Full Configuration Interaction wave function as a formal solution to the Optimized Effective Potential and Kohn-Sham models in finite basis sets

TL;DR

This paper demonstrates how to construct a local Hamiltonian in finite basis sets whose ground state is the FCI wave function, simultaneously representing the exact Kohn-Sham and optimized effective potentials, without proposing a new FCI algorithm.

Contribution

It introduces a method to construct a local Hamiltonian with a potential that yields the FCI wave function as the ground state, unifying Kohn-Sham and optimized effective potential models.

Findings

Constructed a local Hamiltonian with FCI ground state

Unified Kohn-Sham and optimized effective potential representations

Provided a theoretical framework for potential construction

Abstract

Using finite basis sets, it is shown how to construct a local Hamiltonian, such that one of its infinitely many degenerate eigenfunctions is the ground state full configuration interaction (FCI) wave function in that basis set. Formally, the local potential of this Hamiltonian is the optimized effective potential and the exact Kohn-Sham potential at the same time, because the FCI wave function yields the exact ground-state density and energy. It is not the aim of this paper to provide a new algorithm for obtaining FCI wave functions. A new potential is the goal.