.. _conversion: Orbital construction and conversion =================================== The first step for a DMFT calculation is to provide the necessary input based on a DFT calculation. We will not review how to do the DFT calculation here in this documentation, but refer the user to the documentation and tutorials that come with the actual DFT package. Here, we will describe how to use output created by Wien2k, as well as how to use the light-weight general interface. Interface with Wien2k --------------------- We assume that the user has obtained a self-consistent solution of the Kohn-Sham equations. We further have to require that the user is familiar with the main in/output files of Wien2k, and how to run the DFT code. Conversion for the DMFT self-consistency cycle """""""""""""""""""""""""""""""""""""""""""""" First, we have to write the necessary quantities into a file that can be processed further by invoking in a shell the command `x lapw2 -almd` We note that any other flag for lapw2, such as -c or -so (for spin-orbit coupling) has to be added also to this line. This creates some files that we need for the Wannier orbital construction. The orbital construction itself is done by the Fortran program :program:`dmftproj`. For an extensive manual to this program see :download:`TutorialDmftproj.pdf `. Here we will only describe only the basic steps. Let us take the example of SrVO3, a commonly used example for DFT+DMFT calculations. The input file for :program:`dmftproj` looks like .. literalinclude:: images_scripts/SrVO3.indmftpr The first three lines give the number of inequivalent sites, their multiplicity (to be in accordance with the Wien2k *struct* file) and the maximum orbital quantum number :math:`l_{max}`. In our case our struct file contains the atoms in the order Sr, V, O. Next we have to specify for each of the inequivalent sites, whether we want to treat their orbitals as correlated or not. This information is given by the following 3 to 5 lines: #. We specify which basis set is used (complex or cubic harmonics). #. The four numbers refer to *s*, *p*, *d*, and *f* electrons, resp. Putting 0 means doing nothing, putting 1 will calculate **unnormalised** projectors in compliance with the Wien2k definition. The important flag is 2, this means to include these electrons as correlated electrons, and calculate normalised Wannier functions for them. In the example above, you see that only for the vanadium *d* we set the flag to 2. If you want to do simply a DMFT calculation, then set everything to 0, except one flag 2 for the correlated electrons. #. In case you have a irrep splitting of the correlated shell, you can specify here how many irreps you have. You see that we put 2, since eg and t2g symmetries are irreps in this cubic case. If you don't want to use this splitting, just put 0. #. (optional) If you specifies a number different from 0 in above line, you have to tell now, which of the irreps you want to be treated correlated. We want to t2g, and not the eg, so we set 0 for eg and 1 for t2g. Note that the example above is what you need in 99% of the cases when you want to treat only t2g electrons. For eg's only (e.g. nickelates), you set 10 and 01 in this line. #. (optional) If you have specified a correlated shell for this atom, you have to tell if spin-orbit coupling should be taken into account. 0 means no, 1 is yes. These lines have to be repeated for each inequivalent atom. The last line gives the energy window, relative to the Fermi energy, that is used for the projective Wannier functions. Note that, in accordance with Wien2k, we give energies in Rydberg units! After setting up this input file, you run: `dmftproj` Again, adding possible flags like -so for spin-orbit coupling. This program produces the following files (in the following, take *case* as the standard Wien2k place holder, to be replaced by the actual working directory name): * :file:`case.ctqmcout` and :file:`case.symqmc` containing projector operators and symmetry operations for orthonormalized Wannier orbitals, respectively. * :file:`case.parproj` and :file:`case.sympar` containing projector operators and symmetry operations for uncorrelated states, respectively. These files are needed for projected density-of-states or spectral-function calculations in post-processing only. * :file:`case.oubwin` needed for the charge desity recalculation in the case of fully self-consistent DFT+DMFT run (see below). Now we convert these files into an hdf5 file that can be used for the DMFT calculations. For this purpose we use the python module :class:`Wien2kConverter `. It is initialised as:: from pytriqs.applications.dft.converters.wien2k_converter import * Converter = Wien2kConverter(filename = case) The only necessary parameter to this construction is the parameter `filename`. It has to be the root of the files produces by dmftproj. For our example, the :program:`Wien2k` naming convention is that all files are called the same, for instance :file:`SrVO3.