Extending the Potential Energy Landscape Formalism to Quantum Liquids*

Over the last few decades, significant progress has been made in understanding the behavior of liquids near the glass transition. Most computational studies addressing this problem have been based on classical model liquids, which are adequate for the study of conventional substances (e.g., silica). However, for substances composed of light elements (e.g., H₂ and He) or small molecules containing H (e.g., water), the role of nuclear quantum effects (NQE) can be relevant. One successful theoretical and computational approach for the study of classical liquids/glasses is the potential energy landscape formalism (PEL). In this talk, I will extend the PEL formalism to study liquids that obey quantum mechanics, enabling for the description of NQE. Our approach leverages on the Feynman path-integral formalism to map the quantum atoms of a liquid into classical ring-polymers.  The resulting PEL for the (quantum) liquid is temperature-dependent.  Our computer simulations show that the atoms/ring-polymers of a quantum liquid are always collapsed at the local minima of the PEL (inherent structures), facilitating the calculation of important properties of the system, including the vibrational spectrum. Following this observation, we apply the standard Gaussian and harmonic approximations of the PEL and derive expressions for relevant quantum thermodynamic properties. Our theoretical expressions are tested against path-Integral computer simulations of (i) an atomistic model liquid, and (ii) a flexible water model liquid.