Nuclear Quantum Effects on the Equation of State of Water: Insights from the Potential Energy Landscape Formalism

We apply the potential energy landscape (PEL) formalism for quantum liquids, together with path-integral (PI) computer simulations, to derive the equation of state (EOS) for both equilibrium and supercooled water over a wide range of temperatures and pressures. The PEL-EOS for water, which includes nuclear quantum effects (NQE), is in very good agreement with the PI computer simulations, particularly in the proximity of water's liquid-liquid critical point (LLCP). Relative to the classical case, including NQE shifts the overall phase diagram of water toward lower temperatures and slightly lower pressures. In particular, the LLCP temperature and pressure are shifted by ΔTc ≈ 18 K and ΔPc ≈ 49 MPa, with a minor change in the LLCP density, Δρc ≈ 0.002 g/cm3. These values of (ΔPc, ΔTc, Δρc) represent, approximately, a maximum shift for the location of the LLCP for H2O due to isotope substitution (H2O → D2O → T2O). Additionally, NQE also affect the shape of the density and LL spinodal lines in the P-T plane. The PEL of (q-TIP4P/F) water is Gaussian, allowing for the evaluation of the configurational entropy SIS(T, V) and Kauzmann temperature, TK(V). NQE reduce the TK(V) of water by 5-20 K depending on the density, consistent with the observed increase in water diffusion coefficient D at low temperatures upon the inclusion of quantum fluctuations. Notably, the Adam-Gibbs relationship, which relates D and SIS, holds remarkably well at all densities studied. From the perspective of the PEL formalism, NQE primarily modify the curvature of water's PEL basins while the corresponding IS remain unchanged, isomorphic to the IS of classical water. The PEL-based approach employed in this work is versatile and physically intuitive, suitable for calculating the free energy and EOS of quantum liquids beyond water.