Materials that you may find helpful when working through this exercise

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1 Detailed steps illustrating how to use VASP on the Suns in Fitz 177 For use in lab: 11/10/2009 (Original file by Dr. Rachel Getman, 11/18/2007. Editted for use by Dorrell McCalman 11/09/2009.) Note on VASP usage The VASP executable that we have available is compiled to run on a 64- bit AMD Opteron processor, such as the ones installed in the Suns in Fitz 177 and in the Opteron nodes in the CRC. You will likely not be able to run this executable on any other sort of architecture. Materials that you may find helpful when working through this exercise The VASP online manual ( VASP input files (INCAR, KPOINTS, POSCAR, POTCAR) for your gaseous atom, bulk fcc and 111 surface, the Birch-Murnaghan Equation of State fortran fitting script (called murg), a sample murg input file (called fort.2), the vaspgeom script, the serialvaspjob.sh script, the parallelvaspjob.sh script. The VASP input files can be obtained from the course website under the Homework section. Right click the desired file. Select Save Link as. Save the file in the directory of your choosing. Remember that to use the files they must be renamed. For example, INCAR_fcc must simply be called INCAR. Thus it is best to have different directories for each job. The murg, fort.2, vaspgeom, serialvaspjob.sh and parallelvaspjob.sh files can be copied from /afs/nd.edu/user7/dmccalma/public/compchem Introduction to VASP VASP, or Vienna ab-initio Simulation Package, is a Density Functional Theory (DFT) package that utilizes a period supercell (periodic boundary condition) code and planewave basis sets. It is developed by the VASP group in the Theoretical Physics Department at the Institute for Materials Physics in Vienna, Austria. Periodic boundary condition, planewave basis set codes are very useful in describing the electronic structure of solid systems and have successfully been applied to propose bulk crystal structures and compute structure lattice parameters. Specifically, these codes are useful in describing metal systems. This exercise walks you through calculating the gase phase energy of an atom, optimizing the lattice parameter of the bulk metal system and calculating the energy of the 111 surface of an fcc metal.

2 Developing the VASP input files Unlike Gaussian, VASP requires four (not just one) input files. These are INCAR, KPOINTS, POSCAR, and POTCAR. The system geometry goes into the POSCAR file (see the sample files.) The format of the POSCAR file is as follows: The first line is a title card. Put the atomic symbols of each ion in your structure here. The second line is a scaling constant. For the gas phase calculation it multiplies the unit cell vectors to give the dimensions of the unit cell. For bulk calculations that you will do, it is the lattice constant in Angstroms. The 3rd, 4th, and 5th lines are the unit cell lattice vectors with respect to the Cartesian lattice. They are row vectors. Since the metals you will consider possess fcc (face centered cubic) structures, we can equate our lattice vectors to those of a face centered cubic lattice. The 6th line indicates the number of each type of ion. While the ordering is not important, it is important that it is kept consistent in the POSCAR, POTCAR, and sometimes INCAR files. The 7th line tells VASP to use Selective dynamics, which means that we want to choose whether or not to relax all ions in all three lattice directions. Note: This flag is NOT necessary for the bulk calculation and is omitted. It is necessary in surface calculations. The 8th line indicates that we are using a Direct lattice (instead of a Cartesian lattice), which means that we are going to give ion positions in fractional coordinates, which are in relation to the lattice specified in lines 3-5 multiplied by the scaling constant in the second line. If the flag Cartesian is used instead of direct then you must give cartesian coordinates. The 9th line onwards give the fractional coordinates of our ions. If the Selective Dynamics flag is included on the 7th line three T s separated by spaces might be added to the end of each line to tell VASP to relax each ion in all three lattice directions. Three F's would tell VASP to keep those coordinates fixed. A mixture of F and T can also be specified. Note that the coordinates must be ordered according the ordering on the 6th line. Visualizing your POSCAR file with VMD Just like with Gaussian, it is important to visualize your input and output geometries to ensure that they are reasonable before and after running. To visualize VASP geometries, we can use a program called VMD, which is available on AFS. To access it, first load the VMD module, and then call up vmd at the command prompt. Then do the following (note: you may find the tutorial located at

