Abstract
<jats:p>Cavity-based continuum models are a popular choice for modeling solvation or pressure effects on the electronic structure. Conventional atom-centered cavities are static and cannot adapt to changes in the electron density, while physically appealing electron-isodensity cavities have lacked a smooth and differentiable construction. We present ρ-DROP, the first self-consistent and fully differentiable isodensity cavity, constructed using the recent Discretization via Reference-Onto-surface Projection (DROP). We derive and implement the analytic cavity response and nuclear gradients, combined with the CPCM solvation and GOSTSHYP pressure models. Analytic derivatives agree with their numerical counterparts, potential-energy scans and cavity properties are smooth, and SCF and geometry-optimization behavior remains comparable with conventional cavities. We demonstrate that ρ-DROP naturally captures diffuse excited and anionic states, where conventional cavities leave a substantial number of electrons outside the cavity and yield qualitatively different results. Pressure computations with GOSTSHYP and ρ-DROP directly yield pressure-dependent molecular volumes and avoid any negative amplitudes, which are a major source of SCF instability. Overall, ρ-DROP enables the routine use of a self-consistent isodensity cavity with a moderate increase in cost and near-linear scaling behavior. More generally, this work provides a foundation for general density-dependent interfaces and continuum-model components.</jats:p>