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Reduced Matrix Elements for Symmetry-Constructed Systems

Marion Lawrence Ellzey, Jr ; Department of Chemistry, The University of Texas at El Paso, 500 West University, El Paso, Texas 79968, USA

Puni tekst: engleski pdf 1.408 Kb

str. 541-543

preuzimanja: 731



Eigenvalue problems involving symmetry, such as the Schrödinger equation when the Hamiltonian
commutes with a group, can generally be reduced in size using group theoretical techniques such as
the Wigner-Eckart theorem. The key step is calculation of the reduced matrix elements followed by eigenvalue
determination by the secular equation. For finite groups it is usual to obtain reduced matrices by
transformation to the symmetry adapted basis. Direct determination of reduced matrix elements by some
means would be computationally more efficient with better precision.It is shown here that this direct determination
is possible to some extent for symmetry-constructed systems such as symmetry-generated
molecules. A simple illustration is given using the Hûckel treatment of the cyclopropenyl radical (doi:

Ključne riječi

symmetry methods, Wigner-Eckart theorem, group representations

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