Contracted Schrödinger equation and Kohn–Sham effective potentials

 Viktor N. Staroverov

 

ABSTRACT

The precise relationship between the exact expressions for the Kohn–Sham exchange-correlation potential, , deduced by Buijse, Baerends and Snijders and by Ryabinkin, Kohut and Staroverov is clarified. These two expressions differ nontrivially by a single term which in the former method generally involves the three-electron reduced density matrix, whereas in the latter approach the same term is expressed using the two-electron reduced density matrix at most. The link between the two expressions turns out to be the 1,3-contracted Schrödinger equation. An essential feature of these and other similar expressions for is that they produce different results in finite-basis-set calculations and become equivalent only in the basis-set limit.

 

 https://sci-hub.se/https://doi.org/10.1080/00268976.2018.1463470