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DFT.docx
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.
2.
3.
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
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:
