COMPUTATIONAL TOOL. Fig. 4.1 Opening screen of w2web

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1 CHAPTER -4

2 COMPUTATIONAL TOOL Ph.D. Thesis: J. Maibam CHAPTER: The WIEN2k code In this work, all the calculations presented are performed using the WIEN2k software package (Blaha et al., 2001). The WIEN2k code is based on full potential (L)APW+lo method. Fig. 4.1 Opening screen of w2web This program contains several sub-programs, which are described briefly in the following parts. They can be broadly divided into two major parts in the program: the initialization, and the main self-consistent field (SCF) cycle. Many analytical tools like band Chapter 4: Computational tool 36

3 structure, density of states, charge densities, volume optimization, optical properties etc are implemented. Fig. 4.2 shows the flow chart of the code. The initialization is done after creating a new session and a new case directory in the w2web using www-browser by specifying the correct portnumber e.g. firefox where w2web runs:7890 A screen as in fig 4.1 is seen while starting up of w2web. The user interface w2web uses sessions to distinguish between different working environments and to quickly change between different calculations. The new file created will be placed in the home directory if no working directory was designated to this session previously (or if the directory does not exist anymore). A new case-directory can be created by using Session Mgmt. in the change directory. Chapter 4: Computational tool 37

4 LSTART Atomic calculation H E n1 n1 n1 DSTART Superposition of atomic densities n LAPW0 2 VC 8 n V XC (n) V = V C + V XC V MT E k V LAPW1 2 V k Ek k k LCORE Atomic calculation H E n1 n1 n1 E core n core n LAPW2 * val k k EkEF V val MIXER n old n new = n old (n val +n core ) n new STOP YES CONVERGED NO Fig. 4.2 Flow chart of SCF cycle in WIEN2k computer code Chapter 4: Computational tool 38

5 Fig. 4.3 Main window of w2web It also allows selecting an existing. For this example we create a new directory lapw and than NiC using the Create button. After the directory has been created, select current directory should be clicked to assign this newly created directory to the current session. The main window of w2web appears after clicking on Click to restart session (fig. 4.3). A master input file case.strut is created with the help of the struct-file generator using Execution StructGen (see Fig. 4.4). For a new case w2web creates an empty structure template in which we can specify structural data. Later on this information is used to generate the case.struct file. As a first step specify the number of atoms (2 for NiC) and fill in the data given below into the corresponding fields (white boxes). Chapter 4: Computational tool 39

6 Table 4.1 Input parameters For NiC Title NiC Lattice F (for face centered) a Bohr b Bohr c Bohr α, β, γ 90 Atom Ni, enter position (0,0,0) Atom C enter position (0.5, 0.5, 0.5) When the Save Structure and set automatically RMT and continue editing is clicked, Z is updated automatically. This computes the nearest neighbor distances using the program nn and setrmt_lapw determines the optimal RMT values (muffin-tin radius, atomic sphere radius). It essential to keep the RMTs constant within a series of calculations the choice either to do just one single calculation with fixed structural parameters, or whether a relaxation of internal parameters (using forces and min lapw) or a volume optimization (which would required reduced RMT values must be decided at this time. It is better to choose a reduction of 3 % so that the lattice parameter can be optimize later on. Chapter 4: Computational tool 40

7 Fig. 4.4 StructGen window The StructGen file is saved and clean up after the structure generation is completed. This will generate the file NiC.struct, which is the master input file for all subsequent programs. This step also automatically generates the input file for the free atom program lstart (atomic configurations) NiC.inst. Chapter 4: Computational tool 41

8 4.2 Initialization of the calculation (init_lapw) After the two basic input files have been created, initialization of the calculation is done by Execution initialize calc. It also provides instructions to be followed. The main window for initialization calculation is shown in fig 4.5. Some of the steps are briefly described below: x nn: calculates the nearest neighbors up to a specified distance and thus helps to determine the atomic sphere radii. view case.outputnn: check for overlapping spheres, coordination numbers and nearest neighbor distances. Using these distances and co-ordinations, you can check whether you put the proper positions in the struct-file can be checked whether any mistakes were made. nn also checks whether the equivalent atoms are really crystallographically equivalent and eventually writes a new struct-file which may or may not be accepted. s group: calculates the point and space groups for the given structure. view case.outputsgroup: allows either to accept the case.struct file generated by sgroup or keep the original file (default). x symmetry: the space group symmetry operations is generated from a raw case.struct file. It determines the point group of the individual atomic sites, generates the LM expansion for the lattice harmonics (in case.in2 st) and local rotation matrices (in case.struct st) view case.outputs: it is used to check the symmetry operations and the point group symmetry of the atoms (to compare them with the International Tables for X-Ray Crystallography ). If the output does not match your expectations from the Tables, an error is made in specifying the positions. The case.struct file will be updated with symmetry operations, positive or negative atomic counter and the local rotation matrix. x lstart: generates atomic densities and determines how the orbitals are treated in the band structure calculations (i.e. as core or band states, with or without local orbitals,... ). edit NiC.outputst: lstart generates cade.in0_st, in1_st, in2_st, inc_st and inm. The output must be check (for a proper atomic configuration, lstart convergeence, confinement of the core electrons to the atomic sphere). Warnings for the radial mesh can usually be neglected since it affects only the atomic total energy. All generated inputs must be copied (from case.in_ st to case.in*). Chapter 4: Computational tool 42

