Simple and Accurate Exchange Energy for Density Functional Theory.

Teepanis Chachiyo,Hathaithip Chachiyo

doi:10.3390/molecules25153485

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 from 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 accurately than the 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 first- and second-row molecular total energy predictions reported to date despite minimal computational efforts. The calculated bond energies, zero point energies, and dipole moments are also presented, which do not outperform other methods.

Highlights

Total energy is a fundamental quantity in quantum mechanics as exemplified by the Schrödinger equation and the formulation of density functional theory (DFT) [1,2]
We show that a simple and accurate exchange functional can be devised using a model that a free-electron gas is perturbed by the periodic external potential which induces Bragg diffraction of the Fermi electrons
Which governs how the exchange energy is enhanced by electron density gradient in the slowly varying limit

Summary

Introduction

Total energy is a fundamental quantity in quantum mechanics as exemplified by the Schrödinger equation and the formulation of density functional theory (DFT) [1,2]. For over 90 years, the Schrödinger equation for atoms and molecules has never been solved analytically due to mathematical complexity of many-electron system [3]. Alternative to the wave function based methods, DFT rests firmly on a premise that total energy can be determined exactly by the density of electrons [1,2]. It breaks down the total energy into five contributions: kinetic, potential, Coulomb repulsion, exchange, and correlation. The focus of this work is on the exchange energy contribution, but the aim is the same as that of the methods aforementioned. To predict the total energy as accurately as possible

Methods

Results

Discussion

Conclusion