Understanding Isotope Substitution Effects in Water Using the Potential Energy Landscape Formalism for Quantum Liquids

Isotope substitution effects are known to alter the thermodynamic, dynamic, and structural properties of water, particularly, at low temperatures. In this work, we perform path-integral (PI) computer simulations of H₂O, HDO, D₂O, and T₂O, and provide a rigorous description of the H ↔ D ↔ T isotope substitution effects in water based on the potential energy landscape (PEL) formalism for quantum liquids. Our PI computer simulations at 200 ≤ T ≤ 400 K and v = 18.0 cm³/mol (corresponding to a density for H₂O of ρ = 1.00 g/cm³) indicate that the same potential energy minima (inherent structures, IS) are present in the PEL of quantum water and its isotopes (sampled in PI computer simulations). These IS are also isomorphic to (and can be obtained from) the IS of classical water (sampled in classical computer simulations). Isotope substitutions in water (H ↔ D ↔ T) have the only effect of altering the curvature (and shape) of water's PEL basins about the corresponding IS. Specifically, the PEL basins become wider along the sequence H₂O → HDO → D₂O → T₂O, as the atoms delocalization become less pronounced. From a thermodynamic point of view, we find that water and its isotopes at a given temperature, sample different IS of the corresponding PEL, with different curvatures, explaining the subtle variations in the properties of H₂O, HDO, D₂O, and T₂O. It is also shown that the Adam-Gibbs relation remains valid for water and its isotopes implying that, in all these cases, the topography of the PEL controls the dynamics of the system (molecular diffusion) at a given temperature. Overall, this work shows that the PEL formalism for quantum liquids provides an intuitive and rigorous theoretical framework within statistical mechanics that can be used to describe isotopic substitution effects in liquids.