9 x kgen generates a k-mesh in the Brillouin zone (BZ). The number of k-points in the whole BZ must be specified (use 1000 for comparison with the provided output, a good calculations needs many more). view NiC.klist : the number of k-points in the irreducible wedge of the BZ (IBZ and the energy interval specified for the first k-point) must be checked. x dstart generates a starting density for the SCF cycle by superposition of atomic densities generated in lstart. view NiC.outputd (check if gmax >gmin) Initialization of a calculation (running init lapw) will create all inputs for the subsequent SCF calculation choosing some default options and values. Fig. 4.5 Initialization window The SCF calculation Some parameters must be set to perform SCF cycle. The setting of these parameters must be done on w2web as shown in fig 4.6 or through command line. The SCF cycle consists of the following steps: Chapter 4: Computational tool 43

10 LAPW0 (POTENTIAL) Construction of the effective potential from density LAPW1 (BANDS) calculates valence bands (eigenvalues and eigenvectors) by solving the Kohn-Sham equations of valence electrons LAPW2 (RHO) computes valence densities from eigenvectors (construction of the new electron density) LCORE the treatment of the core electrons MIXER mixes input and output densities LAPW0 (POTENTIAL): The Poisson equation is solved and the total potential is computed as the sum of the Coulomb and the exchange-correlation potential in the LAPW0 program. The electron (spin) density is used as input and the spherical (l=0) and the non-spherical parts of the potential are generated. By using a multipolar Fourier expansion introduced by Weinert (1981) the Coulomb potential is calculated. The exchange-correlation potential is computed numerically on a grid. The Hellmann-Feynman force contribution to the force is also determined (Yu, 1991). LAPW1 (BANDS) calculates valence bands (eigenvalues and eigenvectors): In LAPW1 the Hamiltonian and the overlap matrix (Koelling, 1975) are set up. Their diagonalization provides the eigenvalues and eigenvectors. WIEN2k supports both the LAPW and the APW+lo methods. A mix of both is recommended for maximum efficiency, i.e. the APW+lo basis functions are used for physically meaningful l values, while LAPW basis functions are employed to describe higher l-values functions. LAPW2 (RHO) computes valence densities from eigenvectors: The Fermi-energy is computed. The electronic charge densities are expanded according to the representation of eqn (in the previous chapter) for each occupied state and each k-vector. Afterwards the corresponding (partial) charges inside the atomic spheres are obtained by integration. In addition, Pulay-corrections to the forces are calculated. LCORE The treatment of the core electrons: The potential and the charge density of the core electrons are computed. MIXER mixes input and output densities: The electron densities of core, semi-core, and valence states are mixed to give the total new density. Taking only the new densities would lead to instabilities in the iterative SCF process. To have a stable SCF cycle new and old densities need to be mixed, to obtain a new density (1 ) here α is a m 1 m m new new old mixing parameter. In the WIEN2k code this is done (mainly) using the Broyden scheme. The total energy and the atomic forces are computed in mixer, as well. Chapter 4: Computational tool 44

11 Fig. 4.6 Setting of SCF cycle Chapter 4: Computational tool 45

12 4.2 The Elastic constant code: Cubic Elastic The cubic-elastic code: A Package for calculating elastic tensors of cubic phases using Wien2k Package The cubic elastic package is a set of programs and scripts that can calculate elastic tensor calculations for cubic phases (primitive, body-centered, or face centered) by using WIEN. To run this program a valid cubic structure file should exist. This package generates WIEN input files simulating strained structures. It also generates scripts to make WIEN calculate these structures and analyze the results, plot them, and derive their elastic parameters. Scripts and programs of cubic elastic: Cubic elastic package contains three scripts: init_elast: The whole calculation of elastic tensors is prepared by this script. It should be run in a directory that contains valid case.structure and case.inst files. First init_elast makes the following directories and sub-directories:./elast (the main directory),./elast/eos (directory where the calculations leading to K will take place),./elast/tetra (tetragonal distortion calculations directory),./elast/rhomb (rhombohedral distortion (directory for rhombohedral distortion calculation) and./elast/result (directory for storing all the calculations). The file case.struct is taken as the initial unstrained state which is stored as init.struct in the. /elast directory. Then, the template struct files (./elast/eos.templ,./elast/tetra.templ,./elast/rhomb.templ) are generated and the script init_lapw is launched in each of the directories. elast_setup: The elast_setup must be run in the elast directory which was created previously. It generates all the input files for the calculation using init.struct and the *.templ files. The created *,struct files are stored in the elast directory. The elast_setup creates three scripts: eos.job, rhomb.job and tetra.job. With these scripts WIEN calculates the entire set of structure changes automatically. ana_elast: The ana_elast must be run in the elast/result directory where all the calculated results are stored. The script analyzes all the calculated total energies according to eqn. (3.38), eqn. (3.41) and eqn. (3.45) (of the previous chapter) and extracts the elastic constants and pressure. This script also plots the results and generates the number of output files stored in the result/outputs directory. Chapter 4: Computational tool 46