In density functional theory (DFT), there are mainly two classes of approximations of the exchange-correlation (XC) functional that are in wide use: The first one is the semilocal formalism and the other one is the hybrid functional theory. However, higher-order accurate many-body approaches are also possible. Depending on the ingredients used, the XC functionals are classified through Jacob’s ladder. Each rung of the ladder adds an extra ingredient starting from the local density approximation (LDA), generalized gradient approximation (GGA) and meta-GGA. LDA, GGA and meta-GGA are known as semilocal functionals and those are quite accurate in describing several solid-state, surface, and thermochemical properties. From the construction point of view, the semilocal functionals are developed either by satisfying various exact constraints or from exchange hole or by both. A systematic evaluation of the XC approximations is necessary, especially when a new functional is proposed. The motivation of my thesis is largely inspired by the benchmarking of several recent XC functionals and the necessity to improvise the new functionals for obtaining more accurate results.
My thesis involves on the benchmarking of the Tao-Mo (TM) semilocal functional with various approximations. The TM functional is found to be very accurate both for the quantum chemistry and solid-state physics. In this thesis, the performance of several solid-state properties are addressed using the TM functional along with other popularly used GGA and meta-GGA level functionals in the PAW method. Particularly, the accuracy of TM functional with most advanced strongly constrained and appropriately normed (SCAN) meta-GGA functional is noticeable. It is shown in my thesis that for several solid-state properties, TM functional works comparatively better than other meta-GGA and GGA functionals. Utilizing the semilocal exchange hole of the TM functional I also construct the range-separated hybrid functional with long-range semilocal and short-range HF analogous to that of the screened range-separated hybrid functional. To check the accuracy and performance of the constructed functional, it is applied to determine several properties of the molecular and solid-state test.
Besides of the construction of the 3D functionals, my thesis also focuses on the construction of the functional for the 2D quantum systems. It is well known the the 3D functionals actually breakdown when it is applied to the 2D electronic systems. Though in practice the 2D systems are considered as quasi-2D systems (Q2D), yet the 2D functional can be used to explore the systematic DFT investigations for proper explanations of numerous properties of low-dimensional systems. Beyond the 2D-LDA, and 2D-GGA the first ever meta-GGA functional is proposed and applied to the 2D quantum systems. The motivation of the construction is followed from its 3D counterpart based on the DME technique. Further, the newly constructed functional shows improvement when applied to study a few electrons trapped inside parabolic and Gaussian quantum dots. We also explore the behavior of the Kohn-Sham kinetic energy density by taking the two-dimensional parabolic quantum dots as a model system. Also, an improved version of the existing 2D-GGA functional is proposed by extrapolating between the small and large density-gradient limit of the exchange hole.