Internal Symmetries and Additional Quantum Numbers for Nanoparticles
Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that t...
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| Published in | Nanoscale systems mathematical modeling, theory and applications Vol. 2; pp. 96 - 106 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Versita
06.05.2013
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2299-3290 2299-3290 |
| DOI | 10.2478/nsmmt-2013-0006 |
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| Abstract | Wavefunctions of symmetrical nanoparticles are considered
making use of induced representation method. It is shown
that when, at the same total symmetry, the order of local symmetry
group decreases, additional quantum numbers are required
for complete labelling of electron states. It is shown
that the labels of irreducible representations of intermediate
subgroups can be used for complete classification of states
in the case of repeating IRs in symmetry adapted linear combinations.
The intermediate symmetry approach is extended
to singlet and triplet two-electron states making use of Mackey
theorem on symmetrized squares of induced representations. |
|---|---|
| AbstractList | Wavefunctions of symmetrical nanoparticles are considered
making use of induced representation method. It is shown
that when, at the same total symmetry, the order of local symmetry
group decreases, additional quantum numbers are required
for complete labelling of electron states. It is shown
that the labels of irreducible representations of intermediate
subgroups can be used for complete classification of states
in the case of repeating IRs in symmetry adapted linear combinations.
The intermediate symmetry approach is extended
to singlet and triplet two-electron states making use of Mackey
theorem on symmetrized squares of induced representations. |
| Author | Yarzhemsky, V.G. |
| Author_xml | – sequence: 1 givenname: V.G. surname: Yarzhemsky fullname: Yarzhemsky, V.G. organization: Moscow Institute of Physics and Technology, , Institutskii per.,141700, Dolgoprudny, Moscow Region, Russia |
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| Cites_doi | 10.1080/00268978700101911 100506 10.1134/S0020168510090025 10.1002/jcc.21259 10.1088/0305-4470/16/11/011 10.1063/1.526140 10.1063/1.1665292 |
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| References | Mackey (ref161) 1953 Smirnov (ref111) 1981; 22 Bradley (ref171) 1970; 11 (ref191) 2012 Evarestov (ref141) 2009; 30 Cloizeaux (ref131) 1963 Yarzhemsky (ref181) 1997; 22 Macek (ref281) 1961 Kartunen (ref61) 2008 Newman (ref231) 1983; 16 Yarzhemsky (ref291) 2010 Lord (ref01) 2012 Chisholm (ref21) 1976 Newman (ref251) 1987 Ballhausen (ref31) 1962 Yarzhemsky (ref121) 1984 Bernadotte (ref311) 2013 Klein (ref101) 1984; 25 Kustov (ref41) 2008 Yarzhemsky (ref301) 2013 Micklitz (ref221) 2009 Evarestov (ref151) 2007 Racah (ref91) 1965; 28 Landau (ref271) 1991 Altman (ref241) 1977 Yarzhemsky (ref71) 2011 Cracknell (ref261) 1968 Cotton (ref11) 1990 Yarzhemsky (ref211) 1998 Curtis (ref51) 1962 Yarzhemskii (ref81) 2009 |
| References_xml | – start-page: 129 year: 1963 ident: ref131 article-title: des Orthogonal orbitals generalized functions publication-title: Phys Rev – start-page: 53 year: 2012 ident: ref191 article-title: Yarzhemsky Nodal quantum numbers for two - electron states in solids Few - Body publication-title: Systems – year: 2007 ident: ref151 article-title: Quantum Chemistry of Solids Springer Verlag – start-page: 465 year: 2008 ident: ref61 article-title: Au a predicted chiral and spherically aromatic golden fullerene publication-title: Chem – start-page: 1443 year: 1987 ident: ref251 article-title: Intermediate symmetry superposition model induced representations publication-title: Molecular Physics doi: 10.1080/00268978700101911 – year: 2009 ident: ref221 article-title: Odd parity and line nodes in nonsymmorphic superconductors publication-title: Phys Rev doi: 100506 – volume: 22 start-page: 27 year: 1997 ident: ref181 article-title: theorem and two - electron wave function of a multi - centre system Few - Body publication-title: