To increase the accuracy of our implicit solvent modeling, we have implemented a differential geometry based geometric flow solvation model (Thomas, 2013). In this model, polar and nonpolar solvation free energies are coupled and the solvent-solute boundary is determined in a self-consistent manner. Relevant references are provided in Recommended reading. This section provides a brief overview of the method.

The solutions for the electrostatic potential \(\phi\) and the characteristic function \(S\) (related to the solvent density) are obtained by minimizing a free energy functional that includes both polar and nonpolar solvation energy terms. Minimization of the functional with respect to \(\phi\) gives the Poisson-Boltzmann equation with a dielectric coefficient \(\epsilon\) has the solute value \(\epsilon_m\) where \(S = 1\) and the solvent value \(\epsilon_s\) where \(S = 0\). Minimization of the free energy functional with respect to \(S\) gives

\[-\nabla\cdot\left(\gamma\frac{\nabla S}{\parallel\nabla S\parallel}\right)+p-\rho_0U^{att}+\rho_m\phi - \frac{1}{2}\epsilon_m\mid\nabla\phi\mid^2+\frac{1}{2}\epsilon_s\mid\nabla\phi\mid^2=0\]

where \(\gamma\) is the microscopic surface tension, \(p\) is the hydrostatic pressure, and \(U^{att}\) is the attractive portion of the van der Waals dispersion interaction between the solute and the solvent.

Keywords for this calculation type include:

ELEC geoflow-auto keywords:


Although the ion and lpbe keywords will be accepted in the geoflow-auto calculation, the treatment of salt is not currently implemented in APBS geometric flow.