Local Effective Hartree-Fock Potentials Obtained by the Depurated Inversion Method

ALEJANDRA M.P. MENDEZ; DARIO M. MITNIK; JORGE E. MIRAGLIA

Novel Electronic Structure Theory: General Innovations and STrongly Correlated Systems

Academic Press

Lugar: Burlilngton, Massachussetts; Año: 2018; p. 117 - 131

In this work we show the results of a numerical experiment performed on the Hartree?Fock (HF) wave functions in order to understand the relationship between the positionsof the orbital nodes and the inflection points (zeros of their second derivative). This analysisis equivalent to investigating the existence of a physical one-electron local potentialrepresenting the interactions between the electrons. We found that with successiveimprovements in the quality of the numerical methods, the nodes and the inflectionpoints systematically become closer. When the nodes coincide exactly with the inflectionpoints, the existence of an effective local potential would be proven. However, thisrequirement cannot be fulfilled unless an explicit constraint (missing in the standardmethod) is incorporated into the HF procedure. The depurated inversion method(DIM) was devised to obtain detailed nl-orbital potentials for atoms and molecules.The method is based on the inversion of Kohn?Sham-type equations, followed by afurther careful optimization which eliminates singularities and also ensures the fulfillmentof the appropriate boundary conditions. The orbitals resulting from these potentialshave their internal inflection points located exactly at the nodes. In this way, theDIM can be employed to obtain effective potentials that accurately reproduce theHF orbitals.