First-Principles Modeling of Quantum Nuclear Effects and Atomic Interactions in Solid 4He at High Pressure

TL;DR

This study combines advanced computational methods to model quantum nuclear effects in solid helium at high pressures, revealing limitations of traditional approaches and providing new insights into its atomic interactions and energy behavior.

Contribution

It introduces a combined DFT-vdW and DMC approach to accurately model quantum nuclear effects in dense solid helium, highlighting discrepancies with quasi-harmonic DFT methods.

Findings

Kinetic energy of solid 4He remains nearly constant above 85 GPa.

Lindemann ratio in dense 4He is approximately 0.10 regardless of pressure.

Quasi-harmonic DFT significantly underestimates kinetic energies by ~50%.

Abstract

We present a first-principles computational study of solid 4He at T=0K and pressures up to 160GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom in this material, and the diffusion Monte Carlo (DMC) method to solve the Schrodinger equation describing the behavior of the quantum nuclei. For this, we construct an analytical interaction function based on the pairwise Aziz potential that closely matches the volume variation of the cohesive energy calculated with DFT-vdW in dense helium. Interestingly, we find that the kinetic energy of solid 4He does not increase appreciably with compression for P > 85GPa. Also, we show that the Lindemann ratio in dense solid 4He amounts to 0.10 almost independently of pressure. The reliability of customary quasi-harmonic DFT (QH DFT) approaches in the description of quantum nuclear effects in solids is also studied. We find that QH DFT simulations, although provide a reasonable equation of state in agreement with experiments, are not able to reproduce correctly these critical effects in compressed 4He. In particular, we disclose huge discrepancies of at least ~50% in the calculated 4He kinetic energies using both the QH DFT and present DFT-DMC methods.