Abstract
This chapter focuses on the corrections for exchange-correlation functionals that are physically supported. First, the long-range correction, which complements the long-range exchange interaction to exchange functionals, is explained in terms of the formulation, applicabilities, and various long-range corrected functionals in Sect. 6.1. The self-interaction correction, which cancels out the Coulomb and exchange self-interactions, is then reviewed, specifically for the behavior of the kinetic, exchange, and correlation energies originating from the density matrix of self-interacting electrons, in Sect. 6.2. As a correction for correlation functionals, the van der Waals correction is surveyed, with a classification and detailing of the formulations and characteristics of conventional corrections, in Sect. 6.3. The relativistic correction, which is required to calculate heavy atomic systems, is also briefly reviewed, with the derivations and development concepts of these corrections, in Sect. 6.4. Finally, the vector potential correction for describing magnetic properties and current is explained, with derivations and applications, in Sect. 6.5.
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Tsuneda, T. (2014). Corrections for Functionals. In: Density Functional Theory in Quantum Chemistry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54825-6_6
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