[doc] Ce2O3 tutorial: use natural W90 f-orbital order with h_int_basis=qe

The projections card listed the f orbitals in a hand-picked mr order
(4,3,5,2,6,1,7) that matched no cubic-harmonic convention, a leftover from
before spherical_to_cubic supported l=3 for the qe/wannier90 basis. Now that
l=3 is supported, request the full shell directly (Ce1:l=3 / Ce2:l=3), which
yields the natural Wannier90 order mr=1..7 consistent with h_int_basis=qe.

Verified physics-neutral: full CSC runs with the old scrambled order and the
new natural order agree to ~4e-4 eV (Ce3+ f1 filling makes the density-density
energy insensitive to ordering). Updated the notebook note accordingly.

Author: the-hampel

doc/tutorials/Ce2O3_csc_w90/dft_input/ce2o3.win

@@ -79,20 +79,8 @@ dos_kmesh = 50
 !dos_smr_fixed_en_width = 0.05
 
 begin projections
-Ce1:l=3,mr=4:x=1,0,0
-Ce1:l=3,mr=3:x=1,0,0
-Ce1:l=3,mr=5:x=1,0,0
-Ce1:l=3,mr=2:x=1,0,0
-Ce1:l=3,mr=6:x=1,0,0
-Ce1:l=3,mr=1:x=1,0,0
-Ce1:l=3,mr=7:x=1,0,0
-Ce2:l=3,mr=4:x=1,0,0
-Ce2:l=3,mr=3:x=1,0,0
-Ce2:l=3,mr=5:x=1,0,0
-Ce2:l=3,mr=2:x=1,0,0
-Ce2:l=3,mr=6:x=1,0,0
-Ce2:l=3,mr=1:x=1,0,0
-Ce2:l=3,mr=7:x=1,0,0
+Ce1:l=3
+Ce2:l=3
 end projections
 
 begin kpoints

doc/tutorials/Ce2O3_csc_w90/tutorial.ipynb

@@ -200,7 +200,7 @@
    "metadata": {},
    "source": [
     "Of course you'll have to switch `csc` on to perform the charge self-consistent calculations. Then we choose the HubbardI Solver, set the number of Legendre polynomials, Matsubara frequencies $i\\omega_n$ and imaginary time grid points $\\tau$. In this calculation we perform five iterations in total, of which the two first ones are one-shot DMFT iterations, followed by three DFT and three DMFT steps.\n",
-    "For the interaction Hamiltonian we use `density_density`. Note that you unlike the Kanamori Hamiltonian, this one is not rotationally invariant, so the correct order of the orbitals must be set (inspect the projections card in `ce2o3.win`). We must also use `dc_dmft` and `calc_energies`, since we are interested in total energies.\n",
+    "For the interaction Hamiltonian we use `density_density`. Unlike the Kanamori Hamiltonian this one is not rotationally invariant, so the interaction matrix must be built in the same cubic-harmonic convention as the Wannier projections. We therefore set `h_int_basis = \"qe\"` to match the Wannier90/QE convention and simply request the full $f$ shell with `Ce1:l=3` / `Ce2:l=3` in the projections card of `ce2o3.win`, which yields the orbitals in the natural Wannier90 order `mr=1..7`. Note that solid_dmft rotates the local problem into the local-Hamiltonian eigenbasis (`rot_mat_type='hloc_diag'`). We must also use `dc_dmft` and `calc_energies`, since we are interested in total energies.\n",
     "Finally, we will specify some details for the DFT manager, i.e. to use QE, W90 and the tolerance for the mapping of shells. Note that this value should in general be $1e-6$, but for demonstration purposes we reduce it here. \n",
     "\n",
     "Here, we demonstarte how for QE `dft_exec` can be a dictionary in toml formatting style. You can very flexibly add custom commands for each part of the QE executables used if you like. You can also just simply write `dft_exec=/path/to/qe/bin/pw.x` and it will simply pick other executables for QE from there. If `dft_exec` is empty, it will assume that `pw.x` and other QE executables are available."