 555. https://doi.org/10.1016/0009-2614(77)87037-1
  22. Yamaguchi, K. Int. J. Quant. Chem. 1980, S14, 269.
  23. Roos, B. O. Int. J. Quantum Chem. 1980, S14, 175.
  24. Andersson, K.; Malmqvist P.-A.; Roos, B. O. J. Chem. Phys.1992, 96, 1218. https://doi.org/10.1063/1.462209
  25. Haldane, F. D. M. Phys. Lett. 1983, 93A, 464.
  26. Affleck, I.; Kennedy, T.; Lieb, E. H.; Tasaki, H. Phys. Rev. Lett.1987, 59, 799. https://doi.org/10.1103/PhysRevLett.59.799
  27. Anderson, P. W. Phys. Rev. 1958, 112, 1900. https://doi.org/10.1103/PhysRev.112.1900
  28. Ketterle, W. Rev. Mod. Phys. 2002, 74, 1131. https://doi.org/10.1103/RevModPhys.74.1131
  29. Cornell, E. A.; Wieman, C. E. Rev. Mod. Phys. 2002, 74, 875. https://doi.org/10.1103/RevModPhys.74.875
  30. Jaynes, E. T.; Cummings, F. W. Proc. IEEE 1963, 51, 100.
  31. Nishino, M.; Ohnishi, H.; Yamaguchi, K.; Miyashita, S. Phys.Rev. 2000, B62, 9463.
  32. Nishino, M.; Ohnishi, H.; Yamaguchi, K.; Miyashita, S. Phys.Rev. 2000, B58, 9303.
  33. Nakano, M.; Yamaguchi, K. Chem. Phys. 2000, 252, 115. https://doi.org/10.1016/S0301-0104(99)00331-6
  34. Nakano, M.; Yamaguchi, K. J. Chem. Phys. 2000, 112, 2769. https://doi.org/10.1063/1.480851
  35. Phys. Rev. v.A64 Nakano, M.;Yamaguchi, K.
  36. Nakano, M.; Yamaguchi, K. Phys. Rev. 2001, A64, 033415.
  37. Nakano, M.; Yamaguchi, K. J. Chem. Phys. 2002, 116, 10069. https://doi.org/10.1063/1.1471906
  38. Landauer, R. Foundation of Phys. 1986, 16, 551. https://doi.org/10.1007/BF01886520
  39. Ginsberg, A. P. J. Am. Chem. Soc. 1980, 102, 111. https://doi.org/10.1021/ja00521a020
  40. Yamaguchi, K.; Takahara, Y.; Fueno, T. Applied QuantumChem.; Smith, V. H. et al., Eds.; D. Reidel: Boston, MA, 1986; p 155.
  41. Noodleman, L.; Davidson, E. R. Chem. Phys. 1986, 109, 131. https://doi.org/10.1016/0301-0104(86)80192-6
  42. Bencini, A.; Totti, F.; Doul, C. A.; Doclo, K.; Fantucci, P.;Barone, V. Inorg. Chem. 1997, 36, 5022. https://doi.org/10.1021/ic961448x
  43. Ruiz, E.; Cano, J.; Alvarez, S.; Alemany, P. J. Comp. Chem.1999, 20, 1391. https://doi.org/10.1021/ic50219a012
  44. Yamaguchi, K. Chem. Phys. Lett. 1979, 68, 477. https://doi.org/10.1016/0009-2614(79)87242-5
  45. Yamanaka, S.; Okumura, M.; Nakano, M.; Yamaguchi, K. J.Mol. Struct. Theochem. 1994, 310, 205. https://doi.org/10.1016/S0166-1280(09)80099-7
  46. Lowdin, P.-O. Phys. Rev. 1955, 97, 1494; 1955, 97, 1509.
  47. Knowles, P. J.; Handy, N. C. J. Chem. Phys. 1988, 88, 6991. https://doi.org/10.1063/1.454397
  48. Schlegel, H. B. J. Chem. Phys. 1986, 84, 4530. https://doi.org/10.1063/1.450026
  49. Becke, A. D. Phys. Rev. 1988, A38, 3098.
  50. Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785.
