![]() The fourth rung, hyper-GGA, also referred as hybrid GGA, calculates exchange using a mixture of the exact exchange and a GGA exchange functional. The first rung, local spin-density approximation, uses only the local density as input, while the second and third levels, GGA and meta-GGA, respectively, include semilocal terms. The most popular density functional methods can be divided into five categories according to the fifth-rung “Jacob's ladder” presented by Perdew. ![]() Current routinely used computational methods are mainly based on the formulation of DFT addressed by Kohn and Sham (KS), where approximations are used for the exchange-correlation energy E XC, representing the entire unknown part of the energy functional. The modern DFT is based on two Hohenberg-Kohn theorems, which state that the ground-state electron density uniquely determines the potential and thus all properties of the system. However, its accuracy is limited by the errors due to the inaccurate representation of kinetic energy, exchange energy, and the complete neglect of electron correlation. In 1927, Thomas and Fermi independently developed the Thomas-Fermi model, which is the predecessor to modern DFT. ![]() Zhi-Jian Zhao, Jinlong Gong, in Studies in Surface Science and Catalysis, 2017 14.2 Background of DFT-Based Catalyst Screening
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