Nuclear-Electronic Orbital Approach to Quantization of Protons in Periodic Electronic Structure Calculations

TL;DR

This paper extends the nuclear-electronic orbital method to periodic systems, enabling quantum treatment of protons in materials and revealing their significant impact on electronic properties.

Contribution

The authors implement and validate a periodic NEO-DFT approach within FHI-aims, allowing quantum proton treatment in extended systems for the first time.

Findings

Protons' zero-point energy influences density of states.

Electron-proton correlation affects band structures.

Method applied to 2D materials and interfaces.

Abstract

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons, as well as electron-proton correlation, are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.