  51. Becke, A. D. J. Chem. Phys. 1993, 98, 5648. https://doi.org/10.1063/1.464913
  52. Stwalley, W. C.; Nosanow, L. H. Phys. Rev. Lett. 1976, 36, 910. https://doi.org/10.1103/PhysRevLett.36.910
  53. Yamaguchi, K.; Fueno, T. Chem. Phys. 1977, 19, 35. https://doi.org/10.1016/0301-0104(77)80004-9
  54. Yamaguchi, K. Chem. Phys. 1978, 29, 117. https://doi.org/10.1016/0301-0104(78)85065-4
  55. Takatsuka, K.; Fueno, T.; Yamaguchi, K. Theor. Chim. Acta1978, 48, 175. https://doi.org/10.1007/BF00549017
  56. Staroverov, V. N.; Davidson, E. R. Chem. Phys. Lett. 2000, 330,161. https://doi.org/10.1016/S0009-2614(00)01088-5
  57. Staroverov, V. N.; Davidson, E. R. J. Am. Chem. Soc. 2000, 122,7377. https://doi.org/10.1021/ja001259k
  58. Wehri, A. Rev. Mod. Phys. 1978, 50, 221. https://doi.org/10.1103/RevModPhys.50.221
  59. Shannon, C. E. Bell. Syst. Tech. 1948, 27, 379. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  60. Jaynes, E.; Probability, Statics and Statistical Physics;Rosencrants, R., Ed.; Reidel, 1993.
  61. Collins, D. M. Z. Naturforsch 1993, 48A, 68.
  62. Yamaguchi, K. Chem. Phys. Lett. 1975, 35, 230. https://doi.org/10.1016/0009-2614(75)85320-6
  63. Fradkin, E. Field Theories of Condensed Matter Systems; AddisonWesey: Reading, MA, 1991.
  64. Molecular Magnetism; Ito, K.; Kinoshita, M., Eds.; Kodanshya,1999.
  65. Fukui, T.; Kawakami, N. Phys. Rev. 1997, B55, 14709.
  66. Brehmer, S.; Mikeska, H.-J.; Yamamoto, S. J. Phys. Condens.Matter. 1997, 9, 3921. https://doi.org/10.1088/0953-8984/9/19/012
  67. Yamamoto, S.; Brehmer, S.; Mikeska, H.-J. Phys. Rev. 1998,B57, 13610.
  68. Eggert, S.; Affleck, I. Phys. Rev. Lett. 1995, 75, 934. https://doi.org/10.1103/PhysRevLett.75.934
  69. Regnault, L. P.; Renard, J. P.; Dhalenne, G.; Revcolevschi, A.Europhys. Lett. 1995, 32, 579. https://doi.org/10.1209/0295-5075/32/7/007
  70. Fukuyama, H.; Tanimoto, T.; Saito, M. J. Phy. Soc. Jpn. 1996,65, 1182. https://doi.org/10.1143/JPSJ.65.1182
  71. Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. Phys. Rev. 1957, 108,1175. https://doi.org/10.1103/PhysRev.108.1175
  72. Yamaguchi, K.; Takahara, Y.; Fueno, T.; Nasu, K. J. Appl. Phys.1987, 26, L1362. https://doi.org/10.1143/JJAP.26.L1362
  73. Bednort, J. G.; Muller, K. A. Z. Phs. 1986, 64, 189.
  74. Kawakami, T.; Taniguchi, T.; Kitagawa, Y.; Takano, Y.; Nagao,H.; Yamaguchi, K. Mol. Phys. 2002, 100, 2641. https://doi.org/10.1080/00268970210136366
  75. Yamanaka, S.; Yamaki, D.; Shigeta, Y.; Nagao, H.; Yoshioka, Y.;Suzuki, N.; Yamaguchi, K. Int. J. Quant. Chem. 2000, 80, 664. https://doi.org/10.1002/1097-461X(2000)80:4/5<664::AID-QUA15>3.0.CO;2-C
  76. Bose, S. N. Z. Phys. 1924, 26, 178. https://doi.org/10.1007/BF01327326
  77. Einstein, A. Phys. Math. Kl. Bericht 3, 18; Sitzungsber. Press:Akad. Wiss, 1925.
  78. Nagao, H.; Nishino, M.; Shigeta, Y.; Yoshioka, Y.; Yamaguchi,K. J. Chem. Phys. 2000, 113, 11237. https://doi.org/10.1063/1.1327264
  79. Katano, S.; Sato, M.; Yamada, K.; Suzuki, T.; Fukase, T. Phys.Rev. 2000, B62, R14677.
  80. Lake, B.; Aeppli, G.; Clausen, K. N.; McMorrow, D. F.;Lefmann, K.; Hussey, N. E.; Mangkorntong, N.; Nohara, M.;Takagi, H.; Mason, T. E.; Schroder, A. Science 2001, 291, 1759. https://doi.org/10.1126/science.1056986
  81. Lake, B.; Ronnow, H. M.; Christensen, N. B.; Aeppli, G.;Lefmann, K.; McMorrow, D. F.; Vorderwisch, P.; Smeibidl, P.;Mangkorntong, N.; Sasagawa, T.; Nohara, M.; Takagi, H.;Mason, T. E. Nature 2002, 415, 299. https://doi.org/10.1038/415299a
  82. Hoffman, J. E.; Hudson, E. W.; Lang, K. M.; Madhavan, V.;Eisaki, H.; Uchida, S.; Davis, J. C. Science 2002, 295, 466. https://doi.org/10.1126/science.1066974
