DERIVATION OF THE FUNCTIONAL RELATION BETWEEN EXACT POTENTIALS AND THOSE OBTAINED FROM THE LOCAL APPROXIMATION IN DENSITY FUNCTIONAL THEORY FOR CERTAIN FINITE SYSTEMS
DOI:
https://doi.org/10.26512/2446-564X2025e58499Keywords:
DFT, LDAAbstract
This article aims to determine, for certain finite systems, the relation between the exact exchange- correlation potentials — which arise in the description of many-body electronic systems through the Kohn-Sham equations — and those obtained through the Local Density Approximation (LDA) of Density Functional Theory. The possibility of finding such a relationship may allow for the identification of unknown exact potentials in other systems by using known potentials obtained through the LDA. To this end, the relations between these potentials were analyzed for the Beryllium (Be) and Lithium (Li) atoms, using previously obtained exact potentials. The results showed that the exact potential is not determined by simply multiplying the LDA potential by a constant factor for each atom. However, this may serve as an extremely reasonable approximation.
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