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

The project

Part of my undergraduate project for spring 2007 was a collaboration with the Dr. Leeor Kronik and Amir Natan, from the Weizmann Institue.

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 Pz 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.