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103 lines
6.7 KiB
ReStructuredText
103 lines
6.7 KiB
ReStructuredText
.. _nio_csc:
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DFT and projections
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==================================================
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We will perform DFT+DMFT calcluations for the charge-transfer insulator NiO. We start from scratch and provide all necessary input files to do the calculations: First for doing a single-shot calculation.
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.. (and then for charge-selfconsistency).
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VASP setup
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-------------------------------
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We start by running a simple VASP calculation to converge the charge density initially.
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Use the :ref:`INCAR`, :ref:`POSCAR`, and :ref:`KPOINTS` provided and use your
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own :file:`POTCAR` file.
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Let us take a look in the :file:`INCAR`, where we have to specify local orbitals as basis
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for our many-body calculation.
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.. literalinclude:: images_scripts/INCAR
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`LORBIT = 14` takes care of optimizing the projectors in the energy window defined
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by `EMIN` and `EMAX`. We switch off all symmetries with `ISYM=-1` since symmetries
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are not implemented in the later DMFT scripts. Finally, we select the relevant orbitals
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for atom 1 (Ni, d-orbitals) and 2 (O, p-orbitals) by the two `LOCPROJ` lines.
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For details refer to the VASP wiki on the `LOCPROJ <https://cms.mpi.univi
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e.ac.at/wiki/index.php/LOCPROJ>`_ flag. The projectors are stored in the file `LOCPROJ`.
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plovasp
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------------------------------
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Next, we postprocess the projectors, which VASP stored in the file `LOCPROJ`.
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We do this by invoking :program:`plovasp plo.cfg` which is configured by an input file, e.g., named :ref:`plo.cfg`.
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.. literalinclude:: images_scripts/plo.cfg
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Here, in `[General]` we set the basename and the grid for calculating the density of
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states. In `[Group 1]` we define a group of two shells which are orthonormalized with
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respect to states in an energy window from `-9` to `2` for all ions simultanously
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(`NORMION = False`). We define the two shells, which correspond to the Ni d states
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and the O p states. Only the Ni shell is treated as correlated (`CORR = True`), i.e.,
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is supplemented with a Coulomb interaction later in the DMFT calculation.
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Converting to hdf5 file
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-------------------------------
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We gather the output generated by :program:`plovasp` into a hdf5 archive which :program:`dft_tools` is able to read. We do this by running :program:`python converter.py` on the script :ref:`converter.py`:
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.. literalinclude:: images_scripts/converter.py
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Now we are all set to perform a dmft calculation.
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DMFT
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==================================================
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dmft script
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------------------------------
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Since the python script for performing the dmft loop pretty much resembles that presented in the tutorial on :ref:`SrVO3 <srvo3>`, we will not go into detail here but simply provide the script :ref:`nio.py`. Following Kunes et al. in `PRB 75 165115 (2007) <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.165115>`_ we use :math:`U=8` and :math:`J=1`. We se;ect :math:`\beta=5` instead of :math:`\beta=10` to ease the problem slightly. For simplicity we fix the double-counting potential to :math:`\mu_{DC}=59` eV by::
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DC_value = 59.0
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SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_value=DC_value)
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For sensible results run this script in parallel on at least 20 cores. As a quick check of the results, we can compare the orbital occupation from the paper cited above (:math:`n_{eg} = 0.54` and :math:`n_{t2g}=1.0`) and those from the cthyb output (check lines `Orbital up_0 density:` for a t2g and `Orbital up_2 density:` for an eg orbital). They should coincide well.
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Local lattice Green's function for all projected orbitals
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---------------------------------------------------------
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We calculate the local lattice Green's function - now also for the uncorrelated orbitals, i.e., the O p states, for what we use the script :ref:`NiO_local_lattice_GF.py`. The result is saved in the h5 file as `G_latt_orb_it<n_it>`, where `<n_it>` is the number of the last DMFT iteration.
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Spectral function on real axis: MaxEnt
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--------------------------------------
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To compare to results from literature we make use of the `maxent triqs application <https://triqs.github.io/maxent/master/>`_ and calculate the spectral function on real axis. Use this script to perform a crude but quick calculation: :ref:`maxent.py` using a linear real axis and a line-fit analyzer to determine the optimal :math:`\alpha`. The output is saved in the h5 file in `DMFT_results/Iterations/G_latt_orb_w_o<n_o>_it<n_it>`, where `<n_o>` is the number of the orbital and `n_it` is again the number of the last iteration. The real axis information is stored in `DMFT_results/Iterations/w_it<n_it>`.
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.. image:: images_scripts/nio_Aw.png
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:width: 400
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:align: center
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Charge self-consistent DMFT
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==================================================
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In this part we will perform charge self-consistent DMFT calculations. To do so we have to adapt the VASP `INCAR` such that :program:`VASP` reads the updated charge density after each step. We add the lines::
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ICHARG = 5
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NELM = 1000
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NELMIN = 1000
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IMIX=0
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which makes VASP wait after each step of its iterative diagonalization until the file vasp.lock is created. It then reads the update of the charge density in the file `GAMMA`. It is terminated by an external script after a desired amount of steps, such that we deactivate all automatic stoping criterion by setting the number of steps to a very high number.
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We take the respective converged DFT and DMFT calculations from before as a starting point. I.e., we copy the `CHGCAR` and `nio.h5` together with the other :program:`VASP` input files and :file:`plo.cfg` in a new directory. We use a script called :program:`vasp_dmft` to invoke :program:`VASP` in the background and start the DMFT calculation together with :program:`plovasp` and the converter. This script assumes that the dmft sript contains a function `dmft_cycle()` and also the conversion from text files to the h5 file. Additionally we have to add a few lines to calculate the density correction and calculate the correlation energy. We adapt the script straightforardly (for a working example see :ref:`nio_csc.py`). The most important new lines are::
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SK.chemical_potential = SK.calc_mu( precision = 0.000001 )
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SK.calc_density_correction(dm_type='vasp')
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correnerg = 0.5 * (S.G_iw * S.Sigma_iw).total_density()
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where the chemical potential is determined to a greater precision than before, the correction to the dft density matrix is calculated and output to the file :file:`GAMMA`. The correlation energy is calculated via Migdal-Galitzki formula. We also slightly increase the tolerance for the detection of blocks since the DFT calculation now includes some QMC noise.
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To help convergence, we keep the density (i.e., the GAMMA file) fixed for a few DFT iterations. We do so since VASP uses an iterative diagonalization.
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We can start the whole machinery by excecuting::
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vasp_dmft -n <n_procs> -i <n_iters> -j <n_iters_dft> -p <vasp_exec> nio_csc.py
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