# Simple and accurate exchange energy for density functional theory

## TL;DR

This paper introduces a new non-empirical exchange functional for density functional theory that interpolates between known electron density limits, significantly improving the accuracy of molecular energy predictions with minimal computational effort.

## Contribution

A novel exchange functional based on interpolation between density limits, combined with a correlation functional, achieving unprecedented accuracy in molecular energy calculations.

## Key findings

- Total energies for first-row molecules are four times more accurate than Quantum Monte Carlo.
- Core electron exchange energies are corrected for second-row molecules.
- Achieves the most accurate molecular total energy predictions to date.

## Abstract

A non-empirical exchange functional based on an interpolation between two limits of electron density: slowly varying limit and asymptotic limit, is proposed. In the slowly varying limit, we follow the study by Kleinman in 1984 which considered the response of a free-electron gas to an external periodic potential, but further assume that the perturbing potential also induces Bragg diffraction of the Fermi electrons. The interpolation function is motivated by the exact exchange functional of a hydrogen atom. Combined with our recently proposed correlation functional, tests on 56 small molecules show that, for the first-row molecules, the exchange-correlation combo predicts the total energies four times more accurate than presently available Quantum Monte Carlo results. For the second-row molecules, errors of the core electrons exchange energies can be corrected, leading to the most accurate molecular total energy predictions to date despite minimal computational efforts. The calculated bond energies, zero point energies, and dipole moments are also presented.

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Source: https://tomesphere.com/paper/1706.01343