**Pseudo-potential
calculations for periodic systems - Density Of States Graph Module
**

**The project
**

My mission was to add a module to the pseudo-potential DFT calculation programme PARSEC. The purpose of the module was to calculate a Density Of State (DOS) graph for calculations done on periodic systems, which have been newly introduced to PARSEC. The code was written in Fortran 90 and the it can be found in the following link. As for the rest of the PARSEC code can be found in PARSEC project official site. However, the version I've been working on cannot yet be found in the official site.

Pseudo-potential, real-space grid calculation
and K point sampling

The meaning of the name PARSEC is Pseudo-potential
Algorithm for Real-Space Electronic structure Calculations. PARSEC performs Density Functional Theory calculations (about which I
explained here) to determine the properties of
molecules and multi-atomic structures. Unlike Gaussian based DFT programmes which solve the SCF (self consistency) eigenvalue problem by real-space
integration, PARSEC does it by calculating the values of the Hamiltonian in a
real-space grid and diagonilizing it upon that grid. After this diagonilization
is done a new Hamiltonian is created and is mixed with the old one, and so the
calculation goes on until it converges down to the required level. However,
calculating the Hamiltonian using a real-space is problematic near the atoms
where the eigenfunctions oscillate significantly. Therefore instead of the
regular atomic potential, an effective pseudo-potential is used to make the eigenfunctions smooth around the atoms and still have the same form as the
original ones far enough from the atoms. This enables the real-space grid
sampling which reduces the calculation time considerably.

Lately, a new feature has been introduced to PARSEC by Dr. Leeor Kronik's group,
which consists mostly of K-space grid calculation for periodic systems. The
calculation is done similarly on, but now the sampling is done in K-space, as
the eigenfunctions are set as also a function K.

First Results of the project

The project is still ongoing, but there are first results visible. The following
graph shows the DOS calculated for Silicon lattice performed by PARATEC and by
PARSEC. PARATEC is a plane-wave programme that performed the same calculation.
The code I've written is originated from PARATEC, and so the two programme are
suppose to give similar results.

The difference at the end of the graph is because PARATEC calculated 10
energy bands, while PARSEC calculated only 8.

Next in the project

I plan to add to this module the
calculation of Partial DOS. Partial DOS (LDOS) shows the DOS of only a certain mode
of the system (such a the P_{z} orbital of a certain atom). Partial DOS
can give good insight about which mode of the system contributes to a certain
property of the entire structure. Also, I plan to add here visialization of
Carbon Diamond structure and Graphene structure.