A generalized hybrid framework for crystal structures using Kohn-Sham orbitals and Wannier functions

Abstract

High-strength aluminium alloy, such as Al-Mg based alloys, are widely employed in aerospace as structural materials. Even though they show astonishing good fatigue resistance, they are also sensitive to hydrogen embrittlement (HE). An exposure to this phenomena leads to loss of tensile strength and accelerated fatigue crack growth. Unfortunatly the HE mechanism is not yet fully understood. A proposed mechanism is the hydrogen enhanced decohesion, where hydrogen gathers at high triaxial stress location. Since the mechanism is not well known, it poses a significant challenge in term of its theoretical understanding but also how to experimentally prevent it. A precise computational characterization of electronic structures is essential to deepen our understanding of this process.

Over the past decades, ab initio calculations --such as Density Functional Theory (DFT)-- tried to characterize and describe crystal structures. However, solving the Schrödinger equation to obtain ground-state properties presents exponential scaling challenges. Even though DFT makes more feasible electronic structure calculations for many-body systems but it struggles with strongly correlated systems. Recent advancements in quantum computing offer potential solutions to overcome this exponential scaling barriers. Despite progress, current quantum algorithms often exceed the capabilities of modern hardware, with deep circuits leading to errors and optimization challenges in large-scale problems. An alternative is to use hybrid quantum-classical algorithms which are based on the main advantages of both quantum and classical simulations to offset their weaknesses.

We present an interface between Quantum ESPRESSO and Qiskit. Our framework is a three steps method. The electronic structure of the crystal is obtained by the use of the plane-wave based DFT software, Quantum ESPRESSO. We define an active space with the Kohn-Sham orbitals, calculate the one-electron and two-electron integrals for the active space, while the remaining electrons are approximated through the frozen core approximation. The ground-state Hamiltonian is found using the VQE algorithm. Since plane-wave methods struggle in describing local properties such as defects, in our case hydrogen. By using the software Wannier90, it is possible to project the Kohn-Sham plane-waves based orbital onto a basis set of Wannier orbitals. Thus, we can express the electronic Hamiltonian in either a plane-wave and Wannier functions basis set. To this framework, population analysis can be performed by calculation the Bader charges of the crystal structure. This optimized approach aims to deliver accurate descriptions of a crystal structure by providing simultaneously an enhanced electronic ground-state wave-function and of the bader charges located at each atoms.