Finite group theory for large systems. 3. Symmetry-generation of reduced matrix elements for icosahedral C(20) and C(60) molecules.
This paper uses symmetry-generation to simplify the determination of Hamiltonian reduced matrix elements. It is part of a series on using computers to apply finite group theory to quantum mechanical calculations on large systems. Symmetry-generation is an expression of the whole molecule as a sum of symmetry transformations on a smaller reference structure. Then on a suitably-conditioned symmetry-adapted basis, the reduced matrix elements of the Hamiltonian are averages of certain elements of the simpler reference structure matrix. The smaller the reference structure, the greater is the computational savings. Single atom reference structures are used here for the Hückel treatment of icosahedral C(20) and C(60) fullerenes. The analytical power of this approach is illustrated by determining the two bond lengths of C(60) from spectral data.
Ellzey
M L
ML
Department of Chemistry, The University of Texas at El Paso, El Paso, Texas 79968-0513, USA. lellzey@utep.edu