3 helpful): At the command prompt, before getting into VMD, make a copy of your POSCAR file and name this copy [metal symbol].poscar On the VMD main window, select File->New Molecule, and a window labeled Molecule File Browser will pop up. In this new window, in the Determine file type box, select VASP_POSCAR. Load the filename of your POSCAR into the Filename box. Click Load. A window with a black background and a set of axes will appear with seemingly nothing else in it. It contains our structure, but we need to make some modifications to our default view to see it. In the VMD main window, select Graphics -> Representations. Select Drawing Method = VDW. Now some very large spheres will appear in the black backgrounded window. You can use the mouse wheel to zoom in and out. You can also play with the sphere resolution and scale to adjust the view of your ions, as well as adjust ion colors, and do many other things. VMD is very powerful! Whatever you do, you are now looking at your supercell. Make sure it looks reasonable before submitting it for calculation! To see your supercell and its periodic images, go to the Periodic tab in the Graphical Representations window and check some or all of the ±X,Y,Z boxes. Back to developing the VASP input files The k-points grid or generation scheme goes into the KPOINTS file. k- points, very basically, relate to the reciprocal lattice of the supercell. For our purposes: You want to have similar densities of k-points along all reciprocal dimensions. Since reciprocal dimensions are inversely proportional to real dimensions, this means that as your supercell size increases, your reciprocal lattice decreases, and thus the number of necessary k-points decreases. For small molecules and single atoms a k-point mesh of 1x1x1 is sufficient. The first thing you should do when starting calculations on a new supercell is converge the k-point grid. Once you have converged this grid, you can use it on all calculations that use the same supercell and (for the most part)structure. The k-points file is set up to tell VASP to use a Monkhorst-Pack generation scheme. This is a fine scheme to use. Therefore, unless you want to change it, the only editing of the k-points file you ll need to do is to change the grid dimensions (e.g. from 1x1x1to 10x10x10 etc.) See the VASP manual to learn more about k-points.

4 The INCAR file contains information about computational parameters. Your files include several parameters and comments about them in the file. Note some of the values you can control: 1) The optimization algorithm for both the electronic and geometric convergence (IALGO & ALGO (electronic), IBRION (geometric)) 2) The kinetic energy cut-off for the valence electrons (really the highest energy plane wave to include) 3) The electron smearing method and parameter 4)The maximum number of electronic and geometric iterations to take (NELM (electronic), NSW (geometric)) 5)Convergence criterion for the electronic and geometric relaxation (EDIFF (electronic), EDIFFG (geometric)) Most of these parameters, as well as others, will affect the electronic structure and energy outcome. Typically, when you start doing calculations, it is wise to learn how each of these parameters affects your calculation and, to as much of an extent possible, to converge each one. The POTCAR file contains the pseudopotentials for each ion in the calculation. Pseudopotentials are a topic of their own. Basically, a pseudopotential is the potential felt by the valence electrons from the ion nucleus and core electrons. The POTCAR file describes to VASP how to treat this potential when describing the motions of the valence electrons. The pseudopotentials you are using (called PAW or projector augmented wave) are optimized for each atom and empirically based. In addition to the pseudopotential method, the POTCAR file also tells VASP how to describe the motions of the valence electrons, that is, it defines the electron exchange and correlation functional. We are using the PW91 implementation of the GGA, or generalized gradient approximation, which treats exchange and correlation as a function of the electron local density and its local gradient. Two important things to note about the POTCAR file are: 1.It must contain an individual POTCAR for each ion 2.The individual POTCARs must be in the same order as the ions in the POSCAR. When dealing with several types of ions we first have get the POTCAR file for each and then we have concatenated them in to a single file. (A Linux command for this is: cat First_POTCAR Second_POTCAR > POTCAR). Individual POTCAR files are located at /opt/und/vasp/x86/vasp-p/potpaw_gga.