*`, so you would give `filename = "SrVO3"`. The constructor opens an hdf5 archive, named :file:`case.h5`, where all the data is stored. For other parameters of the constructor please visit the :ref:`refconverters` section of the reference manual. After initialising the interface module, we can now convert the input text files to the hdf5 archive by:: Converter.convert_dft_input() This reads all the data, and stores it in the file :file:`case.h5`. In this step, the files :file:`case.ctqmcout` and :file:`case.symqmc` have to be present in the working directory. After this step, all the necessary information for the DMFT loop is stored in the hdf5 archive, where the string variable `Converter.hdf_filename` gives the file name of the archive. At this point you should use the method :meth:`dos_wannier_basis ` contained in the module :class:`SumkDFTTools ` to check the density of states of the Wannier orbitals (see :ref:`analysis`). You have now everything for performing a DMFT calculation, and you can proceed with :ref:`singleshot`. Data for post-processing """""""""""""""""""""""" In case you want to do post-processing of your data using the module :class:`SumkDFTTools `, some more files have to be converted to the hdf5 archive. For instance, for calculating the partial density of states or partial charges consistent with the definition of :program:`Wien2k`, you have to invoke:: Converter.convert_parproj_input() This reads and converts the files :file:`case.parproj` and :file:`case.sympar`. If you want to plot band structures, one has to do the following. First, one has to do the Wien2k calculation on the given :math:`\mathbf{k}`-path, and run :program:`dmftproj` on that path: | `x lapw1 -band` | `x lapw2 -band -almd` | `dmftproj -band` Again, maybe with the optional additional extra flags according to Wien2k. Now we use a routine of the converter module allows to read and convert the input for :class:`SumkDFTTools `:: Converter.convert_bands_input() After having converted this input, you can further proceed with the :ref:`analysis`. For more options on the converter module, please have a look at the :ref:`refconverters` section of the reference manual. Data for transport calculations """"""""""""""""""""""""""""""" For the transport calculations, the situation is a bit more involved, since we need also the :program:`optics` package of Wien2k. Please look at the section on :ref:`Transport` to see how to do the necessary steps, including the conversion. A general H(k) -------------- In addition to the more complicated Wien2k converter, :program:`dft_tools` contains also a light converter. It takes only one inputfile, and creates the necessary hdf outputfile for the DMFT calculation. The header of this input file has to have the following format: .. literalinclude:: images_scripts/case.hk The lines of this header define #. Number of :math:`\mathbf{k}`-points used in the calculation #. Electron density for setting the chemical potential #. Number of correlated atoms in the unit cell #. The next line contains four numbers: index of the atom, index of the correlated shell, :math:`l` quantum number, dimension of this shell. Repeat this line for each correlated atom. #. The last line contains several numbers: the number of irreducible representations, and then the dimensions of the irreps. One possibility is as the example above, another one would be 2 2 3. Thiw would mean, 2 irreps (eg and t2g), of dimension 2 and 3, resp. After these header lines, the file has to contain the Hamiltonian matrix in orbital space. The standard convention is that you give for each :math:`\mathbf{k}`-point first the matrix of the real part, then the matrix of the imaginary part, and then move on to the next :math:`\mathbf{k}`-point. The converter itself is used as:: from pytriqs.applications.dft.converters.hk_converter import * Converter = HkConverter(filename = hkinputfile) Converter.convert_dft_input() where :file:`hkinputfile` is the name of the input file described above. This produces the hdf file that you need, and you cna proceed with the For more options of this converter, have a look at the :ref:`refconverters` section of the reference manual. Wannier90 Converter ------------------- Using this converter it is possible to convert the output of :program:`Wannier90` (http://wannier.org) calculations of Maximally Localized Wannier Functions (MLWF) and create a HDF5 archive suitable for one-shot DMFT calculations with the :class:`SumkDFT ` class. The user must supply two files in order to run the Wannier90 Converter: #. The file :file:`seedname_hr.dat`, which contains the DFT Hamiltonian in the MLWF basis calculated through :program:`wannier90` with ``hr_plot = true`` (please refer to the :program:`wannier90` documentation). #. A file named :file:`seedname.inp`, which contains the required information about the :math:`\mathbf{k}`-point mesh, the electron density, the correlated shell structure, ... (see below). Here and in the following, the keyword ``seedname`` should always be intended as a placeholder for the actual prefix chosen by the user when creating the input for :program:`wannier90`. Once these two files are available, one can use the converter as follows:: from pytriqs.applications.dft.converters