Graph theoretical concepts for the unitary group approach to the many-electron correlation problem

Autor: Isaiah Shavitt
Rok vydání: 2009
Předmět:
Zdroj: International Journal of Quantum Chemistry. 12:131-148
ISSN: 1097-461X
0020-7608
DOI: 10.1002/qua.560120819
Popis: The simplified unitary group formalism for electronic states introduced by Paldus was recast in a form based on a relatively small table of ''distinct rows'' of the array (or tableau) representatives of the appropriate canonical basis functions. This table can be represented effectively and compactly in the form of a two-rooted directed graph. Each member (configuration function) of the canonical basis is represented by a walk connecting the head and tail of the graph, and its canonical index (sequence number) can be determined easily and directly from information contained in the distinct row table or the graph. The calculation of the matrix representation of a quantum mechanical operator in the canonical basis can be organized in terms of various subgraphs of the distinct row graph, and in terms of certain ''loops'' contained in them. A relatively small number of basic subgraphs can be used to generate most of the information needed in the calculation. Certain problems associated with matrix elements of products of generators of the unitary group remain to be solved before an effective formalism for large-scale electronic structure calculations is obtained, but it is hoped that the concepts introduced here can provide insight which will be helpful inmore » solving these problems.« less
Databáze: OpenAIRE
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