6. Example: Electrolyte Solutions

This example, like the previous two, models a 2-D metallic structure, this time, an Ag (100) slab, in water solution. The slab is charged and an electrolyte solution is added. This solution can be thought of as a solvent (whose characteristics we have now implemented a number of times), and electrolyte ions, that are defined based off a set of parameters. The parameters describing the ions are placed in the ENVIRON keyword

&ENVIRON
   env_electrolyte_ntyp = 2
   zion(1) = 1
   zion(2) = -1
   cion(1) = 1.0
   cion(2) = 1.0
   cionmax = 10.0

The env_electrolyte_ntyp parameter sets the number of ionic species that are to be defined, and for each species the charge (zion) and the concentration (cion) are to be specified. Finally the maximum concentration can be set (respresenting the maximum concentration of ions at any point).

A number of electrolyte models can be implemented in Environ. This example iterates through the models based the numerical method, which utilizes the Poisson-Boltzmann equation or some variant. It also includes some analytical analogues that, rather than solve the Poisson-Boltzmann equation, add a correction to the potential. By default, the Poisson-Boltzmann model is set. By specifying the parameter

&ENVIRON
   electrolyte_linearized = .true.

the model is changed to the linear equivalent. Refer to the publications [1], [2] for more details on these models. Some pbc correction (as explained in example 1) is necessary here, since calculations involving the electrolyte require open boundary conditions. In the example, this is set to parabolic, referring to the numerical approach, whereas a change to the gcs correction,

&ELECTROSTATIC
   pbc_correction = 'gcs'

will switch to the analytic approach to solving the relevant Poisson-Boltzmann equation. Note that this does not include the size-modified equation. The page on diffuse-layer models will describe each of the models and how they differ in more detail. In particular, the required parameters for each models do vary slightly. For the linearized Poisson-Boltzmann model and the Poisson-Boltzmann model, the charge and concentrations need to be specified. The additional max concentration (cionmax) parameter should be included when choosing the modified Poisson-Boltzmann model. Notice that the model need not be specified explicitly and is instead inferred by the parameters supplied to the input. The physical models all require at least the concentrations and the charges of the ions. By setting the maximum concentration to be non-zero, Environ will assume the user wishes to use the modified Poisson-Boltzmann model.

Note

The gcs correction (Gouy-Chapman Stern) is a 1-D analytical solution to the Poisson-Boltzmann equation and thus is only valid for 2 dimensional systems. The correction has been shown to produce close results to the numerical equivalents and should therefore be considered if the user is looking to save computational time. The parabolic correction (as seen in previous examples) is a general correction that works in any number of dimensions, however in order for the gcs correction to be valid, there should be no parabolic correction.

As in previous examples, the solvent_mode parameter is set to ‘full’, due to a hole close to the Ag ions. A solvent-accessible but ion-free region in the proximity of the surface (Stern layer) is modeled by introducing an ion-exclusion function as described here [3].

The interface function respresenting the boundary between the quantum mechanical region and the electrolyte embedding environment is set in the BOUNDARY keyword

&BOUNDARY
   electrolyte_mode = 'system'
   electrolyte_distance = 10.0
   electrolyte_spread = 0.5

Here, the electrolyte_mode parameter is set to system, corresponding to a simple analytical function.

[1]
  1. Nattino et al., J. Chem. Phys. 150, 041722 (2019)
[2]
  1. Fisicaro et al., J. Chem. Phys. 144, 014103 (2016)
[3]I. Dabo et al., arXiv 0901.0096 (2008)