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We outline a numerical procedure to incorporate the crystal symmetries in theHelmholtz Fermi-surface harmonics basis set, which are the solutions of theHelmholtz equation defined on the Fermi surface. This improvement allows for anoptimal representation of anisotropic quantities defined on the Fermi surfacein terms of few symmetric elements of the set. We demonstrate the generalvalidity of our approach by identifying the fully symmetric HelmholtzFermi-surface harmonics subset for several representative systems withdifferent crystal structures, namely, FCC-Cu, HEX-MgB$_2$, and BCC-YH$_6$.Furthermore, we illustrate the potential of the method applied to theelectron-phonon problem, showing that the anisotropic electron-phononmass-enhancement parameter $\lambda_{\bf k}$ can be represented to highaccuracy by a handful of coefficients. This works as an effective filter,paving the way for a reduction of several orders of magnitude in thecomputation of superconductivity, impurity problems, or any other Fermi surfacedependent property of metals from first principles.

physical review. b./physical review. b

Symmetric Helmholtz Fermi-surface harmonics for an optimal  representation of anisotropic quantities on the Fermi surface: Application to  the electron-phonon problem