Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson–Boltzmann Solvent

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

Molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. In this work, we develop and assess two multiscale solvation models for computing solvation thermodynamic properties. The new SLIC/CDC model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with new statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). Given the structures of 500 solutes, the SLIC/CDC model predicts Gibbs energies of solvation in water with an average accuracy better than 1 kcal/mol, when compared to experimental measurements, and better than 0.8 kcal/mol, when compared to explicit-solvent molecular dynamics simulations. The individual SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The previously published SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent-accessible surface area (SASA) nonpolar energy mode. With our new, improved parametrization method, the SLIC/SASA model now predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems, compared to experimental and explicit-solvent molecular dynamics, and better than 1.6 kcal/mol average accuracy in ionic liquids, compared to explicit-solvent molecular dynamics. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.