Conditional probability density functional theory

TL;DR

Conditional probability density functional theory (CP-DFT) offers a formally exact approach to determine ground-state energies by directly calculating CP densities, bypassing traditional exchange-correlation functionals, with promising theoretical and practical implications.

Contribution

This work introduces CP-DFT as a new exact framework that computes ground-state energies through CP densities, avoiding approximate XC functionals and expanding the theoretical foundation of DFT.

Findings

CP-DFT is formally exact for ground-state energy calculations.

Direct calculation of CP densities can bypass traditional XC functionals.

Illustrative examples demonstrate the theory and potential of CP-DFT.

Abstract

We present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the CP density from a series of independent Kohn-Sham (KS) DFT calculations. By directly calculating CP densities, we bypass the need for an approximate XC energy functional. In this work we discuss and derive several key properties of the CP density and corresponding CP-KS potential. Illustrative examples are used throughout to help guide the reader through the various concepts and theory presented. We explore a suitable CP-DFT approximation and discuss exact conditions, limitations, and results for selected examples.