Solvation

Implicit solvation models are available for the calculation of the solvation free energies partitioned as

\[\Delta G_{\text{solv}} = \Delta G_{\text{polar}} + \Delta G_{\text{npol}} + \Delta G_{\text{shift}}\]

including the polar contribution \({\Delta G_{\text{polar}}}\) based on electrostatics, the non-polar contribution \({\Delta G_{\text{npol}}}\) based on cavity formation and dispersion, and a constant shift \({\Delta G_{\text{shift}}}\) depending on the thermodynamic state of initial gas and final liquid solution.

ALPB solvation model

The analytical linearized Poisson-Boltzmann (ALPB) model evaluates the polar contribution

\[\Delta G^{\text{ALPB}}_{\text{polar}} = - \frac{1}{2} \left(\frac{1}{\epsilon_{\text{in}}} - \frac{1}{\epsilon_{\text{out}}}\right) \frac{1}{1+\alpha\beta} \sum_{A,B} q_{A} q_{B} \left( \frac{1}{f(R_{AB, a_{A}, a_{B}})} + \frac{\alpha\beta}{\mathcal{A}_{\text{det}}} \right)\]

based on the ALPB constant \({\alpha}\) (set to 0.571214), the solute (\({\epsilon_{\text{in}}=1}\)) and solvent (\({\epsilon_{\text{out}}}\)) dielectric constants combined in \({\beta=\frac{\epsilon_{\text{in}}}{\epsilon_{\text{out}}}}\), atomic partial charges \({q_{A/B}}\), and the electrostatic size of the solute \({\mathcal{A}_{\text{det}}}\). [1] \({f(R_{AB}, a_{A}, a_{B})}\) is the interaction kernel with the Born radii \({a_{A/B}}\) and can take two forms, either

\[f(R_{AB}, a_{A}, a_{B}) = \left( R_{AB}^2 + a_{A} a_{B} \exp\left[-\frac{R_{AB}^2}{4 a_{A} a_{B}} \right] \right)^{\frac{1}{2}}\]

proposed by Still (default in GBSA), or the more recent P16 kernel (default for ALPB):

\[f(R_{AB}, a_{A}, a_{B}) = R_{AB} + \sqrt{a_{A} a_{B}} \left(1+\frac{1.028 R_{AB}}{16 \sqrt{a_{A} a_{B}}} \right)^{16}\]

For specific polar interactions, an atom-wise hydrogen bonding correction is introduced:

\[\Delta G^{\text{HB}}_{\text{polar}} = \sum \Delta G^{\text{HB}}_{\text{A}}\]

In addition to the polar contribution, the non-polar contribution is included with a cavity dispersion solvation term (CDS) based on the atomic surface tension \(\gamma_{A}\) and the solvent-accessible surface area (SASA) \(\sigma_{A}\):

\[\Delta G^{\text{CDS}}_{\text{npol}} = \sum_{A} \gamma_{A} \sigma_{A}\]

An additional empirical constant shift is applied to the solvation free energy. A solution state correction can be activated but is not included by default.

GBSA solvation model

The generalized Born solvation model (GBSA) is a simplified version of ALPB in the limit of an ideal conductor environment (\({\epsilon_{\text{out}}}\rightarrow \infty\) and \({\beta\rightarrow 0}\)). As for ALPB, CDS and a constant shift shift are applied, while a solution state correction can be activated (only if the solvent is specified by name).

CPCM solvation model

The conductor-like polarizable continuum solvation model is implemented based on the domain-decomposition approach and is currently available only for the polar part \({\Delta G_{\text{polar}}}\).

Solution state correction

For solvation free energies, the state of the inital gas and final liquid solution can be changed with a solution state correction. By default no solution state correction is applied (gsolv, default), which is comparable with most other solvation models (SMD, COSMO-RS, …). For normal production runs, the option bar1mol should be used. For explicit comparisons with reference state corrected COSMO-RS, the reference option should be used (includes solvent-specific correction for infinite dilution). Solution state correction is available for the ALPB and GBSA solvation models.

Name	Definition
gsolv (default)	1 L of ideal gas and 1 L of liquid solution
bar1mol	1 bar of ideal gas and 1 mol/L liquid solution
reference	1 bar of ideal gas and 1 mol/L liquid solution at infinite dilution

Literature

[1]

Sebastian Ehlert, Marcel Stahn, Sebastian Spicher, and Stefan Grimme. Robust and efficient implicit solvation model for fast semiempirical methods. J. Chem. Theory Comput., 17(7):4250–4261, 2021. doi:10.1021/acs.jctc.1c00471.