5 In general, to obtain one, go to that directory. Individual elements have their own subdirectories. In each subdirectory is a file called POTCAR.Z, which is a zipped POTCAR file. Copy that file to somewhere on your home directory, then unzip it with the command gunzip. I suggest renaming the unzipped file, for example Cu_POTCAR,s o that you can easily distinguish it, and so that POTCARs do not get overwritten. Running VASP To run VASP on the Suns in Fitz 177, the pathscale compiler must be loaded. Check to make sure it is loaded (it s probably not, the pgi compiler is probably loaded instead.) If it isn t, swap the current compiler for the pathscale compiler (e.g. by typing module swap pgi pathscale.) Finally we are ready to run VASP. To do so, put your INCAR KPOINTS POSCAR POTCAR files into some directory by themselves. Move into that directory, and then type the following command at the command prompt: /opt/und/vasp/x86_64/vasp.4.6/vasp_serial Alternatively you could include these commands in a script in the same directory. The script could look like: #!/bin/csh Module swap pgi pathscale /opt/und/vasp/x86_64/vasp.4.6/vasp_serial Then you can run the script from the desired folder by typing the name of the script and pressing enter. You can find such a script at: /afs/nd.edu/user7/dmccalma/public/compchem It is called serialvaspjob.sh If you want to run on the CRC nodes in the old environment you can log on to the opterona.hpcc.nd.edu front end and use the script parallelvaspjob.sh also located at: /afs/nd.edu/user7/dmccalma/public/compchem The gas phase atom calculation should take just a few minutes to run. When it s done, you ll get several output files. Some of the key files are the OUTCAR file, which contains information about the electronic and geometric convergence, the CHGCAR file which gives the final charge density, and the CONTCAR file, which gives the final geometry of the supercell. You should check to see that all the electronic structures for each geometry step converged and that the geometry converged. To check the latter, you can run vaspgeom on your OUTCAR file (usage: vaspgeom OUTCAR). You should also check your final geometry by visualizing your CONTCAR. Note that several of the VASP output files, e.g. CHG, CHGCAR, OUTCAR, vasprun.xml, WAVECAR, can have very large file sizes. You can tell VASP whether or not print these files by specifying in the INCAR.

6 Converging the bulk lattice parameter Once you have run VASP on the gas phase atom system you can run the bulk calculation at several lattice parameters in order to attempt to find the optimized lattice parameter. To do this, you simply need to change the lattice parameter value in the POSCAR and then re-run the calculation. I suggest you run each new calculation in a different directory so that you don t constantly overwrite files associated with older runs. You ll of course want to compare results from different runs, so you ll need all your files! Once you have generated enough points to create a fit, you can run the murg fitting script on an appropriate fort.2 file. This script fits your data points to the Birch-Murnaghan EOS. The fort.2 file is set up as follows: The 1st line is a guess of the lattice constant (in a.u. but note that VASP works with lengths in Angstroms) that minimizes the electronic energy of your structure. The 2nd through 4th lines are the lattice vectors of your supercell (same as in the POSCAR.) Edit as necessary. The 5th line is an integer, N, which tells murg how many lattice constant/energy combinations you are going to enter. The 6th through [6+(N-1)]th lines give your trial lattice constants (in a.u.) and resultant supercell energies (in Rydberg). The last line of fort.2 is a guess of the minimum supercell energy that corresponds to the lattice constant in the 1st line. Once you have created fort.2, simply run murg from the directory where fort.2 is located. (You ll either need to place murg in that directory or in some place in your search path and you ll need to change its permissions so that you can execute it if it is not executable (chmod +x filename) It will prompt you to enter in a volume, amin, amax. For volume, enter in a guess as to the energy minimizing volume (corresponds to your guess of the energy minimizing lattice constant.) For amin and amax, enter in the minimum and maximum lattice guesses to use in the Birch-Murnaghan fit. After that, the script will complete, and you ll get two output files: fort.10 and fort.11. The former summarizes your fit parameters, including the optimized lattice parameter, at the bottom of the file. You could use these parameters along with the Birch-Murnaghan EOS to plot the electronic energy of your metal as a function of lattice parameter. Once you get the optimized lattice parameter, you should run VASP on your supercell at that lattice parameter to get your optimal electronic energy. Computing a surface energy Now that you have computed the electronic structure and energy of an atom and a bulk metal, it is useful to compute the energy necessary to cleave the bulk structure into some surface structure. To do this, you

