Simple method to obtain symmetry harmonics of point groups.
We propose a simple, self-consistent method to obtain basis functions of irreducible representations of a finite point group. Our method is based on eigenproblem formulation of a projection operator represented as a nonhomogeneous polynomial of angular momentum L. The method is shown to be more efficient than the usual numerical methods when applied to the analysis of high-order symmetry harmonics in cubic and icosahedral groups. For low-order symmetry harmonics the method provides rational coefficients of expansion in the Y(L,M) basis.
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Laboratory of Physics of Nanostructures, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. dmitri.boiko@epfl.ch
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