Response Theory for Static and Dynamic Solvation of Ionic and Dipolar Solutes in Water

The response of polar solvents to ions and polar molecules dictates many fundamental molecular processes. To understand such electrostatically-driven solvation processes, one ideally would probe the dielectric response of a solvent to an idealized point test charge or dipole solute, as envisioned in classic continuum treatments of the problem. However, this is difficult in simulations using standard atomically-detailed solvent models with embedded point charges due to possible overlap with the test charge that lead to singular interaction energies. This problem is traditionally avoided for a realistic charged solute by introducing an excluded volume core that shields its embedded point charge or dipole from the charges in the solvent. However, this core introduces additional molecular-scale perturbations of the solvent density that complicate the interpretation of solvent dielectric response. In this work, we avoid these complications through the use of Gaussian-smoothed test charges and dipoles. Gaussian charges and dipoles can be readily inserted anywhere into an atomistic solvent model without encountering infinite energies. If the Gaussian-smoothing is on the scale of molecular correlations in the solvent, both the thermodynamic and dynamic solvation response is linear. Using this observation, we construct accurate predictive theories for solvation free energies and solvation dynamics for insertion of Gaussian charges and dipoles in polar solvents and demonstrate the accuracy of the theories for a widely-used model of water. Our results suggest that Gaussian test charge distributions can be used as an informative probe of dielectric response in molecular models, and our theories can be used to analytically predict the largest component of solvation free energies of charged and polar solutes.