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90 lines
4.5 KiB
ReStructuredText
90 lines
4.5 KiB
ReStructuredText
.. index:: full charge self consistency
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Full charge self consistency
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============================
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.. warning::
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Before using this tool, you should be familiar with the band-structure package :program:`Wien2k`, since
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the calculation is controlled by the :program:`Wien2k` scripts! See also the :download:`dmftproj tutorial<TutorialDmftproj.pdf>`.
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In order to do charge self-consistent calculations, we have to tell the band structure program about the
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changes in the charge density due to correlation effects. In the following, we discuss how to use the
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:program:`TRIQS` tools in combination with the :program:`Wien2k` program, although an extension to other
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codes is also possible.
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We can use the DMFT script as introduced in sections :ref:`LDADMFTmain` and :ref:`advanced`, with a few simple
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modifications. First, in order to be compatible with the :program:`Wien2k` standards, the DMFT script has to be
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named ``case.py``, where `case` is the name of the :program:`Wien2k` calculation, see the section
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:ref:`interfacetowien` for details. Then we set the variable
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`lda_filename` dynamically::
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import os
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lda_filename = os.getcwd().rpartition('/')[2]
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This sets the `lda_filename` to the name of the current directory. The reminder of the scripts is completely the
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same as in one-shot calculations. Only at the very end we have to calculate the modified charge density,
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and store it in a format such that :program:`Wien2k` can read it. Therefore, after the DMFT loop that we saw in the
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previous section, we symmetrise the self energy, and recalculate the impurity Green function::
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SK.symm_deg_gf(S.Sigma,orb=0)
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S.G <<= inverse(S.G0) - S.Sigma
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S.G.invert()
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These steps are not necessary, but can help to reduce fluctuation of the total energy.
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Now we calculate the modified charge density::
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# find exact chemical potential
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SK.put_Sigma(Sigma_imp = [ S.Sigma ])
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chemical_potential = SK.find_mu( precision = 0.000001 )
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dN,d = SK.calc_density_correction(filename = lda_filename+'.qdmft')
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SK.save()
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First we find the chemical potential with high precision, and after that the routine
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``SK.calc_density_correction(filename)`` calculates the density matrix including correlation effects. The result
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is stored in the file `Filename`, which is later read by the :program:`Wien2k` program. The last statement saves
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the chemical potential into the hdf5 archive.
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We need also the correlation energy, which we evaluate by the Migdal formula::
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correnerg = 0.5 * (S.G * S.Sigma).total_density()
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From this value, we have to substract the double counting energy::
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correnerg -= SK.dc_energ[0]
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and save this value into the file::
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if (mpi.is_master_node()):
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f=open(lda_filename+'.qdmft','a')
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f.write("%.16f\n"%correnerg)
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f.close()
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The above steps are valid for a calculation with only one correlated atom in the unit cell, the most likely case
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where you will apply this method. That is the reason why we give the index `0` in the list `SK.dc_energ`.
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If you have more than one correlated atom in the unit cell, but all of them
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are equivalent atoms, you have to multiply the `correnerg` by their multiplicity, before writing it to the file.
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The multiplicity is easily found in the main input file of the :program:`Wien2k` package, i.e. `case.struct`. In case of
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non-equivalent atoms, the correlation energy has to be calculated for all of them separately (FOR EXPERTS ONLY).
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As mentioned above, the calculation is controlled by the :program:`Wien2k` scripts and not by :program:`python`
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routines. Therefore, you start your calculation for instance by::
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me@home $ run -qdmft -i 10
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The flag `-qdmft` tells the script, that the density matrix including correlation effects is read from the `case.qdmft`
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file, and 10 self-consitency iterations are done. If you run the code on a parallel machine, you can specify the number of
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nodes that are used::
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me@home $ run -qdmft -np 64 -i 10
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with the `-np` flag. In that case, you have to give the proper `MPI` execution statement, e.g. `mpiexec`, in the `run_lapw` script,
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see the corresponding :program:`Wien2k` documentation. In many cases it is advisable to start from a converged one-shot
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calculation.
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For practical purposes, you keep the number of DMFT loops within one DFT cycle low, or even to `loops=1`. If you encouter
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unstable convergence, you have to adjust the parameters such as
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`loops`, `mix`, or `Delta_mix` to improve the convergence.
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In the next section, :ref:`LDADMFTtutorial`, we will see in a detailed
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example, how such a self consistent calculation is performed.
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