Systems – start-page: 924 year: 2010 ident: ref291 article-title: Modeling of interaction between gold nanoparticles and thiols publication-title: Inorganic Materials doi: 10.1134/S0020168510090025 – volume: 28 start-page: 37 year: 1965 ident: ref91 article-title: Group Theory in publication-title: Spectroscopy Springer Tracts Modern Physics – volume: 30 start-page: 2645 year: 2009 ident: ref141 article-title: All LCAO calculations of the LiF crystal phonon spectrum : influence of the basis set the exchange correlation functional and supercell size publication-title: electron Comput Chem doi: 10.1002/jcc.21259 – volume: 16 start-page: 2375 year: 1983 ident: ref231 article-title: Symmetry properties of direct sum systems A publication-title: Phys Math Gen doi: 10.1088/0305-4470/16/11/011 – volume: 22 start-page: 107 year: 1981 ident: ref111 article-title: of Leningrad State University in publication-title: Bulletin – year: 1976 ident: ref21 article-title: Group theoretical techniques in quantum chemistry Academic – start-page: 691 year: 1991 ident: ref271 article-title: Non Theory ed Pergamon publication-title: Quantum Mechanics – volume: 25 start-page: 200 year: 1984 ident: ref101 article-title: induction of group representations publication-title: Math Phys doi: 10.1063/1.526140 – start-page: 117 year: 2013 ident: ref311 article-title: in The of publication-title: Molecules Journal Physical Chemistry – year: 1990 ident: ref11 article-title: Chemical application of group theory – volume: 11 start-page: 1536 year: 1970 ident: ref171 article-title: Kronecker products and symmetrized squares of irreducible representations of space groups publication-title: Math Phys doi: 10.1063/1.1665292 – start-page: 1273 year: 2009 ident: ref81 article-title: ev Orbits and induced representations in the quantum chemistry of nanostructures publication-title: Inorganic Chemistry – year: 1977 ident: ref241 article-title: Induced for Crystals New Academic publication-title: Representations Molecules – start-page: 288 year: 1961 ident: ref281 article-title: Bonding in icosahedral complexes publication-title: Chem Phys – start-page: 53 year: 2008 ident: ref41 article-title: compositions structure classification publication-title: Russian Journal of Inorganic Chemistry – year: 1962 ident: ref51 article-title: theory of finite groups and associative algebras Mathematical publication-title: Representation American Soc – start-page: 417 year: 1968 ident: ref261 article-title: group theory Pergamon publication-title: Applied – start-page: 2147 year: 2011 ident: ref71 article-title: The structure of gold nanoparticles and Au based thiol self - organized monolayers publication-title: Inorganic Chemistry – start-page: 278 year: 1984 ident: ref121 article-title: ev Induced representation method in the theory of molecular orbitals of in publication-title: Academy Sciences – year: 2012 ident: ref01 article-title: New geometries for new materials University – start-page: 1075 year: 2013 ident: ref301 article-title: ev Electronic structure of gold nanoparticles publication-title: Inorganic Materials – start-page: 209 year: 1998 ident: ref211 article-title: Space - group approach to the nodal structure of superconducting order parameter in publication-title: Physica Status Solidi – start-page: 387 year: 1953 ident: ref161 article-title: Symmetric and antisymmetric Kronecker squares and intertwinning numbers of induced representations of finite groups publication-title: Math – year: 1962 ident: ref31 article-title: Introduction to ligand field theory |
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| Snippet | Wavefunctions of symmetrical nanoparticles are considered
making use of induced representation method. It is shown
that when, at the same total symmetry, the... |
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| StartPage | 96 |
| SubjectTerms | 02.20.Bd 05C 20C 61.46-w 71.10-m 81C electron structure group theory Mackey theorem nanoparticles quantum numbers |
| Title | Internal Symmetries and Additional Quantum Numbers for Nanoparticles |
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