import Wannier90Converter Converter = Wannier90Converter(seedname='seedname') Converter.convert_dft_input() The converter input :file:`seedname.inp` is a simple text file with the following format: .. literalinclude:: images_scripts/LaVO3_w90.inp The example shows the input for the perovskite crystal of LaVO\ :sub:`3` in the room-temperature `Pnma` symmetry. The unit cell contains four symmetry-equivalent correlated sites (the V atoms) and the total number of electrons per unit cell is 8 (see second line). The first line specifies how to generate the :math:`\mathbf{k}`-point mesh that will be used to obtain :math:`H(\mathbf{k})` by Fourier transforming :math:`H(\mathbf{R})`. Currently implemented options are: * :math:`\Gamma`-centered uniform grid with dimensions :math:`n_{k_x} \times n_{k_y} \times n_{k_z}`; specify ``0`` followed by the three grid dimensions, like in the example above * :math:`\Gamma`-centered uniform grid with dimensions automatically determined by the converter (from the number of :math:`\mathbf{R}` vectors found in :file:`seedname_hr.dat`); just specify ``-1`` Inside :file:`seedname.inp`, it is crucial to correctly specify the correlated shell structure, which depends on the contents of the :program:`wannier90` output :file:`seedname_hr.dat` and on the order of the MLWFs contained in it. The number of MLWFs must be equal to, or greater than the total number of correlated orbitals (i.e., the sum of all ``dim`` in :file:`seedname.inp`). If the converter finds fewer MLWFs inside :file:`seedname_hr.dat`, then it stops with an error; if it finds more MLWFs, then it assumes that the additional MLWFs correspond to uncorrelated orbitals (e.g., the O-\ `2p` shells). When reading the hoppings :math:`\langle w_i | H(\mathbf{R}) | w_j \rangle` (where :math:`w_i` is the :math:`i`-th MLWF), the converter also assumes that the first indices correspond to the correlated shells (in our example, the V-t\ :sub:`2g` shells). Therefore, the MLWFs corresponding to the uncorrelated shells (if present) must be listed **after** those of the correlated shells. With the :program:`wannier90` code, this can be achieved this by listing the projections for the uncorrelated shells after those for the correlated shells. In our `Pnma`-LaVO\ :sub:`3` example, for instance, we could use:: Begin Projections V:l=2,mr=2,3,5:z=0,0,1:x=-1,1,0 O:l=1:mr=1,2,3:z=0,0,1:x=-1,1,0 End Projections where the ``x=-1,1,0`` option indicates that the V--O bonds in the octahedra are rotated by (approximatively) 45 degrees with respect to the axes of the `Pbnm` cell. The converter will analyse the matrix elements of the local hamiltonian to find the symmetry matrices `rot_mat` needed for the global-to-local transformation of the basis set for correlated orbitals (see section :ref:`hdfstructure`). The matrices are obtained by finding the unitary transformations that diagonalize :math:`\langle w_i | H_I(\mathbf{R}=0,0,0) | w_j \rangle`, where :math:`I` runs over the correlated shells and `i,j` belong to the same shell (more details elsewhere...). If two correlated shells are defined as equivalent in :file:`seedname.inp`, then the corresponding eigenvalues have to match within a threshold of 10\ :sup:`-5`, otherwise the converter will produce an error/warning. If this happens, please carefully check your data in :file:`seedname_hr.dat`. This method might fail in non-trivial cases (i.e., more than one correlated shell is present) when there are some degenerate eigenvalues: so far tests have not shown any issue, but one must be careful in those cases (the converter will print a warning message). The current implementation of the Wannier90 Converter has some limitations: * Since :program:`wannier90` does not make use of symmetries (symmetry-reduction of the :math:`\mathbf{k}`-point grid is not possible), the converter always sets ``symm_op=0`` (see the :ref:`hdfstructure` section). * No charge self-consistency possible at the moment. * Calculations with spin-orbit (``SO=1``) are not supported. * The spin-polarized case (``SP=1``) is not yet tested. * The post-processing routines in the module :class:`SumkDFTTools ` were not tested with this converter. * ``proj_mat_all`` are not used, so there are no projectors onto the uncorrelated orbitals for now. MPI issues ---------- The interface packages are written such that all the file operations are done only on the master node. In general, the philosophy of the package is that whenever you read in something from the archive yourself, you have to *manually* broadcast it to the nodes. An exception to this rule is when you use routines from :class:`SumkDFT ` or :class:`SumkDFTTools `, where the broadcasting is done for you. Interfaces to other packages ---------------------------- Because of the modular structure, it is straight forward to extend the :ref:`TRIQS ` package in order to work with other band-structure codes. The only necessary requirement is that the interface module produces an hdf5 archive, that stores all the data in the specified form. For the details of what data is stored in detail, see the :ref:`hdfstructure` part of the reference manual.