Information-Theoretic Analysis of Selected Water Force Fields: From Molecular Clusters to Bulk Properties

We present a comprehensive information-theoretic evaluation of three widely used rigid water models (TIP3P, SPC, and SPC/ε) through systematic analysis of water clusters ranging from single molecules to 11-molecule aggregates. Five fundamental descriptors-Shannon entropy, Fisher information, disequilibrium, LMC complexity, and Fisher-Shannon complexity-were calculated in both position and momentum spaces to quantify electronic delocalizability, localization, uniformity, and structural sophistication. Clusters containing 1, 3, 5, 7, 9, and 11 molecules (denoted 1 M, 3 M, 5 M, 7 M, 9 M, and 11 M) were selected to balance computational tractability with representative scaling behavior. Molecular dynamics simulations validated the force fields against experimental bulk properties (density, dielectric constant, self-diffusion coefficient), while statistical analysis using Shapiro-Wilk normality tests and Student's <i>t</i>-tests ensured robust discrimination between models. Our results reveal distinct scaling behaviors that correlate with experimental accuracy: SPC/ε demonstrates superior electronic structure representation with optimal entropy-information balance and enhanced complexity measures, while TIP3P shows excessive localization and reduced complexity that worsen with increasing cluster size. The transferability from clusters to bulk properties is established through systematic convergence of information-theoretic measures toward bulk-like behavior. The methodology establishes information-theoretic analysis as a useful tool for comprehensive force field evaluation.