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.