Coupling and dissociation in artificial molecules

European Physical Journal D

Volumn 8, Issue 3, 2001, Pages 373-380

  Yannouleas, C ^a   Landman, U ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETISM; DISSOCIATION; MOLECULAR ORBITALS; MOLECULES; NANOCRYSTALS;

ANTIFERROMAGNETIC ORDERINGS; ARTIFICIAL MOLECULE; DOUBLE QUANTUM DOTS; PROJECTION TECHNIQUES; QUANTUM DOT MOLECULES; STRONG-COUPLING REGIME; UNRESTRICTED HARTREE-FOCK METHOD; WEAK-COUPLING REGIME;

SEMICONDUCTOR QUANTUM DOTS;

EID: 0034258447     PISSN: 14346060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100530170133     Document Type: Article

References (48)

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23. A 3D magnetic-field-free version of the TCO has been used in the description of fission in metal clusters [C. Yannouleas, U. Landman, J. Phys. Chem. 99, 14577 (1995); C. Yannouleas et al., Comm. At. Mol. Phys. 31, 445 (1995)] and nuclei [J. Maruhn, W. Greiner, Z. Phys. 251, 431 (1972); C.Y. Wong, Phys. Lett. B 30, 61 (1969)].
24. A 3D magnetic-field-free version of the TCO has been used in the description of fission in metal clusters [C. Yannouleas, U. Landman, J. Phys. Chem. 99, 14577 (1995); C. Yannouleas et al., Comm. At. Mol. Phys. 31, 445 (1995)] and nuclei [J. Maruhn, W. Greiner, Z. Phys. 251, 431 (1972); C.Y. Wong, Phys. Lett. B 30, 61 (1969)].
25. A 3D magnetic-field-free version of the TCO has been used in the description of fission in metal clusters [C. Yannouleas, U. Landman, J. Phys. Chem. 99, 14577 (1995); C. Yannouleas et al., Comm. At. Mol. Phys. 31, 445 (1995)] and nuclei [J. Maruhn, W. Greiner, Z. Phys. 251, 431 (1972); C.Y. Wong, Phys. Lett. B 30, 61 (1969)].
26. A 3D magnetic-field-free version of the TCO has been used in the description of fission in metal clusters [C. Yannouleas, U. Landman, J. Phys. Chem. 99, 14577 (1995); C. Yannouleas et al., Comm. At. Mol. Phys. 31, 445 (1995)] and nuclei [J. Maruhn, W. Greiner, Z. Phys. 251, 431 (1972); C.Y. Wong, Phys. Lett. B 30, 61 (1969)].
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38. The early electronic model of valence was primarily developed by G.N. Lewis who introduced a symbolism where an electron was represented by a dot, e.g., H:H, with a dot between the atomic symbols denoting a shared electron. Later in 1927 Heitler and London formulated the first quantum mechanical theory of the pair-electron bond for the case of the hydrogen molecule. The theory was subsequently developed by Pauling and others in the 1930's into the modern theory of the chemical bond called the Valence Bond Theory.
39. 6.
40. More precisely our GVB method belongs to a class of Projection Techniques known as Variation before Projection, unlike the familiar in chemistry GVB method of Goddard and coworkers [W.A. Goddard III et al., Acc. Chem. Res. 6, 368 (1973)], which is a Variation after Projection [see P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980), Ch. 11].
41. More precisely our GVB method belongs to a class of Projection Techniques known as Variation before Projection, unlike the familiar in chemistry GVB method of Goddard and coworkers [W.A. Goddard III et al., Acc. Chem. Res. 6, 368 (1973)], which is a Variation after Projection [see P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980), Ch. 11].
42. See section 3.8.7 in Ref. [19](a).
43. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].
44. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].
45. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].
46. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].
47. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].
48. Symmetry breaking in coupled QD's within the LSD has been explored by J. Kolehmainen et al. [Eur. Phys. J. D 13, 731 (2000)]. However, unlike the HF case for which a fully developed theory for the restoration of symmetries has long been established (see, e.g., the book by Ring and Schuck in Ref. [30]), the breaking of space symmetry within the spin-dependent density functional theory poses a serious dilemma [J.P. Perdew et al., Phys. Rev. A 51, 4531 (1995)]. This dilemma has not been fully resolved todate; several remedies (like Projection, ensembles, etc.) are being proposed, but none of them appears to be completely devoid of inconsistencies [A. Savin, in Recent developments and applications of modern density functional theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996), p. 327]. In addition, due to the unphysical self-interaction error, the density-functional theory is more resistant against symmetry breaking [see R. Bauernschmitt, R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996)] than the sS-UHF, and thus it fails to describe a whole class of broken symmetries involving electron localization, e.g., the formation at B = 0 of Wigner molecules in QD's (see footnote 7 in Ref. [7]), the hole trapping at Al impurities in silica [J. Laegsgaard, K. Stokbro, Phys. Rev. Lett. 86, 2834 (2001)], or the interaction driven localization-delocalization transition in d- and f-electron systems, like Plutonium [S.Y. Savrasov et al., Nature 410, 793 (2001)].