One of the canonical examples for polar solvation is the Born ion: a nonpolarizable sphere with a single charge at its center surrounded by an aqueous medium. In the absence of external ions, the polar solvation energy for this system is given by
 where q is the ion charge, a is the ion radius, and the two ε variables denote the internal and external (solution) dielectric constants. This model assumes zero ionic strength.
We can setup a PQR file for the Born ion for use with APBS with the contents:
REMARK This is an ion with a 3 A radius and a +1 e charge ATOM 1 I ION 1 0.000 0.000 0.000 1.00 3.00We're interested in performing two APBS calculations for the charging free energies in homogeneous and heterogeneous dielectric coefficients. We'll assume the internal dielectric coefficient is 1 (e.g., a vacuum) and the external dielectric coefficient is 78.54 (e.g., water). for these settings, the polar Born ion solvation energy expression has the form
 where z is the ion charge in electrons and R is the ion size in Å.
This solvation energy calculation can be setup in APBS with the following input file:
# READ IN MOLECULES read mol pqr born.pqr end elec name solv # Electrostatics calculation on the solvated state mg-manual # Specify the mode for APBS to run dime 97 97 97 # The grid dimensions nlev 4 # Multigrid level parameter grid 0.33 0.33 0.33 # Grid spacing gcent mol 1 # Center the grid on molecule 1 mol 1 # Perform the calculation on molecule 1 lpbe # Solve the linearized Poisson-Boltzmann equation bcfl mdh # Use all multipole moments when calculating the potential pdie 1.0 # Solute dielectric sdie 78.54 # Solvent dielectric chgm spl2 # Spline-based discretization of the delta functions srfm mol # Molecular surface definition srad 1.4 # Solvent probe radius (for molecular surface) swin 0.3 # Solvent surface spline window (not used here) sdens 10.0 # Sphere density for accessibility object temp 298.15 # Temperature calcenergy total # Calculate energies calcforce no # Do not calculate forces end elec name ref # Calculate potential for reference (vacuum) state mg-manual dime 97 97 97 nlev 4 grid 0.33 0.33 0.33 gcent mol 1 mol 1 lpbe bcfl mdh pdie 1.0 sdie 1.0 chgm spl2 srfm mol srad 1.4 swin 0.3 sdens 10.0 temp 298.15 calcenergy total calcforce no end # Calculate solvation energy print energy solv - ref end quitNote that the Born example above can be easily generalized to other polar solvation energy calculations. For example, ions could be added to the solv ELEC, dielectric constants could be modified, surface definitions could be changed (in both ELEC sections!), or more complicated molecules could be examined. Many of the examples included with APBS (e.g.,
solv and ionize) also demonstrate solvation energy calculations.Note that, as molecules get larger, it is important to examine the sensitivity of the calculated polar solvation energies with respect to grid spacings and dimensions.
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