  83. Phys. Rev. v.B66 Herbut, I. F.
  84. Int. J. Quant. Chem. v.37 Yamaguchi, K. https://doi.org/10.1002/qua.560370207
  85. Franz, M.; Tesanovic, Z.; Valek, O. Phys. Rev. 2002, B66, 054535.
  86. Herbut, I. F. Phys. Rev. 2002, B66, 094504.
  87. Yamaguchi, K. Int. J. Quant. Chem. 1990, 37, 167. https://doi.org/10.1002/qua.560370207
  88. Leggett, A. J. Rev. Mod. Phys. 2001, 73, 307. https://doi.org/10.1103/RevModPhys.73.307
  89. Yamaguchi, K.; Yamanaka, S.; Nishino, M.; Takano, Y.; Kitagawa,Y.; Nagao, H.; Yoshioka, Y. Theor. Chem. Acc. 1999, 102, 328. https://doi.org/10.1007/s002140050505
  90. Nagao, H.; Nishino, M.; Shigeta, Y.; Soda, T.; Kitagawa, Y.;Onishi, T.; Yoshioka, Y.; Yamaguchi, K. Coord. Chem. Rev.2000, 198, 265. https://doi.org/10.1016/S0010-8545(00)00231-9
  91. Walls, D. F.; Milburn, G. J. Quantum Optics; Springer-Verlag:Berlin, 1994.
  92. Lin, J. L.; Wolfe, J. P. Phys. Rev. Lett. 1993, 71, 1222. https://doi.org/10.1103/PhysRevLett.71.1222
  93. O'Hara, K. E.; Suilleabhain, L. O.; Wolfe, J. P. Phys. Rev. 1999,B60, 10565.
  94. Nakano, M.; Fujita, H.; Takahata, M.; Yamaguchi, K. J. Am.Chem. Soc. 2002, 124, 9648. https://doi.org/10.1021/ja0115969
  95. Nakamura, Y.; Pashkin, Yu. A.; Tsai, J. S. Nature 1999, 398,786. https://doi.org/10.1038/19718
  96. Scully, M. O.; Zubairy, M. S. Quantum Optics; CambridgeUniversity Press: 1997; Chapter 18.
  97. van der Wal, C. H.; ter Haar, A. C. J.; Wilhelm, F. K.; Schouten,R. N.; Harmans, C. J. P. M.; Orlando, T. P.; Lloyd, S.; Mooij, J.E. Science 2000, 290, 773. https://doi.org/10.1126/science.290.5492.773
  98. Friedman, J. R.; Patel, V.; Chen, W.; Tolpygo, S. K.; Lukens, J. E.Nature 2000, 406, 43. https://doi.org/10.1038/35017505
  99. Yu, Y.; Han, S.; Chu, X.; Chu, S.; Wang, Z. Science 2002, 296, 889. https://doi.org/10.1126/science.1069452
  100. Garcia-Pablos, D.; Garcia, N.; Raedt, H. De. Phys. Rev. 1997,B55, 937.
  101. Raedt, H. De.; Miyashita, S.; Saito, K.; Garcia-Pablos, D.;Garcia, N. Phys. Rev. 1997, B56, 11761.
  102. Rainmond, J. M.; Brune, M.; Harosche, S. Rev. Mod. Phys. 2001,73, 565. https://doi.org/10.1103/RevModPhys.73.565
  103. Kitagawa, M.; Ueda, M. Phys. Rev. 1993, A47, 5138.
  104. Nakakima, T.; Aoki, H. Phys. Rev. 1997, B56, R15550.
  105. Sorensen, A.; Molmer, K. Phys. Rev. Lett. 1999, 85, 2274.
  106. Zhang, W.-M.; Feng, Da. H.; Gilmore, R. Rev. Mod. Phys. 1990,62, 867. https://doi.org/10.1103/RevModPhys.62.867
  107. Kolobov, M. I. Rev. Mod. Phys. 1999, 71, 1539. https://doi.org/10.1103/RevModPhys.71.1539
  108. Braginsky, V. B.; Khalili, F. Ya. Rev. Mod. Phys. 1996, 68, 1. https://doi.org/10.1103/RevModPhys.68.1
  109. Pegg, D. T.; Barnett, S. M. Phys. Rev. 1989, A39, 1665.
  110. Lynch, R. Phys. Rep. 1995, 256, 367. https://doi.org/10.1016/0370-1573(94)00095-K
  111. Bogoliubov, N. N. Sov. Phys. JETP 1958, 7, 41.
  112. de Gennes, P. G. Superconductivity of Metals and Alloys; Benjamin: New York, 1966.
