The Symmetric Group and the Method of Diatomics in Molecules: An Application to Small Lithium Clusters

A new ‘most economical’ algorithm for the construction of diatomics in molecules secular equations is described. The method does not require the basis functions to be written down explicitly, since overlap may be factored out of the equations entirely. The theory is presented in detail for the parti...

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Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1973-04, Vol.333 (1592), p.69-87
Main Author: Pickup, B. T.
Format: Article
Language:English
Subjects:
Alkali metals
Atoms
Energy
Geometry
Ground state
Lithium
Mathematical functions
Molecules
Potential energy
Symmetry
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Summary:A new ‘most economical’ algorithm for the construction of diatomics in molecules secular equations is described. The method does not require the basis functions to be written down explicitly, since overlap may be factored out of the equations entirely. The theory is presented in detail for the particular case of homogeneous alkali metal clusters. A knowledge of the irreducible representations of the symmetric group for the Jahn-Serber basis set is necessary. The irreducible representations are derived by a genealogical procedure. Some preliminary calculations are presented for the molecules Li3 through Li6, Li+3 and Li+4. The lithium clusters are found to be stable with respect to all possible dissociations, and the i.ps of Li3 and Li4 are in agreement with the trends for the species Na3, Na4, K3, K4, etc., whose i.ps have been measured experimentally.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1973.0048