Density functional theory (DFT) uses the Hohenberg-Kohn-Sham theory to map the many-body Schrödinger equation onto a single-body problem. VASP is a DFT software package that uses plane wave basis sets, pseudopotentials to approximate core electrons, and periodic boundary conditions to model materials with up to 200 atoms. VASP input files include INCAR for calculation parameters, POSCAR for geometry, POTCAR for pseudopotentials, and KPOINTS for k-point meshes.

1. Manual
Density Functional Theory (Background):
Why is solving the Schrödinger equation for the many-body problem too difficult
for anything but a relatively small number of electrons?
Solution: The Hohenberg-Kohn-Sham theory: a systematic way to map the many-
body problem onto a single-body problem.
What is a functional?
Suppose f(x) = x
2
; we call f(x) a function since when we give it a number, it
returns a number.
A functional returns a number when we give it a function: e.g.
g(f(x) is functional; if I give it f(x) = sin(x), g(f(x)) returns 2.

4. What is VASP?
• One of the software packages that uses DFT to solve the quantum problem for
materials .
– Uses periodic boundary conditions
– Uses pseudopotential method with a plane waves basis set
– Can model systems with maximum no. of atoms in the range of 100-200
– Commercial software package ~$5000
– Manual http://cms.mpi.univie.ac.at/vasp/vasp/PREC_tag.html
• Other DFT packages – (public license)
– Quantum espresso (www.quantum-espresso.org)
– Abinit ( www.abinit.org)
– Siesta (http://icmab.cat/leem/siesta/)
What are Pseudo-Potentials?
• The core electrons of an atom are computationally expensive with
planewave basis sets

5. – Large number of planewaves are required to expand their
wavefunctions
– Contributions of core electrons versus valence electrons to bonding is
usually negligible
• To address this, we replace the atomic potential due the to core electrons
with a pseudopotential which has the same effect on valence electrons.
VASP provides a database of pseudopotentials based on the Project
Augmented-Wave (PAW) method. These are called PAW potentials.
 Pseudopotentials are not unique.
VASP input files
• INCAR
– User specified parameters that define the calculation
• Global break condition, Energy cutoff, Smearing, Ionic and geometric relaxation
parameters
• POSCAR
– Specifies the periodic simulation cell
– Information regarding geometry of the system
• POTCAR
– Pseudopotential (PP) file
– Information on PP and XC functional
• KPOINTS
– Defines k-point mesh

6. INCAR

7. POSCAR
K-Points

8. POTCAR
OUTPUT
Comments on k-points and smearing
• Smearing
– Guidelines for ISMEAR
• For semiconductors or insulators always use tetrahedron method (ISMEAR=-5)
or if cell is too large use Gaussian smearing (ISMEAR=0)

9. • For relaxations in metals always use ISMEAR=1
– Never use ISMEAR > 0 for insulators and semiconductors.
• For very accurate total energy calculations (no relaxations in metals) use the
tetrahedron method (ISMEAR=-5).
• k- point convergence
– recommended to use even meshes (e.g. 8 × 8 × 8 ) for up to
n = 8
• After that odd meshes are more efficient (e.g. 11 × 11 × 11).
Example Silicon: