Introduction

There is a jungle of DFT tutorials all over the web, and only some of them are good. Only few of them are oriented at DMFT calculations, and even less use w2dynamics. This tutorial is written in the hope of filling this gap, combining a little bit of theory with practical how-tos and input files.

In this tutorial we will compute the DMFT spectral function of NiO, which is a charge transfer insulator. There is a similar tutorial on the triqs documentation which uses VASP + TRIQS. Instead, we will use Quantum ESPRESSO + w2dynamics. Compared to other DFT codes Quantum ESPRESSO has the advantage of being free and open source. Other than that, all DFT codes are essentially equivalent.

The amount of theoretical and practical knowledge needed for this tutorial is large, hence the decision to split it into modules which can be skipped by the uninterested user. 

Structure of the tutorial

• Installation (not in detail)
• Density Functional Theory
  • Setting up a basic DFT calculation
    • Create and visualize the crystal structure using VESTA
    • Choose a pseudopotential
    • Set up of the input file to compute the ground-state charge density
    • Convergence criteria to watch out for: plane wave expansion and Brillouin zone integration
  • Structural relaxation using DFT
    • Set up of the input file for a DFT structural relaxation
  • DFT band structure (with atom projection)
  • DFT density of states (with atom projection)
  • Wannierization 
    • Set up of the calculation
    • Tips and tricks
• Interfacing
  • Fourier transform of the Wannier hamiltonian
• Dynamical Mean Field Theory
  • Set up of the input file for w2dynamics
  • Analytic continuation of the green's function and self-energy
  • Plotting tools

Installation

Quantum ESPRESSO

Easy way:

General installation:

• Install the minimum needed libraries:

  sudo apt-get install libopenmpi-dev     -y
sudo apt-get install libopenblas-dev    -y
sudo apt-get install libfftw3-dev       -y
sudo apt-get install liblapack-dev      -y
sudo apt-get install libscalapack-openmpi-dev -y
sudo apt-get install g++ -y

• Download from the download page (7.1 version)
• Unpack with tar -xvf qe\-ReleasePack.tar
• cd to qe-7.1
• Run the ./configure script
• Run sudo make all 
• Run sudo make install
• If problems arise you have to go through the complaints of make to figure out what's wrong. Fortunately Quantum ESPRESSO has many users so you often find someone else who had the same problem.

VESTA

Can be downloaded from the jp minerals website. Installation is straightforward for all standard operative systems.

Density Functional Theory

Setting up a basic DFT calculation

Create and visualize the crystal structure using VESTA

The first thing you need is information on your crystal structure. It's a CsCl-type cubic crystal with a = 4.1674 Å. We can use this information to visualize the primitive cell. 

• Open VESTA, then click: File → New Structure, a prompt will open
• Click Unit cell and select Cubic, Space Group No. 225 (Fm3m), and enter the lattice parameter

• Now go to Structure parameters → New and add a Ni atom in (0, 0, 0) and O in (1/2, 1/2, 1/2). You should see something like this. Notice that VESTA does the work of recognizing the Wyckoff positions for us. 

Table of contents