Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation

TL;DR

This paper introduces a formalism for accurately calculating the electronic structure and optical properties of quantum crystals, accounting for nuclear quantum and thermal motions within the Born-Oppenheimer approximation, applicable to various electronic theories.

Contribution

The authors develop a new method to incorporate nuclear motion effects into electronic structure calculations, enabling band structure and optical property analysis of quantum crystals.

Findings

Applied to crystalline hydrogen, revealing nuclear motion effects on electronic structure.

Demonstrated the formalism's ability to recover electronic crystal momentum.

Analyzed optical absorption profiles of hydrogen and diamond.

Abstract

We develop a formalism to accurately account for the renormalization of electronic structure due to quantum and thermal nuclear motions within the Born-Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from Quantum Monte Carlo calculations in either the canonical or grand canonical ensembles. The formalism applies as well to effective single electron theories such as those based on Density Functional Theory. We show that electronic (Bloch) crystal momentum can be restored by marginalizing the total electron-ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born-Oppenheimer approximation. Based on the Kubo-Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and in general differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200K and 250 GPa and discuss the optical absorption profile of hydrogen crystal at 200K and carbon diamond at 297K.