Potential Energy Landscape of a Flexible Water Model: Equation-of-State, Configurational Entropy, and Adam-Gibbs Relationship

The potential energy landscape (PEL) formalism is a tool within statistical mechanics that has been used in the past to calculate the equation of states (EOS) of classical rigid model liquids at low temperatures, where computer simulations may be challenging. In this work, we use classical molecular dynamics (MD) simulations and the PEL formalism to calculate the EOS of the flexible q-TIP4P/F water model. This model exhibits a liquid-liquid critical point (LLCP) in the supercooled regime, at ($P_c = 150$ MPa, $T_c = 190$ K, $\rho_c = 1.04$ g/cm$^3$) [using the reaction field technique]. The PEL-EOS of q-TIP4P/F water, and the corresponding location of the LLCP, are in very good agreement with the MD simulations. We show that the PEL of q-TIP4P/F water is Gaussian which allows us to calculate the configurational entropy of the system, $S_{conf}$. The $S_{conf}$ of q-TIP4P/F water is surprisingly similar to that reported previously for rigid water models, suggesting that intramolecular flexibility does not necessarily add roughness to the PEL. We also show that the Adam-Gibbs relation, which relates the diffusion coefficient $D$ with $S_{conf}$, holds for the flexible q-TIP4P/F water model. Overall, our results indicate that the PEL formalism can be used to study molecular systems that include molecular flexibility, the common case in standard force fields. This is not trivial since the introduction of large bending/stretching mode frequencies is problematic in classical statistical mechanics. For example, as shown previously, we find that such high-frequencies lead to an unphysical (negative) entropy for q-TIP4P/F water (yet the PEL formalism can be applied successfully).