Empirical no-go principles for rigid three-point water models: A physically guided manifold of optimality

Rigid three-point water models are widely used in molecular simulations, yet they cannot simultaneously reproduce thermodynamic, dielectric, and dynamical properties. We show that these failures do not stem from incomplete parameter optimization, but from physical constraints that define the topology of the model parameter space. Treating the density anomaly as a master thermodynamic constraint, we find that viable geometries and electrostatics collapse onto a low-dimensional physical manifold governed by scaling relations. Within this framework, we identify two topological constraints, an empirical no-go principle, intrinsic to rigid three-point models with standard Lennard-Jones interactions. First, in the small-angle regime (θ ≲ 108°), matching the experimental dielectric constant requires molecular elongation that destabilizes the hydrogen-bond network and shifts the temperature of maximum density. Second, enforcing the density anomaly increases network rigidity, suppressing molecular mobility, and preventing agreement with the experimental self-diffusion coefficient. Together, these results define the fundamental limits of rigid three-point water models and recast their development as a constrained design problem rather than an empirical optimization task.