  113. Marumori, T. Prog. Theoret. Phys. 1960, 24, 331. https://doi.org/10.1143/PTP.24.331
  114. Yamaguchi, K.; Yamaki, D.; Kitagawa, Y.; Takahata, M.;Kawakami, T.; Osaku, T.; Nagao, H. Int. J. Quant. Chem. inpress.
  115. Yamaki, D. et al. to be publised.
  116. Peirls, R. E.; Yoccoz, J. Proc. Phys. Soc. 1987, 70, 381.
  117. Sawada, K. Phys. Rev. 1957, 106, 372. https://doi.org/10.1103/PhysRev.106.372
  118. Rowe, D. J. Nucl. Phys. 1966, 80, 209. https://doi.org/10.1016/0029-5582(66)90837-6
  119. Thouless, D. J. Nucl. Phys. 1960, 21, 225. https://doi.org/10.1016/0029-5582(60)90048-1
  120. Yamaki, D.; Shigeta, Y.; Yamanaka, S.; Nagao, H.; Yamaguchi,K. Int. J. Quant. Chem. 2000, 80, 701. https://doi.org/10.1002/1097-461X(2000)80:4/5<701::AID-QUA19>3.0.CO;2-K
  121. Takeda, R.; Yamanaka, S.; Yamaguchi, K. Chem. Phys. Lett.2002, 366, 321. https://doi.org/10.1016/S0009-2614(02)01576-2
  122. Nagaosa, N.; Lee, P. A. Phys. Rev. 1992, B4, 966.
  123. Takahashi, A.; Gomi, H.; Aihara, M. Phys. Rev. Lett. 2002, 89,206402.
  124. Gatteschi, D.; Yamaguchi, K. Molecular Magnetism: FromMolecular Assemblies to the Devices; Coronado, E. et al., Eds.;Kluwer, Academic Pub.: Netherland, 1996; p 561.
  125. Sondhi, S. L.; Girvin, S. M.; Carini, J. P.; Shahar, D. Rev. Mod.Phys. 1997, 69, 315. https://doi.org/10.1103/RevModPhys.69.315
  126. Snyder, J.; Slusky, J. S.; Cava, R.; Schffer, P. Nature 2001, 413,48. https://doi.org/10.1038/35092516
  127. Gatteschi, D.; Caneshi, A.; Pardi, L.; Sessoli, R. Science 1994,265, 1054. https://doi.org/10.1126/science.265.5175.1054
  128. Caneschi, A.; Gatteschi, D.; Lalioti, N.; Sangregorio, C.; Sessoli,R.; Venturi, G.; Vindigni, A.; Rettori, A.; Pini, M. G.; Novak, M.A. Angew. Chem. Int. Ed. 2001, 40, 1760. https://doi.org/10.1002/1521-3773(20010504)40:9<1760::AID-ANIE17600>3.0.CO;2-U
  129. Gauber, R. J. J. Math. Phys. 1963, 4, 294. https://doi.org/10.1063/1.1703954
  130. Leuenberger, M. N.; Loss, D. N. Nature 2001, 410, 789. https://doi.org/10.1038/35071024
  131. Yamashita, M. et al. J. Am. Chem. Soc. in press.
  132. den Hertog, B. C.; Gingras, M. J. P. Phys. Rev. Lett. 2000, 84,343.
  133. Blinc, R.; Pirc, R. Theoretical Treatments of Hydrogen Bonding;Hadzi, D., Ed.; John-Wiley: 1997.
  134. Yamaguchi, Y. Functionality of Molecular Systems; Nagakura,S., Ed.; Springer: Tokyo, 1998; vol 1, p 67.
  135. Oda, A.; Nagao, H.; Kitagawa, Y.; Shigeta Y.; Yamaguchi, K. Int.J. Quant. Chem. 2000, 80, 646. https://doi.org/10.1002/1097-461X(2000)80:4/5<646::AID-QUA13>3.0.CO;2-M
  136. Kagaku v.41 Yamaguchi, K.;Fueno, T.
  137. Theumann, W. K.; Erichsenm, R. Jr. Phys. Rev. 2001, E64, 061902.
  138. Ibu, M.; Pribram, K. H.; Yasue, K. Int. J. Mod. Phys. 1996, B10,1735.
  139. Anderson, P. W. Science 1972, 177, 393. https://doi.org/10.1126/science.177.4047.393
  140. Yamaguchi, K.; Fueno, T. Kagaku 1986, 41, 372 (in Japanese).
  141. Yamaguchi, K. Self-Consistent Field, Theory and Applications;Carbo, R., Klobukowski, M., Eds.; Elsevier: 1990.

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