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Quantum Local-density approximation (LDA) Local-density approximations and the Perdew-Burke-Ernzerhof generalized gradient approximation are widely used by physicists and chemists for electronic structure investigation of different body-systems. Local-density approximations (LDA) refer to “a certain class of approximations implemented to the exchange-correlation (XC) energy functional in  DFT, which are dependant on electronic density value at each point in space” (Parr and Weitao, 1994)…

Introduction

Consequently, LDA is generally related to functionals, which are based on HEG approximation. LDA are implemented in realistic systems measurements and calculations (for example, molecules and solids). In a general view, for a spin-unpolarized system, “LDA for the exchange-correlation energy is the following where ? refers to the electronic density and ?xc, the exchange-correlation energy concentration, is a function of the density. The exchange-correlation energy is split into exchange and correlation terms in a linear view: thus separate expressions for Ex and Ec are defined. Separate expressions known for the correlation density lead to numerous different approximations for ?c”. (Parr and Weitao, 1994) LDA is a part of any approximate exchange-correlation functional. Its main function is to “replicate direct results of the HEG for non-varying densities” (Parr and Weitao 1994, p. 35). As a result, LDA is often mentioned as an explicit component of such kind of functional. The Perdew-Burke-Ernzerhof (PBE) Modern scientists and researchers are greatly concerned about updating GGA functionals in their implementation in molecules and solids. ...
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