4/7/16

You are invited to attend a lecture

by

Dor Gabay

Ph.D. candidate of

Professor Amir Boag and Dr. Amir Natan of Electrical Engineering, Physical Electronics Department

The solution of the Poisson equation describing the electrostatic potential plays an important role in first principles methods such as Density Functional Theory (DFT), time dependent DFT (TDDFT), Hartree-Fock (HF), GW, and others. In recent years this is becoming even more important as many DFT methods utilize hybrid functionals that involve the inclusion of Fock exchange or screened exchange. The Poisson equation for the electrostatic potential, , is given by , where  is the electronic density. An alternative approach to solving the Poisson Equation is to write it in its equivalent integral form, i.e. , where  is the volumetric domain of integration and  is the electrostatic Green’s function. The volumetric integral can be efficiently evaluated using the Multi-Dimensional Fast Fourier Transform (FFT) which leads to  scaling for  grid points. The FFT-based method was therefore implemented in PARSEC, a real-space first principles Density Functional Theory (DFT) package.

In developing a Poisson solver using FFT, we analyzed both existing and novel Green’s function kernels. The proposed kernels took both analytical and numerical form. The purely analytical kernels were computationally efficient, but tended to produce insufficiently accurate results. Various optimization methods were used to fine-tune the singular region of the analytically derived kernels. The numerical kernels, although more computationally expensive, could be adjusted in accuracy by considering finer integration schemes or higher orders of approximations, making them more accurate than the non-corrected analytically derived kernels.

Finally, we demonstrate how the errors associated with the solution of the electrostatic potential propagate into errors in the eigenvalues of the Density Functional Theory (DFT) calculations.

Monday, July 4th, 2016, at 17:00

Room 011, Kitot Building