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

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

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

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

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. If the solvent is specified by the dielectric constant, only the polar electrostatics contribution can be included.

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). If the solvent is specified by the dielectric constant, only the polar electrostatics contribution is included.

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#