Density functional theory beyond the Born-Oppenheimer approximation: accurate treatment of the ionic zero-point motion

TL;DR

This paper presents a novel density functional theory method that explicitly accounts for ionic zero-point motion beyond the Born-Oppenheimer approximation, improving accuracy for systems with light atoms like hydrogen.

Contribution

The authors develop a zero-temperature DFT approach incorporating path-integral formulation to go beyond the Born-Oppenheimer approximation, applicable to condensed matter calculations.

Findings

Significant differences from BO approximation in light-atom systems

Zero-point motion fluctuations are comparable to interatomic distances

Method is compatible with existing condensed matter codes like SIESTA

Abstract

We introduce a method to carry out zero-temperature calculations within density functional theory (DFT) but without relying on the Born-Oppenheimer (BO) approximation for the ionic motion. Our approach is based on the finite-temperature many-body path-integral formulation of quantum mechanics by taking the zero-temperature limit and treating the imaginary-time propagation of the electronic variables in the context of DFT. This goes beyond the familiar BO approximation and is limited from being an exact treatment of both electrons and ions only by the approximations involved in the DFT component. We test our method in two simple molecules, H$_2$ and benzene. We demonstrate that the method produces a difference from the results of the BO approximation which is significant for many physical systems, especially those containing light atoms such as hydrogen; in these cases, we find that the fluctuations of the distance from its equilibrium position, due to the zero-point-motion, is comparable to the interatomic distances. The method is suitable for use with conventional condensed matter approaches and currently is implemented on top of the periodic pseudopotential code SIESTA.