Then we create :file:`Ce-gamma.indmftpr` file specifying parameters for construction of Wannier orbitals representing *4f* states:
..literalinclude:: Ce-gamma.indmftpr
First three lines give the number of inequivalent sites, their multiplicity (to be in accordance with the *struct* file) and the maximum orbital quantum number :math:`l_{max}`
The following four lines describe the treatment of Ce *spdf* orbitals by the :program:`dmftproj` program ::
complex
1 1 1 2 ! l included for each sort
0 0 0 0 ! l included for each sort
0
where `complex` is the choice for the angular basis to be used (spherical complex harmonics), in the next line we specify, for each orbital
quantum number, whether it is treated as correlated ('2') and, hence, the corresponding Wannier orbitals will be generated or uncorrelated ('1').
In the latter case the :program:`dmftproj` program will generate projectors to be used in calculations of corresponding partial densities of states (see below).
In the present case we choose the fourth (i. e. *f*) orbitals as correlated.
The next line specify the number of irreducible representations into which a given correlated shell should be split (or
'0' if no splitting is desired, as in the present case). The fourth line specifies whether the spin-orbit interaction should be switched on ('1') or off ('0', as in the present case).
Finally, the last line iof the file ::
-.40 0.40 ! Energy window relative to E_f
specify the energy window for Wannier functions' construction. For a more complete description of :program:`dmftproj` options see its manual.
To prepaire input data for :program:`dmftproj` we execute :program:`lapw2` with the `-almd` option ::
Then :program:`dmftproj` is executed in its default mode (i.e. without spin-polarization or spin-orbit included) ::
dmftproj
This program produces the following files:
*:file:`Ce-gamma.ctqmcout` and :file:`Ce-gamma.symqmc` containing projector operators and symmetry operations for orthonormalized Wannier orbitals, respectively.
*:file:`Ce-gamma.parproj` and :file:`Ce-gamma.sympar` containing projector operators and symmetry operations for uncorrelated states, respectively. These files are needed for projected density-of-states or spectral-function calculations.
We load and convert the :program:`dmftproj` output and initialize the *SumkDFT* class as described in :ref:`DFTDMFTmain` and :ref:`advanced` and then set up the Hubbard-I solver ::
*`use_spin_orbit`: if set 'True' the solver is run with spin-orbit coupling included. To perform actual DFT+DMFT calculations with spin-orbit one should also run :program:`Wien2k` and :program:`dmftproj` in spin-polarized mode and with spin-orbit included. By default, `use_spin_orbit=False`.
*`Nmoments`: the number of moments used to describe high-ferquency tails of the Hubbard-I Green's function and self-energy. By default `Nmoments = 5`
The `Solver.solve(U_int, J_hund)` statement has two necessary parameters, the Hubbard U parameter `U_int` and Hund's rule coupling `J_hund`. Notice that the solver constructs the full 4-index `U`-matrix by default, and the `U_int` parameter is in fact the Slatter `F0` integral. Other optional parameters are:
*`T`: matrix that transforms the interaction matrix from complex spherical harmonics to a symmetry adapted basis. By default, the complex spherical harmonics basis is used and `T=None`.
*`verbosity`: tunes output from the solver. If `verbosity=0` only basic information is printed, if `verbosity=1` the ground state atomic occupancy and its energy are printed, if `verbosity=2` additional information is printed for all occupancies that were diagonalized. By default, `verbosity=0`.
*`Iteration_Number`: the iteration number of the DMFT loop. Used only for printing. By default `Iteration_Number=1`
*`Test_Convergence`: convergence criterion. Once the self-energy is converged below `Test_Convergence` the Hubbard-I solver is not called anymore. By default `Test_Convergence=0.0001`.
In the case of Ce, with the correlated shell occupancy close to 1 the Hubbard energy is close to 0, while the DC correction to energy is about J/4 in accordance with the fully-localized-limit formula, hence, giving the total correction :math:`\Delta E_{HUB}=E_{HUB}-E_{DC} \approx -J/4`, which is in our case is equal to -0.175 eV :math:`\approx`-0.013 Ry.
The band ("kinetic") energy with DMFT correction is ::
Then one needs to load projectors needed for calculations of corresponding projected densities of states, as well as corresponding symmetries. To get access to analysing tools we initialize the `SumkDFTTools` class ::
Then after the solver initialization we load the previously calculated chemical potential and double-counting correction. Having set up atomic levels we then compute the atomic Green's function and self-energy on the real axis::
In result we get the total DOS for spins `up` and `down` (identical in our paramagnetic case) in :file:`DOScorrup.dat` and :file:`DOScorrdown.dat` files, respectively, as well as projected DOSs written in the corresponding files as described in :ref:`analysis`.
In our case, for example, the files :file:`DOScorrup.dat` and :file:`DOScorrup_proj3.dat` contain the total DOS for spin *up* and the corresponding projected DOS for Ce *4f* orbital, respectively. They are plotted below.
As one may clearly see, the Ce *4f* band is split by the local Coulomb interaction into the filled lower Hubbard band and empty upper Hubbard band (the latter is additionally split into several peaks due to the Hund's rule coupling and multiplet effects).