The atomic interactions in liquid and solid helium can be reproduced very accurately by simple analytical functions that solely depend on the distance between particles taken in pairs. Yet, under conditions of large pressures and strain deformations the 4He–4He interactions become more complex due to the electronic repulsions acting between neighbouring atoms, and thus commonly employed pairwise potentials turn out to be unreliable. Examples of failed predictions based on pairwise potentials include the unrealistic description of the equation of state and elastic properties of solid helium at pressures beyond ∼ 1 GPa. A route for improving such modeling drawbacks is to consider higher order terms in the approximations to the atomic interactions. In this context, several three-body energy models have already been proposed like, for instance, the Axilrod-Teller and Brunch-McGee potentials. However, the improvements resulting from those many-body potentials have been proven to be only modest. In this talk, I will present recent work done on the modeling of three-body interactions in highly compressed solid helium. In particular, I will introduce a new set of Brunch-McGee potential parametrizations based on the fitting to ab initio energies and atomic forces obtained with the van der Waals corrected density functional theory method. I will show that an improved general understanding of the energy, structural and elastic properties of solid helium can be attained by using these many-body interaction models in combination with quantum Monte Carlo simulations.
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