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Symmetries of central functions with arbitrarily high angular momentum

4 Symmetries of Central Functions with Arbitrarily High Angular Momentum [Pg.140]

Spherical harmonic functions are important in many problems in Chemistry and Physics. Spherical harmonic functions are central in discussions of rotation, motion in a central potential, multipole expansion, cluster bonding, spherical wave expansions and many more topics. The calculation of symmetrized powers of representations give a way of obtaining the [Pg.140]

In view of the importance of spherical harmonics, an alternative calculator facility is provided, allowing explicit calculation up to T (60) and, indirectly, calculation to any value of J for all point groups of practical interest. The alternative method is based on the multiplication property [Pg.141]

Extension to arbitrary J follows from the fact that, for any finite point group, there is an integer K such that r(7 - - A ) — r(7) is a constant (reducible) character depending (at most) on the value of J mod K. The constant term is either the regular character of the group, or, for centrosymmetric groups, is alternately the g and u halves of the regular character. [Pg.141]

For example, in Civ, r(7) obeys a pattern that repeats every K = 3 steps, i.e. [Pg.141]




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Angular momentum

High momentum

Highly functionalized

Of momentum

Symmetry function

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