clebsch_gordan_coupling

Clebsch-Gordan coupling functions.

clebsch_gordan_coupling(clebsch_gordan_coefficients, ldict, L_R=0, use_permutations=True)[source]

Compute generalized Clebsch-Gordan coefficients for a given L_R.

These are all defined according to the pairwise coupling scheme in Goff et al. 2024.

The approach to construct generalized Clebsch-Gordan coefficients is manually defined for each rank for pedagogical and clarity purposes.

Parameters:

  • clebsch_gordan_coefficients (dict) – Precomputed Clebsch-Gordan coefficients.

  • ldict (dict) – Dictionary of ranks and their corresponding l values.

  • L_R (int) – Resultant angular momentum quantum number. This determines the equivariant character of the rank N descriptor after reduction. L_R=0 corresponds to a rotationally invariant feature, L_R=1 corresponds to a feature that transforms like a vector, L_R=2 a tensor, etc.

  • use_permutations (bool) – Flag to consider permutations of l in generation of coupling coefficients.

Returns:

coupling – Generalized Clebsch-Gordan coefficients, {M_R:{rank:{l:{m:coupling_coefficient}}}

Return type:

dict