ES22-Ayoola

Author: Ayoola, Adeolu - University of Ibadan Nigeria

Title: Formulation of a New Exchange-Correlation Functional for Better Band Gaps in Density Functional Theory

Abstract: In Density Functional Theory formalism, the total energy functional of a system consists of known and unknown parts, the known part consists of kinetic energy of the non-interacting system, the external potential energy and the Hartree or classical coulomb interaction between the electrons. The existence of the unknown part was established by P. Hohenberg and W. Kohn in 1964 and it is known as the Exchange-Correlation Energy which is the major component necessary for accurate prediction of properties of materials.

The true mathematical form of this exchange-correlation Energy is not known, hence, approximations are made for it which reduces the accuracy of DFT, particularly in the case of energy band gaps. In this work, an exchange-correlation potential functional is formulated which is the modification of Hanke and Sham functional in 1998.

The functional was incorporated into the Quantum espresso software package and was used to perform plane-wave based calculation and energy band gaps of some systems were predicted from the formulated functional.

From our functional, we got band gap for Silicon to be 1.10eV which is closer to the experimental value of 1.12eV than that of LDA which is 0.47eV, for Silicon Carbide, experimental value is 2.40eV and we obtained 2.27eV with our functional which is more accurate than 1.35eV from LDA. For Aluminium Phosphate, our method gave 2.28eV while the experimental value is 2.45eV. All these are of error of approximately 6 percent, comparing with the experimental values and LDA results, the exchange-correlation functional in this work has given better predictions of energy band gaps than LDA.

Other authors:
Oyeniyi, Ezekiel. University of Ibadan Nigeria,
O. Akinojo University of Ibadan Nigeria and East African institute for Fundamental Research (EAIFR)