Abstract
The approximation of static fluctuations in the Hubbard model is used to calculate the anticommutator Green’s functions, the thermodynamic averages characterizing the possibilities of electron hopping from site to site, the correlation functions which characterize the probability of finding two electrons on one site of a nanosystem, and the energies of the ground state for the closed atomic structures consisting of three, four, and sixteen gold atoms.
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Jin Zhao, Jinlong Yang, and J. G. Hou, “Theoretical Study of Small Two-Dimensional Gold Clusters,” Phys. Rev. B: Condens. Matter Mater. Phys. 67, 085404 (2003).
J. Wang, G. Wang, and J. Zhao, “Density-Functional Study of Aun (n = 2–20) Clusters: Lowest-Energy Structures and Electronic Properties,” Phys. Rev. B: Condens. Matter Mater. Phys. 66, 035418 (2002).
A. C. Templeton, W. P. Wuelfing, and R. W. Murray, “Monolayer-Protected Cluster Molecules,” Ac. Chem. Res. 33(1), 27–36 (2000).
M. Dorogi, J. Gomez, R. Osifichin, et al., “Room-Temperature Coulomb Blockade from a Self-Assembled Molecular Nanostructure,” Phys. Rev. B: Condens. Matter 52(12), 9071–9077 (1995).
R. L. Whetten, M. N. Shafigullin, J. T. Khoury, et al., “Crystal Structures of Molecular Gold Nanocrystal Arrays,” Ac. Chem. Res. 32(5), 397–406 (1999).
A. Sanchez, S. Abbet, W. D. Schneider, et al., “When Gold is not Noble: Nanoscale Gold Catalysts,” J. Phys. Chem. A 103(48), 9573–9578 (1999).
V. V. Pokrivnyi and L. I. Ovsyannikova, “Electronic Structure and the Infrared Absorption and Raman Spectra of the Semiconductor Clusters C24, B12N12, Si12C12, Zn12O12, and Ga12N12,” Fiz. Tverd. Tela 49(3), 535–561 (2007) [Phys. Sol. St. 49 (3), 562–570 (2007)].
G. I. Mironov, “Calculation of Green’s Functions for Nanostructures in the Hubbard Model in the Approximation of Static Fluctuations,” Fiz. Met. Metalloved. 102(6), 611–620 (2006) [Phys. Met. Metallogr. 102 (6), 568–577 (2006)].
L. N. Sidorov and M. A. Yurovskaya, Fullerenes (Ekzamen, Moscow, 2005) [in Russian].
G. I. Mironov, “Nanosystems in the Static-Fluctuation Approximation Hubbard Model,” Fiz. Tverd. Tela 48(7), 1299–1306 (2006) [Phys. Sol. St. 48 (7), 1378–1386 (2006)].
G. I. Mironov, “Investigation of the Structural Elements of a Fullerene within the Static-Fluctuation Approximation of the Hubbard Model,” Fiz. Tverd. Tela 49(3), 527–534 (2007) [Phys. Sol. St. 49 (3), 552–561 (2007)].
H. Hasegawa, “Nonextensive Thermodynamics of the Two-Site Hubbard Model,” Physica A (Amsterdam) 351(1), 273–285 (2005).
J. P. Bucher, D. C. Douglass, and L. A. Bloomfield, “Magnetic Properties of Free Cobalt Clusters,” Phys. Rev. Lett. 66(23), 3052–3055 (1991).
S. E. Aspel, J. W. Emmert, J. Deng, et al., “Surface-Enhanced Magnetism in Nickel Clusters,” Phys. Rev. Lett. 76(9), 1441–1444 (1996).
J. Hubbard, “Electron Correlations in Narrow Energy,” Proc. R. Soc. London, Ser. A 276(1365), 238–257 (1963).
Yu. A. Izyumov, N. I. Chashchin, and D. S. Alekseev, Theory of Strongly Correlated Systems. Method of Generating Functional (NITs Regulyarnaya i Khaoticheskaya Dinamika, Izhevsk, 2006) [in Russian].
G. I. Mironov, “Antiferromagnetism in the Hubbard Model,” Fiz. Tverd. Tela 39(9), 1594–1599 (1997) [Phys. Sol. St. 39 (9), 1420–1424 (1997)].
G. I. Mironov, “B-B′-U Hubbard Model in the Approximation of Static Fluctuations,” Fiz. Tverd. Tela 41(6), 951–956 (1999) [Phys. Sol. St. 41 (6), 864–869 (1999)].
G. I. Mironov, “The Ground-State Energy of the B-B′-U Hubbard Model in the Static-Fluctuation Approximation,” Fiz. Tverd. Tela 44(2), 209–212 (2002) [Phys. Sol. St. 44 (2), 216–220 (2002)].
V. J. Emery, “Theory of High-T c Superconductivity in Oxides,” Phys. Rev. Lett. 58(26), 2794–2797 (1987).
E. H. Lieb and F. Y. Wu, “Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension,” Phys. Rev. Lett. 20(25), 1445–1448 (1968).
G. I. Mironov, in Structure and Dynamics of Molecular Systems (Kazan, 2003), No. 10, Part 1, pp. 323–326 [in Russian].
G. I. Mironov, in Topical Problems of Physics of Condensed Matter (Kazan, 2004), pp. 235–255 [in Russian].
D. Alamanova, Yi. Dong, H. Rehman, et al., “Structural and Electronic Properties of Gold Clusters,” Comp. Lett. (CoLe), 1(1), 1–12 (2005).
S. V. Tyablikov, Methods in the Quantum Theory of Magnetism (Plenum, New York, 1967; 2nd ed.; Nauka, Moscow, 1975).
G. I. Mironov, “Study of One-Particle Hubbard Model in Bipartite Hubbard Model in Static-Fluctuation Approximation,” Fiz. Nizk. Temp. 31(12), 1388–1394 (2005).
L. M. Falicov and R. H. Victora, “Exact Solution of the Hubbard Model for a Four-Center Tetrahedral Cluster,” Phys. Rev. B: Condens. Matter 30(4), 1695–1699 (1994).
G. J. Hutchings, “New Directions in Gold Catalysis,” Gold Bull. 37(1–2), 3–11 (2004).
M. Haruta, “Gold as a Novel Catalyst in the 21st Century: Preparation, Working Mechanism and Applications,” Gold Bull. 37(1–2), 27–36 (2004).
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Original Russian Text © G.I. Mironov, 2008, published in Fizika Metallov i Metallovedenie, 2008, Vol. 105, No. 4, pp. 355–365.