triqs.operators.util.U_matrix.spherical_to_cubic

triqs.operators.util.U_matrix.spherical_to_cubic(l, convention='triqs')[source]

Get the spherical-to-cubic harmonics transformation matrix.

Parameters:
linteger

Angular momentum of shell being treated (l=2 for d shell, l=3 for f shell).

conventionstring, optional

The basis convention. For l=2 (d shell) the cubic orderings are:

  • ‘triqs’: (“xy”,”yz”,”z^2”,”xz”,”x^2-y^2”),

  • ‘vasp’: same as ‘triqs’,

  • ‘wien2k’: (“z^2”,”x^2-y^2”,”xy”,”yz”,”xz”),

  • ‘wannier90’: (“z^2”,”xz”,”yz”,”x^2-y^2”,”xy”),

  • ‘qe’: same as ‘wannier90’.

For l=3 (f shell) the cubic orderings are:

  • ‘triqs’: (“x(x^2-3y^2)”,”z(x^2-y^2)”,”xz^2”,”z^3”,”yz^2”,”xyz”,”y(3x^2-y^2)”),

  • ‘vasp’: (“y(3x^2-y^2)”,”xyz”,”yz^2”,”z^3”,”xz^2”,”z(x^2-y^2)”,”x(x^2-3y^2)”),

  • ‘wannier90’: (“z^3”,”xz^2”,”yz^2”,”z(x^2-y^2)”,”xyz”,”x(x^2-3y^2)”,”y(3x^2-y^2)”),

  • ‘qe’: same as ‘wannier90’,

  • ‘wien2k’: not supported for l=3 (dmftproj uses site-symmetry-specific transformations; see dmftproj/SRC_templates/case.cf_f_mm2).

Returns:
numpy.ndarray

The spherical-to-cubic harmonics transformation matrix.