Quantum Simulation - DFT

Research Overview 

Meta-GGA Density Functionals: 

The meta-GGA class of density functionals resides at the third tier of Jacob's ladder of density functional approximations (DFAs). They exhibit a comparatively higher level of accuracy compared to GGAs and a lower computational cost than hybrids, rendering them more efficient and valuable for practical applications. Our research delves into how these functionals efficiently predict properties ranging from lattice constants and phase transitions to band structures. In the gKS formalism, the meta-GGAs encompass a portion of the derivative-discontinuity, thereby enhancing their effectiveness in predicting band structures. However, approximations and empirical forms of meta-GGAs still have room for enhancement. I am currently working on the novel development of these functionals and applying them to both finite and periodic systems. Some of my representative research on this topic is showcased below. 

Hybrid Density Functionals:

A hybrid exchange-correlation (XC) functional incorporates a fraction of exact exchange from Hartree-Fock theory alongside semilocal density functionals. The benefits of using hybrid functionals encompass improved handling of self-interaction error, derivative discontinuity, and nonlocal interactions. Both global and range-separated hybrids require the exchange holes derived from the underlying semilocal (GGA or meta-GGA) density functional. A common approach involves reverse engineering the exchange energy functional to construct its corresponding hole.

Non-local Corrections:

DFT at any level starting from LDA, GGA, and meta-GGA to hybrid approximations is unable to account for the weak, long-range van der Walls (vdW) interaction completely. This weak interaction present in the dispersion bonded matter arises due to the long-range correlation between the electrons. The instantaneous quantum electronic charge fluctuations are the causes for such correlations and the construction of local or semilocal approximations do not include such concepts. Density functional approximations behave well when the densities of the considered system overlap, but in the case of vdW interaction, the overlapping of densities is barely encountered. The most common approach is to combine the long-range correlation with the approximated semilocal XC energy functional. 

Exchange Potentials:

The fundamental gap of the Kohn-Sham (KS) system often underestimates the bandwidth, equivalent to the derivative discontinuity. To address this issue, exchange-only potentials are considered due to their computational cost and accuracy advantages. Several well-known potentials fall into this category, such as the GGA type exchange potentials proposed by Leeuwen and Baerends (LB), Gritsenko et al. (GLLB), and the meta-GGA type exchange-only potential proposed by Becke and Johnson (BJ). Notably, the bandgaps of the recently developed TBMBJ potential and our developed mBR-TBMBJ potential exhibit accuracy comparable to costlier hybrid methods, particularly when applied to narrow band gap semiconductors, insulators, oxides, transition metal dichalcogenides, transition metal mono-oxides, and organic crystals. I am actively engaged in the ongoing development of these potentials and exploring their potential applications.