7 need to compute the electronic structure and energy of some surface of your metal. The (111) surface is appropriate. Setting up the POSCAR The method for running VASP on the (111) surface is very similar to that for the bulk, but there are some differences. For example your POSCARs must be set up differently. The surface POSCAR is for a 3-layer 3 ion x 3 ion supercell (3 ions per layer). You should visualize this cell. The scalefactor is equal to 3 x lattice parameter x ( 2/2), (If we were using a 2 ion x 2 ion supercell (4 ions per layer), the scale factor would be equal to lattice parameter x 2. The lattice vectors are also different. The (111) surface of an fcc cell has hexagonal symmetry, and therefore, its lateral lattice vectors form an angle of The vertically pointing lattice vector is not of unit length. This is because we want to study chemistry on the surface, so have left several angstroms of vacuum space between vertical supercell images. Also different is that now we can include the Selective Dynamics flag on the 7 th line. You can tell VASP not to perturb the ions in the bottommost layer, regardless of whether or not they have residual forces acting upon them. When we model surfaces, we assume they are infinitely thick and comprised of an infinite number of bulk-like layers topped off by several surface-like layers which are somewhat relaxed compared to the bulk like layers. An appropriate calculation would therefore model many (i.e. 10+) surface layers. In fact, the number of layers is a quantity that should be converged for an accurate calculation. However, due to computer time and memory restrictions, we can only model a few layers. We can therefore fix the bottommost layer in the calculated bulk positions in order to model the presence of the many bulk-like layers underneath the surface-like layers. Constructing the supercell for a surface can be difficult, and typically is done using some sort of computer program. For example Gaussview can be used to do this. Check out Dr. Chao Wu s website ( Setting up the KPOINTS file Unlike in the case of the bulk, the lattice vectors for the surface are not all equivalent in length. Therefore, the correct k-point densities will not be equivalent either. As demonstrated in your KPOINTS file, equivalent densities are specified for the lateral lattice directions, but these densities are different than that specified for the vertical direction. The appropriate way to specify the k-point grid for the surface is NxNx1. Just like for the bulk, this grid (i.e. the value of N) will need to be converged before performing accurate surface calculations. The INCAR and POTCAR files These files can be set up identically to the anagalous bulk files. Certainly, to be able to correctly compare energies between the surface

8 and bulk, the ENCUT, ISMEAR, SIGMA, PREC, and LREAL parameters should be identical. Computing the surface energy The surface energy computed for the reaction: Bulk Metal -> Unrelaxed(111)Surface is γ = Unrelaxed E(111) ne Bulk 2A The surface energy computed for the reaction: Bulk Metal -> Unrelaxed (111)Surface -> Relaxed (111)Surface is γ = E Unrelaxed (111) 2A ne Bulk E + Re laxed (111) E A Unrelaxed (111) Unrelaxed E ) Here, (111 is the DFT energy of (111) without any relaxation, i.e. with all ions in there calculated bulk position. It is the final energy of the first geometric step of the surface geometry optimization. n is the number of ions in the surface calculation. is the energy from laxed E Re ) the bulk calculation. (111 is the energy of the geometry optimized (111) structure. A is the surface area of the (111)supercell, and for this supercell it is given by: (Surface scalefactor) 2 x sin(120 0 ) Note that this is the cross-product of the two lateral lattice vectors. The latter surface energy equation describes the formation of the surface in two different steps: 1) the cleaving of the surface from the bulk and 2) the relaxation of the surface due to the altered stresses on the atoms near the solid/vacuum interface. The first step results in the formation of two surfaces, one on the top and one on the bottom of the cell. The second step is due to relaxation of the top surface only, as the bottom is kept fixed in calculated bulk positions. E Bulk