MIT 3.320/SMA 5.107/CMI Atomistic Modeling of Materials Spring 2003 1 Lab 2: Handout PWSCF: a first-principles energy code We will be using the PWSCF code as our first-principles energy code. PWSCF is a first-principles energy code that uses pseudopotentials (PP) and ultrasoft pseudopoentials (US-PP) within density functional theory (DFT). It includes linear response methods, which can be used to calculate phonon dispersion curves, dielectric constants, and Born Effective charges. It also implements third-order anharmonic perturbation theory. PWSCF is free for academics. Further information (including online manual) can be found at the PWSCF website http://www.pwscf.org/. PWSCF is currently at version 1.2.0. We will be using version 1.1.2, which can be found here: http://www.pwscf.org/download.htm#previous. There are many other first-principles codes that one can use. These include: ABINIT http://www.abinit.org DFT Plane wave pseudopotential (PP) code. ABINIT is extremely well coded, and free for academics. It includes linear response methods. VASP http://cms.mpi.univie.ac.at/vasp/ DFT Ultra-soft pseudopotential (US-PP) and PAW code. US PP’s are faster than corresponding PP codes, with similar accuracy. An industry standard. Small cost for academics (~$2000) WIEN2k http://www.wien2k.at/ DFT Full-Potential Linearized Augmented Plane-Wave (FLAPW). FLAPW is the most accurate implementation of DFT, but the slowest. Nice interface. Small cost for academics (~$500) Gaussian http://www.gaussian.com Hartree-Fock (HF) code with DFT also. One of the most popular HF codes. Calculates numerous properties of interest to chemists. Moderate cost for academics (~$3000) Crystal http://www.cse.dl.ac.uk/Activity/CRYSTAL HF and DFT code. Small cost for academics (~$500).MIT 3.320/SMA 5.107/CMI Atomistic Modeling of Materials Spring 2003 2This is a tutorial on how to get energies using PWSCF. Some helpful conversions: 1 bohr = 1 a.u. (atomic unit) = 0.529177249 angstroms. 1 Rydberg (R) = 13.6056981 eV 1 eV =1.60217733 x 10-19 Joules SINGAPORE STUDENTS Your lab instructors will help you connect to the computers. They will help you copy (or link) the pw.x program and all of the input files. CAMBRIDGE STUDENTS Your lab instructors will help you connect to Armageddon, and forward you to the appropriate node. MIT STUDENTS Log onto Athena. Add the course locker. Athena$ add 3.320 Next create a directory to store your files (ask if you need help). For example, Assuming you’ve already created the 3.320 directory, Athena$ cd ~<your username here> Athena$ cd 3.320 Athena$ mkdir LAB2 Athena$ cd LAB2 Athena$ mkdir PROBLEM1 Athena$ cd PROBLEM1 In this lab, you do not want to copy the pw.x file, because it is too big. Link it instead: Athena$ cp ~3.320/LAB2/GaP.scf.in . Athena$ ln –s ~3.320/bin/pw.x pw.x Note: Don’t forget a space between GaP.scf.in and the period. The period at the end of cp “~3.320/LAB1/gulp1* .” must be typed. It means you areMIT 3.320/SMA 5.107/CMI Atomistic Modeling of Materials Spring 2003 3copying the files to your current directory. You can also copy over the gulp file , instead of linking. MIT and Singapore, and Cambridge students Problem 1 concerns convergence issues in first-principles calculations. They are sometimes called ab initio calculations, which means “from the beginning” in Latin. They are called this because (in theory) first-principles calculations only rely on the atomic number and build up everything from there. Below is some background for problem 1A and 1B; if you do not think you need it, skip to the section which titled “summary of background”. Background for problem 1A Remember that we are dealing with infinite systems (aka periodic boundary conditions). This means that we can use the Bloch theorem to help us solve the Schrödinger equation. The Bloch theorem says: ()()()knrurkirknvvvvvv⋅= expψ with ()()rGiGGcrknuvvvv⋅=∑exp In these equations, ()rvψ is the wavefunction, ()ruv is a function that is periodic in the same way as the lattice, Gv sums over an infinite number of reciprocal lattice vectors, and cG’s are coefficients in the expansion. In this case, our basis functions (ie what we expand in) are planewaves, or exponentials. They are called “plane waves” because surfaces of constant phase are parallel planes perpendicular to the direction of propagation. In actual calculations, we have to stop the expansion at some point (i.e. stop taking moreGv’s). In first-principles calculations, this is called the energy cutoff. Cutoffs are always given in energy units such as Rydberg or eV. Note: The units of reciprocal lattice are the inverse of the direct lattice, or 1/length. However, we can convert 1/length to energy units (Remember c=λν, and Eh =ν. λ is wavelength, and is in units of 1/length) Problem 1a will be to test cutoff convergence issues. You can always take a higher cutoff than you need, but the calculation will take longer.MIT 3.320/SMA 5.107/CMI Atomistic Modeling of Materials Spring 2003 4Background for Problem 1b. Because of the Bloch theorem, instead of solving the Schroedinger equation with an infinite number of MxM ma rices (M is the number of basis functions), you solve it for a finite number of tkv values, and get a value for E at each kv. This is seen in the schematic below. 010203040506070Energiesk values The picture goes over the first Brillouin zone. If you don’t know what a Brillouin zone is, don’t worry about it too much. Just know that to get a value for E, the energy of the crystal, you need to integrate the values of E over the first Brillouin zone, where the bands are occupied, and divide by the volume. Numerically, this means calculating sum over E for all kv points, where the bands are occupied, then divide by the number of kv points. Thus, summing over a finite number of kvpoints is an approximation to performing an integral. You will need to make sure you have enough kv-points to have a converged value for the energy. Summary of background. For all first-principles calculations, you must pay attention to two convergence issues. The first is energy cutoffs, which is the cutoff for the wavefunction expansion. The second is number of kv-points, which measures how well your discrete grid has approximated the continuous integral. The input filesMIT 3.320/SMA 5.107/CMI Atomistic